characterisation of the interlaminar properties of

Characterisation of the Interlaminar Properties of Composites at High Strain Rates: A Review

J. VAN BLITTERSWYK, L. FLETCHER, F. PIERRON

Faculty of Engineering and the Environment, University of Southampton, Southampton SO17 1BJ, UK

(Received 30 June 2017; accepted XX June 2017)

Abstract

This paper provides a review of the strain rate effect on the through-thickness mechanical properties of fibre-reinforced polymercomposites. The challenges and limitations associated with existing methods for through-thickness testing are discussed. Spe-cific attention is given to the split Hopkinson pressure bar, and implications of the intrinsic limitations for measuring mechanicalproperties. The influence of strain rate on elastic modulus, ultimate strength and ultimate strain is provided for compressive,tensile and shear loading conditions. The review is concluded with a discussion on the direction of future research focussedaround full-field imaging techniques.

Keywords: high strain rate, interlaminar properties, fibre-reinforced polymer composites, test methods

1. Introduction

Fibre-reinforced polymer (FRP) composite materials havebecome popular in many sectors such as aerospace, naval,automotive and infrastructure. The incorporation of thesematerials in design has resulted in necessarily thicker sec-tions to support complex three-dimensional stress states. Of-ten, these structures are subjected to high-rate loading thatcan generate significant through-thickness stresses. For ex-ample: bird and foreign object strikes, vehicle collisions,ballistic impacts, blast, etc. Due to the relatively lowerstrength in the through-thickness direction, these stressescan lead to micro cracking or delaminations and prematurefailure of the material. Advances in computational mod-elling power have enabled designers to simulate such com-plex loading conditions with the objective of designing saferstructures. However, achieving the full potential of numeri-cal simulations hinges on the accuracy of constitutive mod-els for the through-thickness response of the material. Theworks by Daniel et al. [1] and Gillespie et al. [2] are amongthe few efforts to calibrate/modify existing failure modelsto account for strain rate effects in the through-thickness di-rection. The effects of strain rate are still not well under-stood, largely due to the lack of standard testing procedures,experimental data, and limitations inherent to existing testmethods. Existing studies suggest a strain rate dependencyon the through-thickness elastic stiffness and strength prop-erties [3–6]. Unfortunately, high levels of scatter, betweenand within studies, has prevented establishment of reliablematerial models.

The development of test methods for measuring through-thickness parameters at quasi-static and high strain rates haslagged behind in-plane testing. This is partly due to thestrong influence of the aerospace industry, where many com-posite sections could be adequately characterized by theirin-plane properties. Now, the desire to use thicker compos-ite structures in the aerospace industry (i.e.: brackets, wingspar box, etc.) is driving the need for reliable through thick-ness properties. At high strain rates, numerous factors make

testing materials particularly challenging for both in-planeand the through-thickness directions. One factor is the rel-atively small through-thickness dimension of a typical thinlaminate, which does not facilitate adaptation of traditionalin-plane tests. The small through-thickness dimension in-troduces complications with gripping and alignment of thespecimen [7–9]. The common solution is to increase the sizeof the specimen to enable traditional coupon designs to beused. However, this must be done carefully to ensure prop-erties obtained from the test specimen is representative of atypical laminate. For woven fibre reinforcements, the min-imum dimensions are governed by the size of a represen-tative volume element [7, 10], while for laminates, highervoid concentrations may introduce a significant volume ef-fect. Apart from geometrical considerations, additional dif-ficulties are encountered when testing composites at highstrain rates.

The management of inertial effects becomes critical whentesting at strain rates above 100 s−1 (Fig. 1 in [11]). Thistends to be particularly problematic for many existing tech-niques, which make use of limited information and rely on anumber of assumptions to quantify the material’s response.The best example of this is the popular split Hopkinson pres-sure bar (SHPB), which acts as a dynamic load cell un-der very specific conditions (in particular, one-dimensionalwave propagation, elastic bar deformation, quasi-static equi-librium conditions). Quasi-static equilibrium can be quitedifficult to achieve, particularly for materials with low wavespeeds. This significantly restricts achievable strain rates toapproximately 1-2 x 103 s−1 for failure properties in com-pression [4, 12] and an order of magnitude lower in ten-sion [6].

The purpose of this paper is to provide an overview of ex-isting techniques for measuring properties of FRP compos-ites in the through-thickness direction at intermediate andhigh strain rates. A brief summary of challenges associatedwith quasi-static through-thickness testing is first provided,

1


Jared Van BLITTERSWYK1, Lloyd FLETCHER2 and Fabrice PIERRON3 1, 2, 3 Faculty of Engineering and the Environment, University of Southampton, Southampton SO17 1BJ, UK

(Received 30 June 2017; accepted 30 June 2017)

Abstract: This paper provides a review of the strain rate effect on the through-thickness mechanical properties of fibre-reinforced polymer composites. The challenges and limitations associated with existing methods for through-thickness testing are discussed. Specific attention is given to the split Hopkinson pressure bar, and implications of the intrinsic limitations for measuring mechanical properties. The influence of strain rate on elastic modulus, ultimate strength and ultimate strain is provided for compressive, tensile and shear loading conditions. The review is concluded with a discussion on the direction of future research focussed around full-field imaging techniques. Keywords: High strain rate, Interlaminar properties, Fibre-reinforced polymer composites, Test methods

Advanced Experimental Mechanics, Vol.2 (2017), 3-28

Copyright Ⓒ 2017 JSEM

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they are sufficiently simple to enable limited amounts ofinformation to be used to extract constitutive parametersgoverning the dynamic behaviour. For example, the Tay-lor impact test [31], uses post-impact measurements of plas-tic deformation to infer dynamic flow stresses in the ma-terial. However, the Taylor impact test has limited appli-cation for thermoset fibre-reinforced composites, which ex-hibit small strains to failure and minimal plastic deforma-tion. Similarly, a drop weight test [11] attempts to use theimpactor as a load cell. Similar to high speed load frames,inertial ringing within the impactor may mask the under-lying mechanical response. The Kolsky pressure bar [32],also known as the Split Hopkinson Pressure Bar (SHPB)(Fig. 1), operates similarly in that the loading bars areused as a dynamic load cell. This arrangement is only validfor a very specific set of conditions and relies on numer-ous assumptions about the dynamic response of the material.[33].

The key is that all available techniques make use of limitedinformation. The test data is generally provided by a fewpoint measurements typically provided by strain gauges. Asa result, all current test methods suffer from many intrinsiclimitations, a number of which are particularly challengingto overcome when testing more compliant materials like uni-directional composites in transverse tension or shear. Fol-lowing discussions will focus on the SHPB due to its over-whelming popularity for high strain rate testing of compos-ites. Particular attention is given to explaining the variationsfor tensile, compression and shear testing, and the intrin-sic limitations most relevant to through-thickness testing ofFRP composites.

3.1. Split-Hopkinson Pressure Bar (SHPB) Test-ing

The SHPB has played an invaluable role in obtaining infor-mation on the high strain rate response of FRP composites inthe through-thickness direction [2, 4–6, 10]. With this tech-nique, a specimen is generally subjected to a compressiveloading pulse while being sandwiched between two elasticbars, denoted as the incident and transmitter bars (Fig. 1a).In this configuration, a striker is used to impact the inci-dent bar and induce a compressive pulse. The specimenmay also be loaded by direct impact (Fig. 1b); however, thisapproach is less common due to issues with alignment andpulse transmission. In the two bar configuration, the pulsefrom the striker propagates towards the specimen, with theinput pulse recorded via the strain gauge on the bar. Oncethe pulse reaches the specimen, some of the compressivepulse is transmitted through the specimen into the transmit-ter bar, and some is reflected back through the incident barat the specimen interface. The amount of the pulse whichis reflected or transmitted is dependent on the impedancemismatch between the bars and the specimen. Under spe-cific conditions, the pulses measured on the incident andtransmitter bars can be used to deduce the stress state withinthe specimen using one-dimensional wave theory. In thesecases, the portion of the wave transmitted through the speci-men describes the stress in the specimen, while the reflected

Incident/Input BarSpecimen

Striker Bar Transmitter/Output Bar

Strain Gauge Strain Gauge

Specimen


Strain Gauge

(a)




Specimen


Strain Gauge

(b)

Figure 1: Schematic of two forms of a pressure bar apparatus: a) Split-Hopkinson Pressure Bar, and b) direct impact pressure bar. Adapted fromGama et al. [34].

pulse describes the strain rate [5]. Most efforts have focusedon obtaining the dynamic compressive properties of com-posites in the through-thickness direction due to the relativesimplicity of implementing the test [11]. The compressionSHPB test has been adapted to permit high rate testing ofmaterials in tension, shear, torsion, bending, and combinedload states [2, 5, 34, 35].

The principles of a tensile SHPB are similar to compres-sion. In the case of tensile loading, the main differenceslie in the means of generating the pulse, typical specimengeometries, and gripping/attachment to the input and trans-mitter bars [33]. Tensile pulses are most commonly appliedusing a direct impact on a flange attached to the incident bar,or through the release of a static tensile stress in the incidentbar [20]. Tensile pulses may also be applied using a top hatspecimen and hollow transmitter bars, or using the reflectedpulse from the transmitter bar with a collar used to protectthe specimen in compression. The reader is referred to refer-ence [20] for further details. U-shaped striker bars have alsobeen considered as a means of generating longer pulses andextending the range of achievable strain rates [36].

An alternative approach to the two-bar reflected pulse sys-tem is the single bar spalling test [37]. In this case, thespecimen is attached on one side to the end of the inputbar and the transmitter bar is removed so one edge of thespecimen is free. The specimen in loaded in tension afterthe compressive pulse reflects off of the free edge and be-comes tensile. Strain gauge measurements and point-wiselaser Doppler velocimetry may be used to infer the tensilestrength of the material. This is accomplished using an an-alytical solution for the specimen stress state based on theassumption of one-dimensional wave propagation [37]. Thespall test is particularly useful for loading the specimen witha single pulse, as long as the compressive strength largelyexceeds the tensile strength. This enables the input pulseto be tailored such that no damage is caused during com-pressive loading, but the reflected tensile wave causes fail-ure.

For direct tensile loading, the specimen is generally attachedto the incident and transmitted bars using threaded inserts oradhesives [38]. Mechanical inserts have the disadvantage of

3

with particular attention to those issues also relevant to highstrain rate testing (Section 2). This is followed by a reviewof existing approaches for through-thickness testing at highstrain rates in Section 3. Further attention is given to theSHPB and implications of the intrinsic assumptions for test-ing composites. Section 4 offers a review of the state-of-the-art understanding of the strain rate effect on elastic modulus,strength and ultimate strain under tension, compression andshear loading. Finally, Section 5 discusses the use of full-field optical measurements with particular attention to thepotential advancement and development of new and exist-ing test methods.

2. Challenges Common to Quasi-Static and High StrainRate Tests

Obtaining material properties for composites in the through-thickness direction is a long outstanding problem. The chal-lenges faced by experimentalists for quasi-static loading arefirst reviewed here as many apply to high strain rate test-ing. For instance, introducing a tensile load generally re-quires gripping of the specimen. Often this causes prema-ture failure due to eccentric loading (bending stresses) orstress concentrations at the grips. This is especially prob-lematic for through-thickness testing due to the inherentlysmaller specimen dimensions. Manufacturing and machin-ing quality can also have significant influence on the failurebehaviour. For thick specimens formed by bonding severalsmaller laminates, failure can occur near the bond interface,resulting in failure strengths that are not representative of anoriginal laminate [7]. Composites also show a strong vol-ume effect. Void content from manufacturing increases withvolume causing a degradation of matrix properties and re-duced tensile and shear strengths [13, 14]. Pre-defects areespecially critical as failure can initiate prematurely fromvoids or micro cracks cause by the machining process. Allof these issues have created a notable sensitivity of materialproperties to test method [15–17]. For the interested reader,a review of available quasi-static test methods can be foundin references [7, 8, 13]. In addition to the aforementionedchallenges, several others present themselves at high strainrates, which will be discussed in the next section.

3. Through-Thickness Test Methods for Intermediateand High Strain Rates

This section provides a brief summary of available methodsto test composites in the through-thickness direction at in-termediate and high strain rates. The reader is referred tothe review by Field et al. [11] for a more general overviewof testing methods applicable to both in-plane and through-thickness directions.

One of the key challenges for testing at high strain rates isthe accurate measurement of strain and force. At intermedi-ate strain rates, high speed load frames are commonly used.Such systems allow the crosshead to be accelerated to thedesired speed prior to engaging the grip mechanism. Un-fortunately, force measurement may be unreliable at highloading speeds due to inertial effects and ‘ringing’ in the

load cell [18–20]. As a result, high speed load frames aretypically limited to strain rates well below 100 s−1.

Inertia-induced ringing is also problematic for contact straininstruments such as mechanical extensometers. Straingauges have been used extensively for dynamic testing dueto their simplicity and sufficiently high dynamic response,which can be sampled with available data acquisition sys-tems (typically sampled at MHz rates [2]). Non-contact ap-proaches, such as high speed optical extensometers [19, 20]or laser Doppler velocimetry [20, 21], have been used tomeasure global deformation. Unfortunately, these tech-niques are not well-suited to characterise heterogeneous de-formations resulting from inertia. With advancements incomputing power and high speed imaging technology, full-field measurements offer a viable alternative to traditionalstrain gauges for high strain rate testing [22–26].

Full-field optical techniques, particularly digital image cor-relation (DIC), has seen widespread use for quasi-static test-ing, but limited use at high strain rates [18, 19, 22, 26, 27].‘Full-field’ refers to the large number of measurement pointsobtained via automated image processing. At the neces-sary frame rates for high strain rate testing, the resolutionof traditional high speed cameras is inadequate to performmeaningful full-field measurements in the case of heteroge-neous states of deformation. This is a result of the mem-ory readout structure, which requires spatial resolution tobe sacrificed for temporal resolution. Limited spatial res-olution is problematic for DIC, which requires correlationover a relatively large subset of pixels. A new generationof high speed cameras, known as ‘ultra-high speed cameras’(frame rates in excess of 1 Mfps) provides much greater spa-tial resolution at the cost of record length [28]. With thesecameras, DIC is more feasible; however, the grid methodoffers a better compromise between spatial and measure-ment resolution [29, 30]. The grid method, is similar toDIC but relies on tracking of a regular grid rather than arandom pattern. This approach is particularly well suitedfor measuring small strains (i.e.: ultimate strains for com-posites in the through-thickness direction), which is a chal-lenge for DIC. The combination of ultra high speed imag-ing and the grid method has shown promise in recent lit-erature for obtaining full-field measurements of displace-ment and strain at high strain rates [23–25]. In these stud-ies, the measurement resolution is high enough that in-verse identification procedures, such as the virtual fieldsmethod (VFM), can be used to identify constitutive prop-erties. However, this technique is still in its early stagesof development and has yet to be used for high strain ratetesting of composite materials in the through-thickness di-rection. Further discussion surrounding the potential of thisapproach for high strain rate testing will be presented inSection 5.

To extract material properties from the limited informationprovided by typical instruments (i.e.: strain gauges) requiresa number of assumptions about the material response. Theseassumptions impose constraints on the complexity of thetest. This is a commonality in existing techniques, in that

2

J. V. BLITTERSWYK, L. FLETCHER and F. PIERRON

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they are sufficiently simple to enable limited amounts ofinformation to be used to extract constitutive parametersgoverning the dynamic behaviour. For example, the Tay-lor impact test [31], uses post-impact measurements of plas-tic deformation to infer dynamic flow stresses in the ma-terial. However, the Taylor impact test has limited appli-cation for thermoset fibre-reinforced composites, which ex-hibit small strains to failure and minimal plastic deforma-tion. Similarly, a drop weight test [11] attempts to use theimpactor as a load cell. Similar to high speed load frames,inertial ringing within the impactor may mask the under-lying mechanical response. The Kolsky pressure bar [32],also known as the Split Hopkinson Pressure Bar (SHPB)(Fig. 1), operates similarly in that the loading bars areused as a dynamic load cell. This arrangement is only validfor a very specific set of conditions and relies on numer-ous assumptions about the dynamic response of the material.[33].

The key is that all available techniques make use of limitedinformation. The test data is generally provided by a fewpoint measurements typically provided by strain gauges. Asa result, all current test methods suffer from many intrinsiclimitations, a number of which are particularly challengingto overcome when testing more compliant materials like uni-directional composites in transverse tension or shear. Fol-lowing discussions will focus on the SHPB due to its over-whelming popularity for high strain rate testing of compos-ites. Particular attention is given to explaining the variationsfor tensile, compression and shear testing, and the intrin-sic limitations most relevant to through-thickness testing ofFRP composites.

3.1. Split-Hopkinson Pressure Bar (SHPB) Test-ing

The SHPB has played an invaluable role in obtaining infor-mation on the high strain rate response of FRP composites inthe through-thickness direction [2, 4–6, 10]. With this tech-nique, a specimen is generally subjected to a compressiveloading pulse while being sandwiched between two elasticbars, denoted as the incident and transmitter bars (Fig. 1a).In this configuration, a striker is used to impact the inci-dent bar and induce a compressive pulse. The specimenmay also be loaded by direct impact (Fig. 1b); however, thisapproach is less common due to issues with alignment andpulse transmission. In the two bar configuration, the pulsefrom the striker propagates towards the specimen, with theinput pulse recorded via the strain gauge on the bar. Oncethe pulse reaches the specimen, some of the compressivepulse is transmitted through the specimen into the transmit-ter bar, and some is reflected back through the incident barat the specimen interface. The amount of the pulse whichis reflected or transmitted is dependent on the impedancemismatch between the bars and the specimen. Under spe-cific conditions, the pulses measured on the incident andtransmitter bars can be used to deduce the stress state withinthe specimen using one-dimensional wave theory. In thesecases, the portion of the wave transmitted through the speci-men describes the stress in the specimen, while the reflected




Specimen


Strain Gauge

(a)




Specimen


Strain Gauge

(b)

Figure 1: Schematic of two forms of a pressure bar apparatus: a) Split-Hopkinson Pressure Bar, and b) direct impact pressure bar. Adapted fromGama et al. [34].

pulse describes the strain rate [5]. Most efforts have focusedon obtaining the dynamic compressive properties of com-posites in the through-thickness direction due to the relativesimplicity of implementing the test [11]. The compressionSHPB test has been adapted to permit high rate testing ofmaterials in tension, shear, torsion, bending, and combinedload states [2, 5, 34, 35].

The principles of a tensile SHPB are similar to compres-sion. In the case of tensile loading, the main differenceslie in the means of generating the pulse, typical specimengeometries, and gripping/attachment to the input and trans-mitter bars [33]. Tensile pulses are most commonly appliedusing a direct impact on a flange attached to the incident bar,or through the release of a static tensile stress in the incidentbar [20]. Tensile pulses may also be applied using a top hatspecimen and hollow transmitter bars, or using the reflectedpulse from the transmitter bar with a collar used to protectthe specimen in compression. The reader is referred to refer-ence [20] for further details. U-shaped striker bars have alsobeen considered as a means of generating longer pulses andextending the range of achievable strain rates [36].

An alternative approach to the two-bar reflected pulse sys-tem is the single bar spalling test [37]. In this case, thespecimen is attached on one side to the end of the inputbar and the transmitter bar is removed so one edge of thespecimen is free. The specimen in loaded in tension afterthe compressive pulse reflects off of the free edge and be-comes tensile. Strain gauge measurements and point-wiselaser Doppler velocimetry may be used to infer the tensilestrength of the material. This is accomplished using an an-alytical solution for the specimen stress state based on theassumption of one-dimensional wave propagation [37]. Thespall test is particularly useful for loading the specimen witha single pulse, as long as the compressive strength largelyexceeds the tensile strength. This enables the input pulseto be tailored such that no damage is caused during com-pressive loading, but the reflected tensile wave causes fail-ure.

For direct tensile loading, the specimen is generally attachedto the incident and transmitted bars using threaded inserts oradhesives [38]. Mechanical inserts have the disadvantage of

3

with particular attention to those issues also relevant to highstrain rate testing (Section 2). This is followed by a reviewof existing approaches for through-thickness testing at highstrain rates in Section 3. Further attention is given to theSHPB and implications of the intrinsic assumptions for test-ing composites. Section 4 offers a review of the state-of-the-art understanding of the strain rate effect on elastic modulus,strength and ultimate strain under tension, compression andshear loading. Finally, Section 5 discusses the use of full-field optical measurements with particular attention to thepotential advancement and development of new and exist-ing test methods.

2. Challenges Common to Quasi-Static and High StrainRate Tests

Obtaining material properties for composites in the through-thickness direction is a long outstanding problem. The chal-lenges faced by experimentalists for quasi-static loading arefirst reviewed here as many apply to high strain rate test-ing. For instance, introducing a tensile load generally re-quires gripping of the specimen. Often this causes prema-ture failure due to eccentric loading (bending stresses) orstress concentrations at the grips. This is especially prob-lematic for through-thickness testing due to the inherentlysmaller specimen dimensions. Manufacturing and machin-ing quality can also have significant influence on the failurebehaviour. For thick specimens formed by bonding severalsmaller laminates, failure can occur near the bond interface,resulting in failure strengths that are not representative of anoriginal laminate [7]. Composites also show a strong vol-ume effect. Void content from manufacturing increases withvolume causing a degradation of matrix properties and re-duced tensile and shear strengths [13, 14]. Pre-defects areespecially critical as failure can initiate prematurely fromvoids or micro cracks cause by the machining process. Allof these issues have created a notable sensitivity of materialproperties to test method [15–17]. For the interested reader,a review of available quasi-static test methods can be foundin references [7, 8, 13]. In addition to the aforementionedchallenges, several others present themselves at high strainrates, which will be discussed in the next section.

3. Through-Thickness Test Methods for Intermediateand High Strain Rates

This section provides a brief summary of available methodsto test composites in the through-thickness direction at in-termediate and high strain rates. The reader is referred tothe review by Field et al. [11] for a more general overviewof testing methods applicable to both in-plane and through-thickness directions.

One of the key challenges for testing at high strain rates isthe accurate measurement of strain and force. At intermedi-ate strain rates, high speed load frames are commonly used.Such systems allow the crosshead to be accelerated to thedesired speed prior to engaging the grip mechanism. Un-fortunately, force measurement may be unreliable at highloading speeds due to inertial effects and ‘ringing’ in the

load cell [18–20]. As a result, high speed load frames aretypically limited to strain rates well below 100 s−1.

Inertia-induced ringing is also problematic for contact straininstruments such as mechanical extensometers. Straingauges have been used extensively for dynamic testing dueto their simplicity and sufficiently high dynamic response,which can be sampled with available data acquisition sys-tems (typically sampled at MHz rates [2]). Non-contact ap-proaches, such as high speed optical extensometers [19, 20]or laser Doppler velocimetry [20, 21], have been used tomeasure global deformation. Unfortunately, these tech-niques are not well-suited to characterise heterogeneous de-formations resulting from inertia. With advancements incomputing power and high speed imaging technology, full-field measurements offer a viable alternative to traditionalstrain gauges for high strain rate testing [22–26].

Full-field optical techniques, particularly digital image cor-relation (DIC), has seen widespread use for quasi-static test-ing, but limited use at high strain rates [18, 19, 22, 26, 27].‘Full-field’ refers to the large number of measurement pointsobtained via automated image processing. At the neces-sary frame rates for high strain rate testing, the resolutionof traditional high speed cameras is inadequate to performmeaningful full-field measurements in the case of heteroge-neous states of deformation. This is a result of the mem-ory readout structure, which requires spatial resolution tobe sacrificed for temporal resolution. Limited spatial res-olution is problematic for DIC, which requires correlationover a relatively large subset of pixels. A new generationof high speed cameras, known as ‘ultra-high speed cameras’(frame rates in excess of 1 Mfps) provides much greater spa-tial resolution at the cost of record length [28]. With thesecameras, DIC is more feasible; however, the grid methodoffers a better compromise between spatial and measure-ment resolution [29, 30]. The grid method, is similar toDIC but relies on tracking of a regular grid rather than arandom pattern. This approach is particularly well suitedfor measuring small strains (i.e.: ultimate strains for com-posites in the through-thickness direction), which is a chal-lenge for DIC. The combination of ultra high speed imag-ing and the grid method has shown promise in recent lit-erature for obtaining full-field measurements of displace-ment and strain at high strain rates [23–25]. In these stud-ies, the measurement resolution is high enough that in-verse identification procedures, such as the virtual fieldsmethod (VFM), can be used to identify constitutive prop-erties. However, this technique is still in its early stagesof development and has yet to be used for high strain ratetesting of composite materials in the through-thickness di-rection. Further discussion surrounding the potential of thisapproach for high strain rate testing will be presented inSection 5.

To extract material properties from the limited informationprovided by typical instruments (i.e.: strain gauges) requiresa number of assumptions about the material response. Theseassumptions impose constraints on the complexity of thetest. This is a commonality in existing techniques, in that

2

1




Abstract: This paper provides a review of the strain rate effect on the through-thickness mechanical properties of fibre-reinforced polymer composites. The challenges and limitations associated with existing methods for through-thickness testing are discussed. Specific attention is given to the split Hopkinson pressure bar, and implications of the intrinsic limitations for measuring mechanical properties. The influence of strain rate on elastic modulus, ultimate strength and ultimate strain is provided for compressive, tensile and shear loading conditions. The review is concluded with a discussion on the direction of future research focussed around full-field imaging techniques. Keywords: High strain rate, Interlaminar properties, Fibre-reinforced polymer composites, Test methods 5 ページ目

3.1 Split-Hopkinson pressure bar (SHPB) testing Fig. 1 Schematic of two forms of a pressure bar apparatus: a) Split-Hopkinson Pressure Bar, and b) direct impact pressure bar. Adapted from Gama et al. [34] 6 ページ目

3.1.1 Assumptions and limitations associated with the SHPB Fig. 2 Compression stress-strain response highlighting the influence of wave dispersion effects on the linear response measured using a SHPB at a strain rate of 6,000 s–1. Cubic specimens, 10 mm thick, carbon/epoxy 3D weave. Taken from Gerlach et al. [10] Fig. 3 Schematic of anvil-type specimen subjected to arbitrary end loads 7 ページ目 Fig. 4 Verification of quasi-static stress equilibrium for a through-thickness compression test at an average strain rate of 1,125 s–1. Cubic specimens, 12.7 mm thick, plain weave S-2 glass/vinyl ester composite. Taken from Gama et al. [45]

4.1 Strain rate effects on compressive properties 4.1.1 Compressive elastic modulus

8 ページ目 Fig. 5 Summary of relative strain rate sensitivity for compressive modulus from the literature. ‘PP’ and ‘W’ denote pre-preg and plain weave reinforcement, respectively. Red symbol outline denotes that values are quoted with respect to modulus at lowest strain rate considered (1,275 s–1 for [12]). Error bars denote the range of reported sensitivity and not standard deviation. Data taken from [4, 10, 12, 47, 50, 54]

4.1.2 Compressive strength 9 ページ目 Fig. 6 Summary of relative strain rate sensitivity for compressive strength from the literature. ‘PP’ and ‘W’ denote pre-preg and plain weave reinforcement, respectively. Red symbol outline denotes that values are quoted with respect to strength at lowest strain rate considered (1,275 s–1 for [12]). Error bars denote the range of reported sensitivity and not standard deviation. Data taken from [4, 9, 10, 12, 27, 45, 47, 50–55]

4.1.3 Ultimate compressive strain 10 ページ目 Fig. 7 Summary of relative strain rate sensitivity for ultimate compressive strain from the literature. ‘PP’ and ‘W’ denote pre-preg and plain weave reinforcement, respectively. Red symbol outline denotes that values are quoted with respect to strain at lowest strain rate considered (1,275 s–1 for [12] and 1,007 s–1 for [55]). Error bars denote the range of reported sensitivity and not standard deviation. Data taken from [4, 9, 12, 27, 45, 47, 50–55] 10 ページ目続き

4.2 Strain rate effects on tensile properties

4.2.1 Tensile elastic modulus

4.2.2 Tensile strength

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Advanced Experimental Mechanics, Vol.2 (2017)

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the form of Eq. (1),

F1(t)+F2(t) = ρe∫ L

0

∫ b/2

−b/2ax(x,y, t)dxdy (1)

where F1(t) and F2(t), denote the forces at the incident andtransmitter bar interfaces, respectively, b and L denote thespecimen width and length, respectively, ρ is the densityof the material (assumed constant here), and ax is the lo-cal acceleration in the x direction. Stress equilibrium as-sumes that the force at the incident bar-specimen interfaceis equivalent to that at the transmitter bar-specimen interface(i.e.: acceleration is neglected). When the pulse reaches thespecimen the input force generates a stress wave in the spec-imen (i.e.: inertial effects caused by transient acceleration).This stress wave travels through the specimen to the out-put bar where some is transmitted and some reflects and re-verberates in the specimen. When the stress wave initiallytravels through the specimen, a heterogeneous stress stateresults, violating the assumption of quasi-static equilibrium(condition 3). In the case of softer materials, the stressesarising from inertial effects are large and mask the true me-chanical response until the waves eventually damp out aftermultiple reverberations [38, 43]. The contributions of iner-tia are difficult to identify as no obvious effects are createdin the apparent stress-strain behaviour. In a state of quasi-static equilibrium, the sum of incident and reflected pulseswill equal the transmitted pulse (εI + εR = εT ) [38, 45]. Forthrough-thickness tests, this condition is not satisfied untillate in the test, as illustrated by the work of Gama et al. [45](Fig. 4). A general criterion is that quasi-static stress equi-librium occurs after approximately three or four reverbera-tions of the pulse through the specimen [43, 44]. Rather thancounting reverberations, Gillespie et al. [2] used an ‘R cri-terion’, based on the difference between incident and trans-mitted signals, to assess the validity of a test. Regardlessof the technique used to determine when quasi-static stressequilibrium conditions have been achieved, this assumptionis always a source of discussion [34]. Therefore, it is gener-ally accepted that the SHPB is simply inadequate to reliablymeasure initial material stiffness [4, 33, 34, 43].

The low wave speed in the through-thickness direction ofFRP composites, coupled with the low strains to failure, im-pose significant restrictions on the achievable strain rates(typically less than 103 s−1 [35]). The problem with in-ertia for the SHPB is exacerbated by the quasi-brittle na-ture of the material, the low wave speed, and the low sig-nal to noise ratio [41, 46]. Low strains at failure meansthat a state of quasi-static stress equilibrium may not beachieved before the test is complete. Short specimens andpulse shaping may be used to reduce the time to achievequasi-static equilibrium and improve the uniformity of strainrate [34, 43, 47]; however, quasi-static equilibrium still maynot be achieved prior to failure and short specimens may suf-fer from more significant end friction effects [38]. Notwith-standing the fact that for tension, the specimens cannot bevery short. Gorham [48] showed that no aspect ratio effec-tively removes inertial effects. Softer materials also sufferfrom low signal-to-noise levels in the reflected pulse [38].

Figure 4: Verification of quasi-static stress equilibrium for a through-thickness compression test at an average strain rate of 1,125 s−1. Cubicspecimens, 12.7 mm thick, plain weave S-2 glass/vinyl ester composite.Taken from Gama et al. [45].

Efforts to improve this include reducing the cross-sectionand stiffness of the input bars, using more sensitive straingauges, using polymer bars [49], or direct force measure-ment [38]. Unfortunately, these approaches generally sufferfrom higher levels of wave dispersion and inertial ringing,making force measurement more unreliable.

4. Review of Interlaminar Properties at High StrainRates

A review of current literature reporting on the sensitivityof through-thickness properties to strain rate will now bediscussed. A compilation of references for compression,tension and shear properties is presented in Appendix A inTables 1, 2 and 3, respectively. It must be noted that the fol-lowing discussion focusses on relative trends between quasi-static and high strain rate properties. This is a result of theinconsistency in the literature regarding material composi-tion (fibre and matrix materials, fibre volume fraction, rein-forcement architecture, etc.), which makes direct compari-son of quoted properties uninformative. Also, failure strainrate is defined inconsistently in the literature with some re-porting an average strain rate and others reporting instan-taneous strain rates. Defining a failure strain rate using aSHPB is difficult and not necessarily reliable due to the de-pendency on damage progression in composite materials.Therefore, no attempt is made by the present authors to con-vert reported strain rates to an equivalent metric across allstudies.

4.1. Strain rate effects on compressive properties4.1.1. Compressive elastic modulusAs discussed in the previous section, effects from inertiatend to mask the initial behaviour of the material under dy-namic loading using a SHPB. Therefore, measurements ofthe modulus using the SHPB can only be regarded as ‘ap-parent’. The degree to which inertia influences the mea-surement of strain is difficult to resolve using strain mea-surements on the incident and transmitter bars. This maycontribute to the lack of general agreement in the literatureregarding the sensitivity of the dynamic modulus to strainrate.

5

creating additional reflections and dispersion of the wave,affecting the accuracy of the measurement using SHPB the-ory [19, 20]. The grips can also introduce stress concentra-tions and heterogeneous deformation. Specimen geometryis an important consideration for tensile testing. A waistedcylindrical specimen is commonly used to ensure failure oc-curs within the gauge section [22, 33]. However, due to thecontribution of the non-waisted section to the response ofthe material, calculation of stress and strain are more com-plicated using standard one-dimensional wave theory [22].Further, the specimens must be designed such that the gaugesection undergoes uniform axial stress. The appropriate ge-ometry is dependent on the material [22].

The SHPB has also been used to measure the interlaminarshear properties. There are two common configurations. Asingle or double lap shear joint loaded in compression usinga SHPB was common in early studies. A shortcoming of thelap joint is high normal stresses at the ends of the overlap,which typically dominates the initiation of failure [39, 40].An alternative approach is to load thin-walled tubular speci-mens in shear using a torsional SHPB [5, 41]. This arrange-ment is very similar to the compression SHPB, with the ex-ception that a shear wave is induced by applying a torquepre-load on the incident bar.

3.1.1. Assumptions and limitations associated with theSHPB

A number of assumptions are required for strain gauge mea-surements on the bars to be used to infer the stress and strainstates in the specimen for a SHPB test. The assumptions arebriefly summarised below, and the interested reader is re-ferred to the paper by Gama et al. [34] for a more in-depthreview. The assumptions to be satisfied for a valid test in-clude:

1. one-dimensional stress wave propagation in the inci-dent and transmission bars (i.e.: negligible wave dis-persion);

2. interfaces between the specimen and bars remain pla-nar at all times;

3. the specimen is in a condition of quasi-static stressequilibrium (i.e., the forces exerted at both specimenends are equal in magnitude and opposite in sign), and;

4. friction effects at the specimen-bar interfaces can beneglected.

Tests suffering from high amounts of dispersion (violatingassumption 1) exhibit a non-linear initial region of the stress-strain curve, followed by oscillations about the straight linethat would exist for a bar free of distortion [34]. An ex-ample is shown in the work by Gerlach et al. [10], wherethe stress-strain response at high strain rate exhibits a clearoscillatory behaviour (Fig. 2). A number of corrective ap-proaches have been developed [34], but, the effects of dis-persion are never completely removed. Aside from min-imising misalignment at the bar-specimen interfaces, ‘pulseshaping’ is the only other approach to reduce the amount of

dispersion by smoothing and limiting high frequency con-tent in the compressive pulse [34, 42]. Pulse shaping isgenerally achieved by modifying the shape of the impactoror placing a thin layer of low impedance material, or plas-tically deforming metal, between the striker and input bar.This however limits the strain rate that the tested specimenwill see.

Figure 2: Compression stress-strain response highlighting the influence ofwave dispersion effects on the linear response measured using a SHPB at astrain rate of 6,000 s−1. Cubic specimens, 10 mm thick, carbon/epoxy 3Dweave. Taken from Gerlach et al. [10].

The second assumption is generally satisfied for FRP com-posites in the through-thickness direction due to the rela-tively low acoustic impedance compared to the bars. Thiscondition is more problematic for harder materials that maycause local deformation of the bars [34]. The issue of stressequilibrium (assumption 3) for SHPB testing has been stud-ied extensively in the literature [34, 43, 44]. A schematicdiagram an anvil type specimen of constant thickness e, in aSHPB test is shown in Fig. 3.

x

y

L

h

F2 (t)bF1 (t)

Figure 3: Schematic of anvil-type specimen subjected to arbitrary endloads.

The specimen is subjected to two time varying end loadsfrom the reactions at the incident and transmitter bar inter-faces. Assuming the loads are applied normal to the speci-men end faces, the local equilibrium for this specimen has

4

1













4.2.2 Tensile strength 1














1















―6―

the form of Eq. (1),

F1(t)+F2(t) = ρe∫ L

0

∫ b/2

−b/2ax(x,y, t)dxdy (1)

where F1(t) and F2(t), denote the forces at the incident andtransmitter bar interfaces, respectively, b and L denote thespecimen width and length, respectively, ρ is the densityof the material (assumed constant here), and ax is the lo-cal acceleration in the x direction. Stress equilibrium as-sumes that the force at the incident bar-specimen interfaceis equivalent to that at the transmitter bar-specimen interface(i.e.: acceleration is neglected). When the pulse reaches thespecimen the input force generates a stress wave in the spec-imen (i.e.: inertial effects caused by transient acceleration).This stress wave travels through the specimen to the out-put bar where some is transmitted and some reflects and re-verberates in the specimen. When the stress wave initiallytravels through the specimen, a heterogeneous stress stateresults, violating the assumption of quasi-static equilibrium(condition 3). In the case of softer materials, the stressesarising from inertial effects are large and mask the true me-chanical response until the waves eventually damp out aftermultiple reverberations [38, 43]. The contributions of iner-tia are difficult to identify as no obvious effects are createdin the apparent stress-strain behaviour. In a state of quasi-static equilibrium, the sum of incident and reflected pulseswill equal the transmitted pulse (εI + εR = εT ) [38, 45]. Forthrough-thickness tests, this condition is not satisfied untillate in the test, as illustrated by the work of Gama et al. [45](Fig. 4). A general criterion is that quasi-static stress equi-librium occurs after approximately three or four reverbera-tions of the pulse through the specimen [43, 44]. Rather thancounting reverberations, Gillespie et al. [2] used an ‘R cri-terion’, based on the difference between incident and trans-mitted signals, to assess the validity of a test. Regardlessof the technique used to determine when quasi-static stressequilibrium conditions have been achieved, this assumptionis always a source of discussion [34]. Therefore, it is gener-ally accepted that the SHPB is simply inadequate to reliablymeasure initial material stiffness [4, 33, 34, 43].

The low wave speed in the through-thickness direction ofFRP composites, coupled with the low strains to failure, im-pose significant restrictions on the achievable strain rates(typically less than 103 s−1 [35]). The problem with in-ertia for the SHPB is exacerbated by the quasi-brittle na-ture of the material, the low wave speed, and the low sig-nal to noise ratio [41, 46]. Low strains at failure meansthat a state of quasi-static stress equilibrium may not beachieved before the test is complete. Short specimens andpulse shaping may be used to reduce the time to achievequasi-static equilibrium and improve the uniformity of strainrate [34, 43, 47]; however, quasi-static equilibrium still maynot be achieved prior to failure and short specimens may suf-fer from more significant end friction effects [38]. Notwith-standing the fact that for tension, the specimens cannot bevery short. Gorham [48] showed that no aspect ratio effec-tively removes inertial effects. Softer materials also sufferfrom low signal-to-noise levels in the reflected pulse [38].

Figure 4: Verification of quasi-static stress equilibrium for a through-thickness compression test at an average strain rate of 1,125 s−1. Cubicspecimens, 12.7 mm thick, plain weave S-2 glass/vinyl ester composite.Taken from Gama et al. [45].

Efforts to improve this include reducing the cross-sectionand stiffness of the input bars, using more sensitive straingauges, using polymer bars [49], or direct force measure-ment [38]. Unfortunately, these approaches generally sufferfrom higher levels of wave dispersion and inertial ringing,making force measurement more unreliable.

4. Review of Interlaminar Properties at High StrainRates

A review of current literature reporting on the sensitivityof through-thickness properties to strain rate will now bediscussed. A compilation of references for compression,tension and shear properties is presented in Appendix A inTables 1, 2 and 3, respectively. It must be noted that the fol-lowing discussion focusses on relative trends between quasi-static and high strain rate properties. This is a result of theinconsistency in the literature regarding material composi-tion (fibre and matrix materials, fibre volume fraction, rein-forcement architecture, etc.), which makes direct compari-son of quoted properties uninformative. Also, failure strainrate is defined inconsistently in the literature with some re-porting an average strain rate and others reporting instan-taneous strain rates. Defining a failure strain rate using aSHPB is difficult and not necessarily reliable due to the de-pendency on damage progression in composite materials.Therefore, no attempt is made by the present authors to con-vert reported strain rates to an equivalent metric across allstudies.

4.1. Strain rate effects on compressive properties4.1.1. Compressive elastic modulusAs discussed in the previous section, effects from inertiatend to mask the initial behaviour of the material under dy-namic loading using a SHPB. Therefore, measurements ofthe modulus using the SHPB can only be regarded as ‘ap-parent’. The degree to which inertia influences the mea-surement of strain is difficult to resolve using strain mea-surements on the incident and transmitter bars. This maycontribute to the lack of general agreement in the literatureregarding the sensitivity of the dynamic modulus to strainrate.

5

creating additional reflections and dispersion of the wave,affecting the accuracy of the measurement using SHPB the-ory [19, 20]. The grips can also introduce stress concentra-tions and heterogeneous deformation. Specimen geometryis an important consideration for tensile testing. A waistedcylindrical specimen is commonly used to ensure failure oc-curs within the gauge section [22, 33]. However, due to thecontribution of the non-waisted section to the response ofthe material, calculation of stress and strain are more com-plicated using standard one-dimensional wave theory [22].Further, the specimens must be designed such that the gaugesection undergoes uniform axial stress. The appropriate ge-ometry is dependent on the material [22].

The SHPB has also been used to measure the interlaminarshear properties. There are two common configurations. Asingle or double lap shear joint loaded in compression usinga SHPB was common in early studies. A shortcoming of thelap joint is high normal stresses at the ends of the overlap,which typically dominates the initiation of failure [39, 40].An alternative approach is to load thin-walled tubular speci-mens in shear using a torsional SHPB [5, 41]. This arrange-ment is very similar to the compression SHPB, with the ex-ception that a shear wave is induced by applying a torquepre-load on the incident bar.

3.1.1. Assumptions and limitations associated with theSHPB

A number of assumptions are required for strain gauge mea-surements on the bars to be used to infer the stress and strainstates in the specimen for a SHPB test. The assumptions arebriefly summarised below, and the interested reader is re-ferred to the paper by Gama et al. [34] for a more in-depthreview. The assumptions to be satisfied for a valid test in-clude:

1. one-dimensional stress wave propagation in the inci-dent and transmission bars (i.e.: negligible wave dis-persion);

2. interfaces between the specimen and bars remain pla-nar at all times;

3. the specimen is in a condition of quasi-static stressequilibrium (i.e., the forces exerted at both specimenends are equal in magnitude and opposite in sign), and;

4. friction effects at the specimen-bar interfaces can beneglected.

Tests suffering from high amounts of dispersion (violatingassumption 1) exhibit a non-linear initial region of the stress-strain curve, followed by oscillations about the straight linethat would exist for a bar free of distortion [34]. An ex-ample is shown in the work by Gerlach et al. [10], wherethe stress-strain response at high strain rate exhibits a clearoscillatory behaviour (Fig. 2). A number of corrective ap-proaches have been developed [34], but, the effects of dis-persion are never completely removed. Aside from min-imising misalignment at the bar-specimen interfaces, ‘pulseshaping’ is the only other approach to reduce the amount of

dispersion by smoothing and limiting high frequency con-tent in the compressive pulse [34, 42]. Pulse shaping isgenerally achieved by modifying the shape of the impactoror placing a thin layer of low impedance material, or plas-tically deforming metal, between the striker and input bar.This however limits the strain rate that the tested specimenwill see.

Figure 2: Compression stress-strain response highlighting the influence ofwave dispersion effects on the linear response measured using a SHPB at astrain rate of 6,000 s−1. Cubic specimens, 10 mm thick, carbon/epoxy 3Dweave. Taken from Gerlach et al. [10].

The second assumption is generally satisfied for FRP com-posites in the through-thickness direction due to the rela-tively low acoustic impedance compared to the bars. Thiscondition is more problematic for harder materials that maycause local deformation of the bars [34]. The issue of stressequilibrium (assumption 3) for SHPB testing has been stud-ied extensively in the literature [34, 43, 44]. A schematicdiagram an anvil type specimen of constant thickness e, in aSHPB test is shown in Fig. 3.

x

y

L

h

F2 (t)bF1 (t)

Figure 3: Schematic of anvil-type specimen subjected to arbitrary endloads.

The specimen is subjected to two time varying end loadsfrom the reactions at the incident and transmitter bar inter-faces. Assuming the loads are applied normal to the speci-men end faces, the local equilibrium for this specimen has

4

1














1














1















―7―

A summary of relative change in compressive elastic modu-lus as a function of strain rate is shown in Fig. 5. The major-ity of studies report a general increase in apparent moduluswith increasing strain rate [4, 47, 50–53]. This behaviour isexpected for a matrix-dominated behaviour as reported forthermoset resins tested without reinforcing fibres [46]. Therelative increase in modulus is highly variable among stud-ies, with increases ranging between 60 % [47, 53] and 150 %at strain rates around 103 s−1 [4]. According to the tests per-formed by Yokoyama and Nakai [4], the level of sensitivityappears to be more dependent on the reinforcement archi-tecture (i.e.: cross-ply versus plain weave) compared to re-inforcement material (glass versus carbon fibres). Despitehaving a lower compressive strength, the cross-ply lami-nates absorbed more energy compared to the plain weavecomposites. No physical explanation is provided for thisbehaviour. This may be a result of the increased void con-tent for the plain weave architecture. In the work by Ho-sur et al. [54], the only other study to consider cross-plylaminates, the compressive modulus was higher comparedto quasi-static values, but decreased with increasing strainrate. No physical explanation was offered by the authors forthis trend.

The influence of fibre architecture is unclear, as very fewstudies consider pre-preg laminates, as illustrated in Fig. 5.Considering only studies that analyse plain weave architec-tures [9, 10, 12, 27, 45, 47, 51–53, 55], the magnitude ofstrain rate sensitivity is difficult to discern due to large scat-ter in reported measurements (see Table 1). For example,Song et al. [47] and Akil et al. [52] report increases instiffness ranging from 75 % to 115 % (for strain rates near1,000 s−1), where as Shen et al. [51] report a mean increaseof 350 % at 1,200 s−1. The unrealistically high effect ofstrain rate on the modulus measured by Shen et al. [51] sug-gests that specimens are unlikely to be in stress equilibrium.Alternatively, a number of studies on plain weave compos-ites [9, 10, 12, 27] show negligible variations of the modulusover a similar range of strain rates.

It is not surprising that many studies using the SHPB re-port an increase in compressive elastic modulus. In the earlystages of a test, the reaction force on the input bar does notequal the force on the transmitter bar due to a significantcontribution from acceleration (see Eq. (1)). As a result, thestrains measured by the input bar are lower, and stress in thespecimen, computed using the force on the transmitter bar,is higher. This leads to a perceived stiffening of the material.This effect is likely to increase with increasing strain rate asa greater portion of the impact force is expended in acceler-ating the material. The degree to which inertia affects a testis dependent on several factors, contributing to the scatter inthe relative increases in stiffness across the literature.

In general, a review of the literature indicates that the com-pressive elastic modulus is matrix dominated and proba-bly increases with increasing strain rate. The magnitude ofthis sensitivity is uncertain due to high scatter in the litera-ture.

10−2 100 102 104

Strain rate [s−1]

-100

0

100

200

300

400

500

Relativesensitivity[%

] CFRP - PPCFRP - WGFRP - WHYBRID - W3D - W

Compression: Elastic Modulus

Figure 5: Summary of relative strain rate sensitivity for compressive mod-ulus from the literature. ‘PP’ and ‘W’ denote pre-preg and plain weavereinforcement, respectively. Red symbol outline denotes that values arequoted with respect to modulus at lowest strain rate considered (1,275 s−1

for [12]). Error bars denote the range of reported sensitivity and not stan-dard deviation. Data taken from [4, 10, 12, 47, 50, 54].

4.1.2. Compressive strengthA summary of relative change in compressive strength asa function of strain rate is shown in Fig. 6. From Fig. 6it is clear that there is high variability associated with themagnitude of change in strength with increasing strain rate.The trend at intermediate strain rates appears much more de-fined, showing a near linear positive sensitivity. There is asmall group of studies that show good consistency at higherstrain rates, reporting a moderate and positive increase instrength for strain rates below 1,000 s−1 [4, 9, 50–52]. Re-ported increases vary between 6 % and 23 % for both CFRPand GFRP. The remaining studies report large relative in-creases in strength compared to quasi-static values: 33 %[45] (reaching a near asymptotic value at 700 s−1), 46 %[12], 56 % [53], 80 % (between 1,000 and 1,940 s−1) [55]and 180 % [27]. The large increase in strength at high strainrates reported by Woo et al. [55] (80 %) was attributed tohigh energy absorption by the kevlar fibres. The maximumstrain rate achievable by Woo et al. [55] was limited by lowpulse transmission (as low as 10 %) through the specimen.This creates higher signal-to-noise ratio for strain measure-ment on the transmission bar, which is used to infer stressin the specimen. Quasi-static values were also not providedfor comparison. In the study by Pankow et al. [27], thestress-strain response was highly non-linear and was heav-ily contaminated by dispersion. This introduces uncertaintywhen attempting to determine ultimate properties. In con-trast to these results, Gerlach et al. [10] reported that fail-ure strength remains approximately constant with increasingstrain rate (quoted up to 6,000 s−1).

A small number of studies report mixed trends for strengthat high strain rates [4, 47, 54]. Hosur et al. [54] reporteda positive sensitivity to strain rate, but peak stresses thatare below quasi-static values. The specimens were loadedto failure under quasi-static conditions; however, at 82 s−1

and 164 s−1 the compressive input pulse was not strongenough to damage the specimens. Therefore, comparisons

6

made by the authors between peak stress at these strain ratesand quasi-static strength are not equivalent. Therefore, onlymeasurements collected at 817 s−1 can be used to assess theeffect of strain rate on compressive strength. From this case,strain rate causes a decrease in strength by 37 %. The au-thors attributed this to a progressive change in failure mech-anism from splitting and crushing at 163 s−1 to crushingand shearing at 817 s−1. The instability of compressiveloading tends to cause the specimen to fail in shear accord-ing to the strength of the matrix. Therefore, the change infailure mode is unlikely to be an intrinsic property of thematerial and more a result of the experimental setup (struc-tural behaviour). Song et al. [47] reported lower strengthsat strain rates up to 800 s−1 compared to quasi-static val-ues. At higher strain rates (> 1,000 s−1), the dynamicstrength exceeds the quasi-static one. The authors offer noexplanation for this behaviour. Similar to the compressionmodulus, Yokoyama & Nakai [4] found that compressivestrength was sensitive to reinforcement architecture. Thewoven glass-epoxy laminate exhibited a positive strain ratesensitivity, whereas the carbon/epoxy cross-ply pre-preg andplain weave laminates had a negative sensitivity. This wasattributed to the properties of the fibres, however, the car-bon/epoxy laminates had 15-20% higher fibre volume frac-tions. The potential dependency on reinforcement architec-ture (i.e: pre-preg., weave, etc.) is difficult to ascertain sincethe majority of studies focus on one type of reinforcementand have large scatter.

Other factors contributing to scatter include specimen ge-ometry and uncertainty associated with quasi-static values.All studies in the literature use cubic or cylindrical speci-mens. A study by Tagarielli et al. [56] showed that thecompressive strength and strain is highly sensitive to speci-men geometry. For the same contact surface area, cylindri-cal specimens were found to fail at lower stress and straincompared to cubic specimens. As the volume of the cylin-drical specimens was larger, this may indicate a volume ef-fect. In any case, there appears to be a sensitivity to geome-try and/or volume, which differs between studies in the liter-ature. Another source of difficulty for comparing studies isthat some work do not report quasi-static values at the samestrain rates. Considering relative changes in strength overthe high strain rate tests only, the values range between -5 %and +30 % compared to the range of -40 % to +40 %, whencompared against quasi-static values, as shown in Fig. 6.This does not necessarily imply better accuracy, and insteadsuggests that high strain rate tests are reasonably repeatableunder different conditions.

Compressive strength is heavily dominated by structuralfailure due to the inherent instability of the loading condi-tion. Specimens will tend to fail in shear, which is deter-mined by the strength of the resin. Some authors reporta change in failure mode, which is attributed to strain ratesensitivity [27, 50, 51]. This highlights the challenge asso-ciated with measuring compressive strength and is likely astrong contributor to scatter in the literature. The intrinsicinstability of the test makes the measured strength highly

10−2 100 102 104

Strain rate [s−1]

-50

0

50

100



Compression: Strength

Figure 6: Summary of relative strain rate sensitivity for compressivestrength from the literature. ‘PP’ and ‘W’ denote pre-preg and plain weavereinforcement, respectively. Red symbol outline denotes that values arequoted with respect to strength at lowest strain rate considered (1,275 s−1

for [12]). Error bars denote the range of reported sensitivity and not stan-dard deviation. Data taken from [4, 9, 10, 12, 27, 45, 47, 50–55].

sensitive to variations in manufacturing, fibre volume frac-tion, defects, void content, specimen geometry, specimenpreparation (flat contact surfaces) and alignment.

In summary, the literature suggests that there is likely a pos-itive sensitivity of compression strength to strain rate but themagnitude is uncertain. The sensitivity to fibre material andarchitecture is also difficult to determine as a consequenceof limited studies and high scatter.

4.1.3. Ultimate compressive strain

As with strength and stiffness, the influence of strain rateon failure strain is uncertain. Many authors report a slightdecrease (less than 14 %) or negligible influence of strainrate on failure strains as shown in Fig. 7 [4, 9, 27, 50, 52,53]. Song et al. [47] reported a negative sensitivity, butone that is much stronger than reported by most (-62 %).Pankow et al. [27], Shah Khan et al. [50] and Gama etal. [45] reported a negligible sensitivity to strain rate. Inthe study by Shah Khan et al. [50], only strain rates up to10 s−1 were considered. The results from Gama et al. [45]and Pankow et al. [27] illustrate the effects of dispersion.Both studies show oscillations in the initial portion of thestress-strain curve. Further, strain measurements with 2DDIC by Pankow et al. [27] showed significant heterogeneitythroughout the entire test. This was attributed to the coarsetextile architecture and local variations in wave speed withinthe material. However, the reliability of this conclusion isquestionable due to the poor spatial and temporal resolutionof the measurements.

The studies mentioned above report an opposite effect ofstrain rate to the positive sensitivity reported by Gerlachet al. [46] for an RTM-6 resin tested without reinforce-ment. A positive sensitivity was also established by Naiket al. [12] (+34 % between 1,275 s−1 and 1,503 s−1) andGama et al. [45] (up to +108 % at 1,125 s−1). The notablyhigher sensitivity from Gama et al. [45] is likely unreliable

7

CFRP - PPCFRP - WGFRP - WHYBRID - W3D - W


1














1















―8―

A summary of relative change in compressive elastic modu-lus as a function of strain rate is shown in Fig. 5. The major-ity of studies report a general increase in apparent moduluswith increasing strain rate [4, 47, 50–53]. This behaviour isexpected for a matrix-dominated behaviour as reported forthermoset resins tested without reinforcing fibres [46]. Therelative increase in modulus is highly variable among stud-ies, with increases ranging between 60 % [47, 53] and 150 %at strain rates around 103 s−1 [4]. According to the tests per-formed by Yokoyama and Nakai [4], the level of sensitivityappears to be more dependent on the reinforcement archi-tecture (i.e.: cross-ply versus plain weave) compared to re-inforcement material (glass versus carbon fibres). Despitehaving a lower compressive strength, the cross-ply lami-nates absorbed more energy compared to the plain weavecomposites. No physical explanation is provided for thisbehaviour. This may be a result of the increased void con-tent for the plain weave architecture. In the work by Ho-sur et al. [54], the only other study to consider cross-plylaminates, the compressive modulus was higher comparedto quasi-static values, but decreased with increasing strainrate. No physical explanation was offered by the authors forthis trend.

The influence of fibre architecture is unclear, as very fewstudies consider pre-preg laminates, as illustrated in Fig. 5.Considering only studies that analyse plain weave architec-tures [9, 10, 12, 27, 45, 47, 51–53, 55], the magnitude ofstrain rate sensitivity is difficult to discern due to large scat-ter in reported measurements (see Table 1). For example,Song et al. [47] and Akil et al. [52] report increases instiffness ranging from 75 % to 115 % (for strain rates near1,000 s−1), where as Shen et al. [51] report a mean increaseof 350 % at 1,200 s−1. The unrealistically high effect ofstrain rate on the modulus measured by Shen et al. [51] sug-gests that specimens are unlikely to be in stress equilibrium.Alternatively, a number of studies on plain weave compos-ites [9, 10, 12, 27] show negligible variations of the modulusover a similar range of strain rates.

It is not surprising that many studies using the SHPB re-port an increase in compressive elastic modulus. In the earlystages of a test, the reaction force on the input bar does notequal the force on the transmitter bar due to a significantcontribution from acceleration (see Eq. (1)). As a result, thestrains measured by the input bar are lower, and stress in thespecimen, computed using the force on the transmitter bar,is higher. This leads to a perceived stiffening of the material.This effect is likely to increase with increasing strain rate asa greater portion of the impact force is expended in acceler-ating the material. The degree to which inertia affects a testis dependent on several factors, contributing to the scatter inthe relative increases in stiffness across the literature.

In general, a review of the literature indicates that the com-pressive elastic modulus is matrix dominated and proba-bly increases with increasing strain rate. The magnitude ofthis sensitivity is uncertain due to high scatter in the litera-ture.

10−2 100 102 104

Strain rate [s−1]

-100

0

100

200

300

400

500




Figure 5: Summary of relative strain rate sensitivity for compressive mod-ulus from the literature. ‘PP’ and ‘W’ denote pre-preg and plain weavereinforcement, respectively. Red symbol outline denotes that values arequoted with respect to modulus at lowest strain rate considered (1,275 s−1

for [12]). Error bars denote the range of reported sensitivity and not stan-dard deviation. Data taken from [4, 10, 12, 47, 50, 54].

4.1.2. Compressive strengthA summary of relative change in compressive strength asa function of strain rate is shown in Fig. 6. From Fig. 6it is clear that there is high variability associated with themagnitude of change in strength with increasing strain rate.The trend at intermediate strain rates appears much more de-fined, showing a near linear positive sensitivity. There is asmall group of studies that show good consistency at higherstrain rates, reporting a moderate and positive increase instrength for strain rates below 1,000 s−1 [4, 9, 50–52]. Re-ported increases vary between 6 % and 23 % for both CFRPand GFRP. The remaining studies report large relative in-creases in strength compared to quasi-static values: 33 %[45] (reaching a near asymptotic value at 700 s−1), 46 %[12], 56 % [53], 80 % (between 1,000 and 1,940 s−1) [55]and 180 % [27]. The large increase in strength at high strainrates reported by Woo et al. [55] (80 %) was attributed tohigh energy absorption by the kevlar fibres. The maximumstrain rate achievable by Woo et al. [55] was limited by lowpulse transmission (as low as 10 %) through the specimen.This creates higher signal-to-noise ratio for strain measure-ment on the transmission bar, which is used to infer stressin the specimen. Quasi-static values were also not providedfor comparison. In the study by Pankow et al. [27], thestress-strain response was highly non-linear and was heav-ily contaminated by dispersion. This introduces uncertaintywhen attempting to determine ultimate properties. In con-trast to these results, Gerlach et al. [10] reported that fail-ure strength remains approximately constant with increasingstrain rate (quoted up to 6,000 s−1).

A small number of studies report mixed trends for strengthat high strain rates [4, 47, 54]. Hosur et al. [54] reporteda positive sensitivity to strain rate, but peak stresses thatare below quasi-static values. The specimens were loadedto failure under quasi-static conditions; however, at 82 s−1

and 164 s−1 the compressive input pulse was not strongenough to damage the specimens. Therefore, comparisons

6

made by the authors between peak stress at these strain ratesand quasi-static strength are not equivalent. Therefore, onlymeasurements collected at 817 s−1 can be used to assess theeffect of strain rate on compressive strength. From this case,strain rate causes a decrease in strength by 37 %. The au-thors attributed this to a progressive change in failure mech-anism from splitting and crushing at 163 s−1 to crushingand shearing at 817 s−1. The instability of compressiveloading tends to cause the specimen to fail in shear accord-ing to the strength of the matrix. Therefore, the change infailure mode is unlikely to be an intrinsic property of thematerial and more a result of the experimental setup (struc-tural behaviour). Song et al. [47] reported lower strengthsat strain rates up to 800 s−1 compared to quasi-static val-ues. At higher strain rates (> 1,000 s−1), the dynamicstrength exceeds the quasi-static one. The authors offer noexplanation for this behaviour. Similar to the compressionmodulus, Yokoyama & Nakai [4] found that compressivestrength was sensitive to reinforcement architecture. Thewoven glass-epoxy laminate exhibited a positive strain ratesensitivity, whereas the carbon/epoxy cross-ply pre-preg andplain weave laminates had a negative sensitivity. This wasattributed to the properties of the fibres, however, the car-bon/epoxy laminates had 15-20% higher fibre volume frac-tions. The potential dependency on reinforcement architec-ture (i.e: pre-preg., weave, etc.) is difficult to ascertain sincethe majority of studies focus on one type of reinforcementand have large scatter.

Other factors contributing to scatter include specimen ge-ometry and uncertainty associated with quasi-static values.All studies in the literature use cubic or cylindrical speci-mens. A study by Tagarielli et al. [56] showed that thecompressive strength and strain is highly sensitive to speci-men geometry. For the same contact surface area, cylindri-cal specimens were found to fail at lower stress and straincompared to cubic specimens. As the volume of the cylin-drical specimens was larger, this may indicate a volume ef-fect. In any case, there appears to be a sensitivity to geome-try and/or volume, which differs between studies in the liter-ature. Another source of difficulty for comparing studies isthat some work do not report quasi-static values at the samestrain rates. Considering relative changes in strength overthe high strain rate tests only, the values range between -5 %and +30 % compared to the range of -40 % to +40 %, whencompared against quasi-static values, as shown in Fig. 6.This does not necessarily imply better accuracy, and insteadsuggests that high strain rate tests are reasonably repeatableunder different conditions.

Compressive strength is heavily dominated by structuralfailure due to the inherent instability of the loading condi-tion. Specimens will tend to fail in shear, which is deter-mined by the strength of the resin. Some authors reporta change in failure mode, which is attributed to strain ratesensitivity [27, 50, 51]. This highlights the challenge asso-ciated with measuring compressive strength and is likely astrong contributor to scatter in the literature. The intrinsicinstability of the test makes the measured strength highly

10−2 100 102 104

Strain rate [s−1]

-50

0

50

100




Figure 6: Summary of relative strain rate sensitivity for compressivestrength from the literature. ‘PP’ and ‘W’ denote pre-preg and plain weavereinforcement, respectively. Red symbol outline denotes that values arequoted with respect to strength at lowest strain rate considered (1,275 s−1

for [12]). Error bars denote the range of reported sensitivity and not stan-dard deviation. Data taken from [4, 9, 10, 12, 27, 45, 47, 50–55].

sensitive to variations in manufacturing, fibre volume frac-tion, defects, void content, specimen geometry, specimenpreparation (flat contact surfaces) and alignment.

In summary, the literature suggests that there is likely a pos-itive sensitivity of compression strength to strain rate but themagnitude is uncertain. The sensitivity to fibre material andarchitecture is also difficult to determine as a consequenceof limited studies and high scatter.

4.1.3. Ultimate compressive strain

As with strength and stiffness, the influence of strain rateon failure strain is uncertain. Many authors report a slightdecrease (less than 14 %) or negligible influence of strainrate on failure strains as shown in Fig. 7 [4, 9, 27, 50, 52,53]. Song et al. [47] reported a negative sensitivity, butone that is much stronger than reported by most (-62 %).Pankow et al. [27], Shah Khan et al. [50] and Gama etal. [45] reported a negligible sensitivity to strain rate. Inthe study by Shah Khan et al. [50], only strain rates up to10 s−1 were considered. The results from Gama et al. [45]and Pankow et al. [27] illustrate the effects of dispersion.Both studies show oscillations in the initial portion of thestress-strain curve. Further, strain measurements with 2DDIC by Pankow et al. [27] showed significant heterogeneitythroughout the entire test. This was attributed to the coarsetextile architecture and local variations in wave speed withinthe material. However, the reliability of this conclusion isquestionable due to the poor spatial and temporal resolutionof the measurements.

The studies mentioned above report an opposite effect ofstrain rate to the positive sensitivity reported by Gerlachet al. [46] for an RTM-6 resin tested without reinforce-ment. A positive sensitivity was also established by Naiket al. [12] (+34 % between 1,275 s−1 and 1,503 s−1) andGama et al. [45] (up to +108 % at 1,125 s−1). The notablyhigher sensitivity from Gama et al. [45] is likely unreliable

7

CFRP - PPCFRP - WGFRP - WHYBRID - W3D - W


1














1















―9―

10−2 100 102 104

Strain rate [s−1]

-100

-50

0

50

100

150


] CFRP - PPCFRP - WGFRP - WHYBRID - W

Compression: Ultimate Strain

Figure 7: Summary of relative strain rate sensitivity for ultimate com-pressive strain from the literature. ‘PP’ and ‘W’ denote pre-preg andplain weave reinforcement, respectively. Red symbol outline denotesthat values are quoted with respect to strain at lowest strain rate consid-ered (1,275 s−1 for [12] and 1,007 s−1 for [55]). Error bars denote therange of reported sensitivity and not standard deviation. Data taken from[4, 9, 12, 27, 45, 47, 50–55].

due to significant contamination from dispersion. However,the magnitude of this sensitivity is similar to that reportedby Kapoor et al. [57] for a Kevlar 29/polypropylene (PP)2D woven composite (+134 % up to 4,300 s−1). A largermagnitude of sensitivity is to be expected for the through-thickness behaviour that is dominated by a ductile thermo-plastic matrix due to the stronger molecule mobility. Hosuret al. [54] found that failure strains increased with increas-ing strain rate, but were lower than quasi-static values. Asdiscussed in Section 4.1.2, this was attributed to a change infailure mode. Further, the strain rate sensitivity cannot beassessed for intermediate strain rates in that study since thespecimens did not fail. Song et al. [47] reported a decreasein ultimate strain between 500 s−1 and 800 s−1, followed byan increase at strain rates above 1,000 s−1. No explanationwas provided by the authors for this behaviour.

In general, the effect of strain rate on ultimate strains hasyet to be established. A number of studies reveal that the ef-fects of dispersion may still have significant influence on themeasurement of ultimate properties, which may contributeto the high levels of disparity of conclusions reported withinthe literature.

4.2. Strain rate effects on tensile propertiesComparatively fewer studies are available on the ten-sile strain rate dependency of composites in the through-thickness direction. This is because testing in tension ismore complicated than it is in compression. As describedin Section 2, additional challenges are introduced with spec-imen gripping, alignment and sensitivity to stress concentra-tions. Studies on resin strength in tension are also very lim-ited and the majority of available studies are of little benefitsince tensile specimens loaded with a SHPB commonly failoutside of the gauge region and thus have high scatter [46].All of these issues tend to impose additional restrictions onthe attainable strain rates using a tensile SHPB.

4.2.1. Tensile elastic modulusVery few studies have reported measurements of high strainrate elastic modulus [6, 9, 35, 46, 58, 59]. A summary offindings from the literature is provided in Fig. 8. Lifshitzand Leber [58] used a tensile SHPB to test carbon/epoxypre-preg and glass/epoxy woven composites. They reporteda greater increase in modulus for the pre-preg (+40%) com-pared to the woven composite (+18 %) for strain rates upto 195 s−1. Similar trends were reported by Medina andHarding [59] at strain rates up to 950 s−1 (+31 % for car-bon/epoxy pre-preg, -13 % for glass/epoxy weave). At suchhigh strain rates, it is likely that inertia has significant in-fluence on the apparent modulus. Dispersion may also actto mask the true mechanical response. This is shown inlongitudinal and transverse strain measurements within thespecimen, which exhibit oscillations throughout the dura-tion of the test (Fig. 3 in [59]). Comparison of carbon andglass epoxy weaves show that the tensile modulus appearsto be insensitive to fibre material. Nakai and Yokoyama[6, 35] noted a substantial increase in the ‘apparent’ mod-ulus, which was thought to be a result of the viscoelasticmodulus of the resin. This explanation is in agreement withstudies on the tensile properties of epoxy resins, which showa marked increase in apparent modulus at high strain rates[46].

Hufenbach et al. [60] used direct tensile loading in a two-bar SHPB configuration to test two glass/polypropylene wo-ven composites. A very large sensitivity to strain rate (up to+500 %) and considerable scatter was observed. The largescatter led to the conclusion that the SHPB technique wasunsuitable for studying coarse reinforcement architectures[60]. Hufenbach et al. [60] also comment on the influenceof manufacturing on the measured tensile modulus. Com-paction levels were reported to be much higher for L-shapedbeam specimens compared to the dog bone specimens usedwith the SHPB. This resulted in a much higher modulus forthe L-shaped beams.

In summary, the tensile modulus is a parameter that isscarcely investigated in the literature. There is some indi-cation of a positive sensitivity to strain rate but high scatterand the lack of studies makes this difficult to say with anycertainty.

4.2.2. Tensile strengthThe majority of studies which focus on tensile strengthutilise some form of a tensile SHPB, with strain rates gen-erally lower than 400 s−1 [6, 18, 19, 35, 58, 60, 61]. Asummary of relative strain rate sensitivity reported in the lit-erature is provided in Fig. 9. While most studies report anincrease in strength at high strain rates, the magnitude is un-clear due to high inter and intra study scatter. Some reportmoderate increases in strength of around 30 % comparedto quasi-static values [58, 59], while others report muchmore significant increases of up to several hundred percent[6, 35, 61]. In the case of Naik et al. [61], it appears thatthe reaction forces on the specimen are not equal for muchof the test (not in quasi-static stress equilibrium). This is

8

10−2 100 102 104

Strain rate [s−1]

-200

0

200

400

600

800


] CFRP - PPCFRP - WGFRP - W

Tension: Elastic Modulus

Figure 8: Summary of relative strain rate sensitivity for tensile modulusfrom the literature. ‘PP’ and ‘W’ denote pre-preg and plain weave rein-forcement, respectively. Error bars denote the range of reported sensitivityand not standard deviation. Data taken from [58–60].

difficult to confirm due to poor sampling of strain gauge sig-nals from the incident and transmitter bars. In the studies byNakai and Yokoyama [6, 35], where much lower strain ratesare considered, it appears that quasi-static stress equilibriumis obtained. Those studies report large increases in strength,which is expected for a matrix-dominated property based onstudies of an unreinforced epoxy resin [46].

Studies by Gerlach et al. [10] and Govender et al. [9]report higher strain rates up to 11,000 s−1 and 1,800 s−1,respectively. In the case of Gerlach et al. [10], tensileloading was induced using a customised fixture to load anoverlapping joint, or ‘cross’ specimen, using a compressiveSHPB. In that study, it is unclear how strain rate was defined,or how the effects of the custom loading fixture were ac-counted for. Govender et al. [9] used a spall test configura-tion to measure the tensile failure strength of a woven glassfibre-vinyl ester composite. Pulse time-shifting was em-ployed to estimate forces in the specimen at failure. This ap-proach removes the requirement for quasi-static stress equi-librium, allowing much higher strain rates to be achieved.However, the approach requires corrections for dispersionand the assumption of one-dimensional wave propagationthrough the bar and specimen. The failure location wasdetermined post-mortem with the strength estimated usingthe maximum computed stress seen by that position. Somefailed specimens exhibited substantial residual strength af-ter a crack had initiated. Failure surfaces showed signs offibre bridging, which suggests that the interlaminar failureis not purely brittle [9]. The results from this study couldnot be used to assess the effect of strain rate as only onestrain rate was considered and no quasi-static values werereported for comparison. Quasi-static testing was unsuc-cessful due to consistent failure within the grips. Instead, theauthors compare strength to the manufacturer’s quoted resinstrength. While the spall test arrangement appears promis-ing for higher strain rate characterisation, more informationmust be collected during the test in order to remove the lim-iting assumptions of the SHPB that remain.

10−2 100 102 104

Strain rate [s−1]

-100

0

100

200

300

400


] CFRP - PPGFRP - PPCFRP - WGFRP - W3D - W

Tension: Strength

Figure 9: Summary of relative strain rate sensitivity for tensile strengthfrom the literature. ‘PP’ and ‘W’ denote pre-preg and plain weave rein-forcement, respectively. Error bars denote the range of reported sensitivityand not standard deviation. Data taken from [6, 9, 10, 18, 19, 35, 58–61].For reference [9] (shaded symbols) values are reported relative to the matrixproperties.

The scatter in reported strengths have been attributed to anumber of issues associated with tensile testing. Machin-ing defects prevented Lifshitz and Leber [58] from obtain-ing reliable strength measurements on their carbon/epoxyspecimens. For tensile testing in the through-thickness di-rection, machining defects are particularly problematic ascracks can easily propagate between plies. Specimen ge-ometry was shown to have a significant influence on thedynamic response. Using full-field measurements, Gilat etal. [22] showed that less than half of the gauge region on awaisted specimen was subjected to uniform stress. This re-sults in overestimation of strain and strain rate using SHPBtheory. Lifshitz and Leber [58] also had issues obtainingconsistent bonds between specimen halves (machined in twopieces). This is also expected to have an effect on those stud-ies where the specimens are directly bonded to the input bar[9, 58, 61]. Others have chosen to introduce the load bybonding the specimen onto threaded inserts [10, 35, 59, 60].Slight misalignments between the specimen and loadingaxis will introduce bending stresses in the specimen, re-sulting in considerable scatter in measured strength values.Similar issues have been reported for high strain rate tensiletesting of epoxy resins [41, 46]. Variability in the techniqueused to introduce the load contributes to scatter and is a re-sult of the lack of test standards for high strain rates.

In summary, scatter across the literature is too large to con-clude that there is any influence of strain rate on tensilestrength.

4.2.3. Ultimate tensile strain

Similar to tensile strength, it is difficult to obtain reliablestrain measurements with existing techniques. In studiesperformed by Gerlach et al., the gauge region dimensions[19], or customised loading fixtures [10] prevented mea-surements of strain to be made. Some studies report val-ues of ultimate strain at high strain rates, but do not supply

9

CFRP - PPCFRP - WGFRP - WHYBRID - W


1














1














1














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―10―

10−2 100 102 104

Strain rate [s−1]

-100

-50

0

50

100

150


] CFRP - PPCFRP - WGFRP - WHYBRID - W


Figure 7: Summary of relative strain rate sensitivity for ultimate com-pressive strain from the literature. ‘PP’ and ‘W’ denote pre-preg andplain weave reinforcement, respectively. Red symbol outline denotesthat values are quoted with respect to strain at lowest strain rate consid-ered (1,275 s−1 for [12] and 1,007 s−1 for [55]). Error bars denote therange of reported sensitivity and not standard deviation. Data taken from[4, 9, 12, 27, 45, 47, 50–55].

due to significant contamination from dispersion. However,the magnitude of this sensitivity is similar to that reportedby Kapoor et al. [57] for a Kevlar 29/polypropylene (PP)2D woven composite (+134 % up to 4,300 s−1). A largermagnitude of sensitivity is to be expected for the through-thickness behaviour that is dominated by a ductile thermo-plastic matrix due to the stronger molecule mobility. Hosuret al. [54] found that failure strains increased with increas-ing strain rate, but were lower than quasi-static values. Asdiscussed in Section 4.1.2, this was attributed to a change infailure mode. Further, the strain rate sensitivity cannot beassessed for intermediate strain rates in that study since thespecimens did not fail. Song et al. [47] reported a decreasein ultimate strain between 500 s−1 and 800 s−1, followed byan increase at strain rates above 1,000 s−1. No explanationwas provided by the authors for this behaviour.

In general, the effect of strain rate on ultimate strains hasyet to be established. A number of studies reveal that the ef-fects of dispersion may still have significant influence on themeasurement of ultimate properties, which may contributeto the high levels of disparity of conclusions reported withinthe literature.

4.2. Strain rate effects on tensile propertiesComparatively fewer studies are available on the ten-sile strain rate dependency of composites in the through-thickness direction. This is because testing in tension ismore complicated than it is in compression. As describedin Section 2, additional challenges are introduced with spec-imen gripping, alignment and sensitivity to stress concentra-tions. Studies on resin strength in tension are also very lim-ited and the majority of available studies are of little benefitsince tensile specimens loaded with a SHPB commonly failoutside of the gauge region and thus have high scatter [46].All of these issues tend to impose additional restrictions onthe attainable strain rates using a tensile SHPB.

4.2.1. Tensile elastic modulusVery few studies have reported measurements of high strainrate elastic modulus [6, 9, 35, 46, 58, 59]. A summary offindings from the literature is provided in Fig. 8. Lifshitzand Leber [58] used a tensile SHPB to test carbon/epoxypre-preg and glass/epoxy woven composites. They reporteda greater increase in modulus for the pre-preg (+40%) com-pared to the woven composite (+18 %) for strain rates upto 195 s−1. Similar trends were reported by Medina andHarding [59] at strain rates up to 950 s−1 (+31 % for car-bon/epoxy pre-preg, -13 % for glass/epoxy weave). At suchhigh strain rates, it is likely that inertia has significant in-fluence on the apparent modulus. Dispersion may also actto mask the true mechanical response. This is shown inlongitudinal and transverse strain measurements within thespecimen, which exhibit oscillations throughout the dura-tion of the test (Fig. 3 in [59]). Comparison of carbon andglass epoxy weaves show that the tensile modulus appearsto be insensitive to fibre material. Nakai and Yokoyama[6, 35] noted a substantial increase in the ‘apparent’ mod-ulus, which was thought to be a result of the viscoelasticmodulus of the resin. This explanation is in agreement withstudies on the tensile properties of epoxy resins, which showa marked increase in apparent modulus at high strain rates[46].

Hufenbach et al. [60] used direct tensile loading in a two-bar SHPB configuration to test two glass/polypropylene wo-ven composites. A very large sensitivity to strain rate (up to+500 %) and considerable scatter was observed. The largescatter led to the conclusion that the SHPB technique wasunsuitable for studying coarse reinforcement architectures[60]. Hufenbach et al. [60] also comment on the influenceof manufacturing on the measured tensile modulus. Com-paction levels were reported to be much higher for L-shapedbeam specimens compared to the dog bone specimens usedwith the SHPB. This resulted in a much higher modulus forthe L-shaped beams.

In summary, the tensile modulus is a parameter that isscarcely investigated in the literature. There is some indi-cation of a positive sensitivity to strain rate but high scatterand the lack of studies makes this difficult to say with anycertainty.

4.2.2. Tensile strengthThe majority of studies which focus on tensile strengthutilise some form of a tensile SHPB, with strain rates gen-erally lower than 400 s−1 [6, 18, 19, 35, 58, 60, 61]. Asummary of relative strain rate sensitivity reported in the lit-erature is provided in Fig. 9. While most studies report anincrease in strength at high strain rates, the magnitude is un-clear due to high inter and intra study scatter. Some reportmoderate increases in strength of around 30 % comparedto quasi-static values [58, 59], while others report muchmore significant increases of up to several hundred percent[6, 35, 61]. In the case of Naik et al. [61], it appears thatthe reaction forces on the specimen are not equal for muchof the test (not in quasi-static stress equilibrium). This is

8

10−2 100 102 104

Strain rate [s−1]

-200

0

200

400

600

800




Figure 8: Summary of relative strain rate sensitivity for tensile modulusfrom the literature. ‘PP’ and ‘W’ denote pre-preg and plain weave rein-forcement, respectively. Error bars denote the range of reported sensitivityand not standard deviation. Data taken from [58–60].

difficult to confirm due to poor sampling of strain gauge sig-nals from the incident and transmitter bars. In the studies byNakai and Yokoyama [6, 35], where much lower strain ratesare considered, it appears that quasi-static stress equilibriumis obtained. Those studies report large increases in strength,which is expected for a matrix-dominated property based onstudies of an unreinforced epoxy resin [46].

Studies by Gerlach et al. [10] and Govender et al. [9]report higher strain rates up to 11,000 s−1 and 1,800 s−1,respectively. In the case of Gerlach et al. [10], tensileloading was induced using a customised fixture to load anoverlapping joint, or ‘cross’ specimen, using a compressiveSHPB. In that study, it is unclear how strain rate was defined,or how the effects of the custom loading fixture were ac-counted for. Govender et al. [9] used a spall test configura-tion to measure the tensile failure strength of a woven glassfibre-vinyl ester composite. Pulse time-shifting was em-ployed to estimate forces in the specimen at failure. This ap-proach removes the requirement for quasi-static stress equi-librium, allowing much higher strain rates to be achieved.However, the approach requires corrections for dispersionand the assumption of one-dimensional wave propagationthrough the bar and specimen. The failure location wasdetermined post-mortem with the strength estimated usingthe maximum computed stress seen by that position. Somefailed specimens exhibited substantial residual strength af-ter a crack had initiated. Failure surfaces showed signs offibre bridging, which suggests that the interlaminar failureis not purely brittle [9]. The results from this study couldnot be used to assess the effect of strain rate as only onestrain rate was considered and no quasi-static values werereported for comparison. Quasi-static testing was unsuc-cessful due to consistent failure within the grips. Instead, theauthors compare strength to the manufacturer’s quoted resinstrength. While the spall test arrangement appears promis-ing for higher strain rate characterisation, more informationmust be collected during the test in order to remove the lim-iting assumptions of the SHPB that remain.

10−2 100 102 104

Strain rate [s−1]

-100

0

100

200

300

400


] CFRP - PPGFRP - PPCFRP - WGFRP - W3D - W

Tension: Strength

Figure 9: Summary of relative strain rate sensitivity for tensile strengthfrom the literature. ‘PP’ and ‘W’ denote pre-preg and plain weave rein-forcement, respectively. Error bars denote the range of reported sensitivityand not standard deviation. Data taken from [6, 9, 10, 18, 19, 35, 58–61].For reference [9] (shaded symbols) values are reported relative to the matrixproperties.

The scatter in reported strengths have been attributed to anumber of issues associated with tensile testing. Machin-ing defects prevented Lifshitz and Leber [58] from obtain-ing reliable strength measurements on their carbon/epoxyspecimens. For tensile testing in the through-thickness di-rection, machining defects are particularly problematic ascracks can easily propagate between plies. Specimen ge-ometry was shown to have a significant influence on thedynamic response. Using full-field measurements, Gilat etal. [22] showed that less than half of the gauge region on awaisted specimen was subjected to uniform stress. This re-sults in overestimation of strain and strain rate using SHPBtheory. Lifshitz and Leber [58] also had issues obtainingconsistent bonds between specimen halves (machined in twopieces). This is also expected to have an effect on those stud-ies where the specimens are directly bonded to the input bar[9, 58, 61]. Others have chosen to introduce the load bybonding the specimen onto threaded inserts [10, 35, 59, 60].Slight misalignments between the specimen and loadingaxis will introduce bending stresses in the specimen, re-sulting in considerable scatter in measured strength values.Similar issues have been reported for high strain rate tensiletesting of epoxy resins [41, 46]. Variability in the techniqueused to introduce the load contributes to scatter and is a re-sult of the lack of test standards for high strain rates.

In summary, scatter across the literature is too large to con-clude that there is any influence of strain rate on tensilestrength.

4.2.3. Ultimate tensile strain

Similar to tensile strength, it is difficult to obtain reliablestrain measurements with existing techniques. In studiesperformed by Gerlach et al., the gauge region dimensions[19], or customised loading fixtures [10] prevented mea-surements of strain to be made. Some studies report val-ues of ultimate strain at high strain rates, but do not supply

9

CFRP - PPCFRP - WGFRP - W


CFRP - PPGFRP - PPCFRP - WGFRP - W3D - W

Tension: Strength

2

11 ページ目 Fig. 8 Summary of relative strain rate sensitivity for tensile modulus from the literature. ‘PP’ and ‘W’ denote pre-preg and plain weave reinforcement, respectively. Error bars denote the range of reported sensitivity and not standard deviation. Data taken from [58–60] Fig. 9 Summary of relative strain rate sensitivity for tensile strength from the literature. ‘PP’ and ‘W’ denote pre-preg and plain weave reinforcement, respectively. Error bars denote the range of reported sensitivity and not standard deviation. Data taken from [6, 9, 10, 18, 19, 35, 58–61]. For reference [9] (shaded symbols) values are reported relative to the matrix properties

4.2.3 Ultimate tensile strain 12 ページ目

4.3 Strain rate effects on interlaminar shear properties

4.3.1 Shear modulus Fig. 10 Summary of relative strain rate sensitivity for ultimate tensile strain from the literature. ‘PP’ and ‘W’ denote pre-preg and plain weave reinforcement, respectively. Error bars denote the range of reported sensitivity and not standard deviation. Data taken from [6, 35, 59, 60] 13 ページ目 Fig. 11 Summary of relative strain rate sensitivity for shear modulus strain from the literature. ‘PP’ and ‘W’ denote pre-preg and plain weave reinforcement, respectively. Orange and purple symbols denote testing in the 1-3 and 2-3 directions, respectively. White denotes that direction is not specified. Error bars denote the range of reported sensitivity and not standard deviation. Data taken from [5, 39, 40]

4.3.2 Shear strength

4.3.3 Ultimate shear strain 14 ページ目 Fig. 12 Summary of relative strain rate sensitivity for shear strength from the literature. ‘PP’ and ‘W’ denote pre-preg and plain weave reinforcement, respectively. Red symbol outline denotes that values are quoted with respect to strain at lowest strain rate considered (260 s–1 for [2], 0.04 s–1 for [21] and 300 s–1 for [62]). Orange and purple symbols denote testing in the 1-3 and 2-3 directions, respectively. White denotes that direction is not specified. Error bars denote the range of reported sensitivity and not standard deviation. Data taken from [2, 3, 5, 10, 21, 39, 40, 60, 62, 64, 65] Fig. 13 Summary of relative strain rate sensitivity for ultimate shear strain from the literature. ‘PP’ and ‘W’ denote pre-preg and plain weave reinforcement, respectively. Red symbol outline denotes that values are quoted with respect to strain at lowest strain rate considered (496 s–1 and 576 s–1 for [5], and 0.04 s–1 for [21]). Orange and purple symbols denote testing in the 1-3 and 2-3 directions, respectively. White denotes that direction is not specified. Error bars denote the range of reported sensitivity and not standard deviation. Data taken from [3, 5, 21, 40, 60]

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quasi-static values for comparison [58, 61]. In other studies,the focus was on obtaining measurements of strength andstiffness, and ultimate strains were not reported [9, 18, 52].Strain gauges have been used to measure strain directlyfrom the specimen [58, 59]. Medina and Harding [59] mea-sured a 22 % and 65 % increase in failure strain at 950 s−1

for carbon/epoxy pre-preg and woven composites, respec-tively. This study highlights two challenges with using straingauges. In their study, it was difficult to place the straingauge appropriately so that it was positioned on the failureplane. A similar challenge was reported by Liftshitz andLeber [58]. An additional issue experienced by Medina andHarding [59] was premature failure of the strain gauges. Theultimate strains measured by Medina and Harding [59] atsuch high strain rates (950 s−1) are likely to be contaminatedby inertia effects. Therefore, the trends reported by Medinaand Harding [59] are unlikely to be reliable representationsof the true effect of strain rate on ultimate strain.

There are a few studies that report failure strains based onSHPB theory [6, 35, 60], but the reported trends are incon-clusive. A summary of the failure strains presented in the lit-erature is shown in Fig. 10. Nakai and Yokoyama performedtwo studies on carbon/epoxy pre-preg composites [6, 35].They reported a general increase in failure strain for strainrates up to approximately 100 s−1. The reported magnitudeis unreliable due to the high scatter in their measurements(strain rate sensitivity ranges from -50 % to + 90 % withinscatter). Hufenbach et al. [60] reported that failure strainhas little sensitivity to strain rate between quasi-static andstrain rates up to 400 s−1.

In summary, obtaining reliable strain measurements at highstrain rates has proven to be a challenge. As a result, veryfew studies report ultimate strains. From those that attemptto measure ultimate strains, the influence of strain rate can-not be determined with certainty.

The limited available literature suggests there is much out-standing work to be done to develop testing procedures toyield reliable through-thickness tensile properties. Tensiletests are highly sensitive to gripping, alignment and stressconcentrations. This does not facilitate reliable measure-ment of material properties using existing techniques, whichrely on a number of assumptions about the material re-sponse. Further, not only is there significant scatter in themeasured high strain rate properties, but there is high scat-ter in the quasi-static measurements to which they are com-pared. A potential alternative to strain gauges is opticalfull-field measurement techniques. Full-field measurementsprovide far more information about the specimen response,which is required to alleviate assumptions and advance highstrain rate tensile characterisation.

4.3. Strain rate effects on interlaminar shear proper-ties

4.3.1. Shear modulus

The combined stress states induced in many existing sheartests complicates the matter of obtaining a true estimate for

10−2 100 102 104

Strain rate [s−1]

-100

0

100

200

300

400

500

600

700



Tension: Ultimate Strain

Figure 10: Summary of relative strain rate sensitivity for ultimate tensilestrain from the literature. ‘PP’ and ‘W’ denote pre-preg and plain weavereinforcement, respectively. Error bars denote the range of reported sensi-tivity and not standard deviation. Data taken from [6, 35, 59, 60].

the shear modulus. Therefore, far fewer studies attemptto extract the interlaminar shear modulus, compared to theinterlaminar shear strength (ILSS). A summary of relativestrain rate sensitivity for shear modulus is presented in Fig.11.

Bouette et al. [39] reported no appreciable variation in shearmodulus measured using double and single lap joints. Themodulus was estimated using failure stress and strain assum-ing linear elastic behaviour to failure. However, strain gaugemeasurements by Bouette et al. [39] reveal a non-linear be-haviour near failure, and would act to reduce the ‘apparentmodulus’. Hallett et al. [40] also used single lap specimensand reported an average decrease in stiffness with increasingstrain rate. The magnitude of sensitivity is difficult to deter-mine as their measurements had significant variance. Theauthors suggested that normal stresses at the notches wereresponsible for the scatter. Using thin-walled tubular spec-imens, Naik et al. [5] reported a net increase in apparentshear modulus (+33 % for glass/epoxy and +41 % for car-bon epoxy) up to 1,000 s−1. Similar to the study by Bouetteet al. [39], the shear response was found to be non-linearby Naik et al. [5]. This makes it difficult to obtain an es-timate of the true shear modulus. Naik et al. [5] providedan estimate on the lower bound of shear modulus by fittinga line between the origin and a point on the curve near peakstress. Naik et al. [5] also claimed that the values obtainedwith the tubular specimens are more representative of thetrue behaviour since notch effects are eliminated. Interest-ingly, this did not seem to have a significant effect on thelevel of scatter in their measurements. Scatter in propertiesmeasured using tubular specimens may be attributed to mi-cro cracks/damage induced from machining [5], specimengeometry (fillet radius, wall thickness) [5, 62], and layuporientation [62].

In summary, the effect of strain rate on shear modulus is notclearly understood. This is primarily due to mixed stressstates in the specimen leading to biased estimates of shearmodulus, as well as inherent limitations of the Hopkinson

10

10−2 100 102 104

Strain rate [s−1]

-40

-20

0

20

40

60

80



Shear: Elastic Modulus

Figure 11: Summary of relative strain rate sensitivity for shear modulusstrain from the literature. ‘PP’ and ‘W’ denote pre-preg and plain weavereinforcement, respectively. Orange and purple symbols denote testing inthe 1-3 and 2-3 directions, respectively. White denotes that direction isnot specified. Error bars denote the range of reported sensitivity and notstandard deviation. Data taken from [5, 39, 40].

bar analysis as for the tensile modulus.

4.3.2. Shear strength

The through-thickness response of composites is partic-ularly sensitive to combined states of tension and shear.When tensile stresses are present, the interlaminar shearstrength has shown to decrease significantly [3, 63]. It isvery difficult to achieve the desired state of pure shear inquasi-static and high strain rate testing and therefore, moststudies are limited to reporting ‘apparent shear strength’ [2,7, 16]. The influence of strain rate on shear strength, basedon studies from the literature, is illustrated in Fig. 12.

Single and double lap specimens were initially the most pop-ular choices for high strain rate shear testing since they couldbe tested using a compressive SHPB. Bouette et al. [39],Harding and Li [64] and Harding and Dong [3] used doublelap specimens to extract the ILSS. These studies found thatlap joint specimens are unreliable since failure initiates nearthe ends of the overlap under a state of combined shear andnormal stresses. The same was found for single-lap speci-mens [3, 39, 40]. The work with single lap specimens showsthat the amplitude of stress concentration can be reduced ifthe overlap is kept small [39, 40]. While gauge region ge-ometry can be altered to reduce the combined stress state itcannot be eliminated. This is a likely contributor to the highlevels of experimental scatter on reported shear modulus andfailure stresses.

Other approaches to measuring the interlaminar shear prop-erties include the use of the double V-notch shear test(Iosipescu) [21], the out-of-plane off-axis tests [2], the dou-ble notched shear test in dynamic compression [65], shortbeam shear tests [65], and thin-walled tubular specimensloaded using a torsional SHPB [5, 62]. Yokoyama and Nakai[65] found that strengths obtained with the double-notchedshear specimens compared well with the short-beam sheartests. Further, measured ILSS values agree well with sim-

ulated stress levels in the centre of the specimens. Thislead them to conclude that the influences of the stress con-centrations from the notches were negligible. Further, thecompressive normal stresses at the notches acted to sup-press delamination. The result was much lower levels ofscatter compared to previous studies using a single or dou-ble lap specimen. Hufenbach et al. [21] used a lightweightIosipescu fixture for testing at intermediate strain rates up toapproximately 60 s−1 [21]. This appeared to work reason-ably well for testing in the 2-3 plane, but yielded unaccept-able levels of scatter in strength measurements for the 1-3plane and thus, the strain rate sensitivity could not be deter-mined. This was attributed to low stress and strain levels andmeasurement resolution of the load cell. Naik et al. [5] com-pared thin-walled tubular specimens, loaded with a torsionalSHPB, to single-lap specimens loaded in dynamic compres-sion using a SHPB. Tubular specimens were selected for de-tailed analysis as they created a purer state of shear stress.The level of scatter from single lap specimens was similarbut produced slightly lower strength values. This is likely aresult of the combined tension-shear stress state. The oppo-site was found by Gowtham et al. [62] who reported lowerstrengths measured using a torsional SHPB compared to asingle lap shear joint. This was attributed to stress concen-trations from the weave reinforcement in the failure planeof the tubular specimens. The weave reinforcement wasshown to create variations in stiffness and stress along theradial and circumferential directions, acting as stress con-centrations. This violates one of the primary assumptionsthat stress is uniform throughout the thickness.

A common characteristic to many of these studies is thehigh levels of scatter, which prohibits definitive claims frombeing made about the strain rate sensitivity [10, 21, 40].Qualitative trends may still be useful, and there appears tobe more of a general agreement between studies in thesetrends. Many studies report that the interlaminar shearstrength increases moderately with increasing strain rate[2, 3, 5, 62, 65]. The level of strain rate sensitivity hasyet to be determined reliably, with reports of strength in-creases ranging from 15% [62] to 200% [62]. There isalso a collection of studies that report a constant strength[39, 60, 65].

In summary, there is some indication of a positive influenceof strain rate on interlaminar shear strength. However, thepresence of combined tension and shear stresses, and stressconcentrations have prevented reliable characterisation ofthe high strain rate behaviour.

4.3.3. Ultimate shear strain

In the majority of cases, it appears that strain was eithernot reliably measured [21], or the focus of the study wason shear strength and thus, strains at failure were not re-ported [2, 62, 65]. Some fixtures and specimen geometriesmake shear strain measurements challenging or impossible[10]. Of the remaining studies, there is very little agreementas to the effect of strain rate on failure strain. The variationin strain rate sensitivity across the literature is presented in

11



2








2








2








2








2









―12―

quasi-static values for comparison [58, 61]. In other studies,the focus was on obtaining measurements of strength andstiffness, and ultimate strains were not reported [9, 18, 52].Strain gauges have been used to measure strain directlyfrom the specimen [58, 59]. Medina and Harding [59] mea-sured a 22 % and 65 % increase in failure strain at 950 s−1

for carbon/epoxy pre-preg and woven composites, respec-tively. This study highlights two challenges with using straingauges. In their study, it was difficult to place the straingauge appropriately so that it was positioned on the failureplane. A similar challenge was reported by Liftshitz andLeber [58]. An additional issue experienced by Medina andHarding [59] was premature failure of the strain gauges. Theultimate strains measured by Medina and Harding [59] atsuch high strain rates (950 s−1) are likely to be contaminatedby inertia effects. Therefore, the trends reported by Medinaand Harding [59] are unlikely to be reliable representationsof the true effect of strain rate on ultimate strain.

There are a few studies that report failure strains based onSHPB theory [6, 35, 60], but the reported trends are incon-clusive. A summary of the failure strains presented in the lit-erature is shown in Fig. 10. Nakai and Yokoyama performedtwo studies on carbon/epoxy pre-preg composites [6, 35].They reported a general increase in failure strain for strainrates up to approximately 100 s−1. The reported magnitudeis unreliable due to the high scatter in their measurements(strain rate sensitivity ranges from -50 % to + 90 % withinscatter). Hufenbach et al. [60] reported that failure strainhas little sensitivity to strain rate between quasi-static andstrain rates up to 400 s−1.

In summary, obtaining reliable strain measurements at highstrain rates has proven to be a challenge. As a result, veryfew studies report ultimate strains. From those that attemptto measure ultimate strains, the influence of strain rate can-not be determined with certainty.

The limited available literature suggests there is much out-standing work to be done to develop testing procedures toyield reliable through-thickness tensile properties. Tensiletests are highly sensitive to gripping, alignment and stressconcentrations. This does not facilitate reliable measure-ment of material properties using existing techniques, whichrely on a number of assumptions about the material re-sponse. Further, not only is there significant scatter in themeasured high strain rate properties, but there is high scat-ter in the quasi-static measurements to which they are com-pared. A potential alternative to strain gauges is opticalfull-field measurement techniques. Full-field measurementsprovide far more information about the specimen response,which is required to alleviate assumptions and advance highstrain rate tensile characterisation.

4.3. Strain rate effects on interlaminar shear proper-ties

4.3.1. Shear modulus

The combined stress states induced in many existing sheartests complicates the matter of obtaining a true estimate for

10−2 100 102 104

Strain rate [s−1]

-100

0

100

200

300

400

500

600

700




Figure 10: Summary of relative strain rate sensitivity for ultimate tensilestrain from the literature. ‘PP’ and ‘W’ denote pre-preg and plain weavereinforcement, respectively. Error bars denote the range of reported sensi-tivity and not standard deviation. Data taken from [6, 35, 59, 60].

the shear modulus. Therefore, far fewer studies attemptto extract the interlaminar shear modulus, compared to theinterlaminar shear strength (ILSS). A summary of relativestrain rate sensitivity for shear modulus is presented in Fig.11.

Bouette et al. [39] reported no appreciable variation in shearmodulus measured using double and single lap joints. Themodulus was estimated using failure stress and strain assum-ing linear elastic behaviour to failure. However, strain gaugemeasurements by Bouette et al. [39] reveal a non-linear be-haviour near failure, and would act to reduce the ‘apparentmodulus’. Hallett et al. [40] also used single lap specimensand reported an average decrease in stiffness with increasingstrain rate. The magnitude of sensitivity is difficult to deter-mine as their measurements had significant variance. Theauthors suggested that normal stresses at the notches wereresponsible for the scatter. Using thin-walled tubular spec-imens, Naik et al. [5] reported a net increase in apparentshear modulus (+33 % for glass/epoxy and +41 % for car-bon epoxy) up to 1,000 s−1. Similar to the study by Bouetteet al. [39], the shear response was found to be non-linearby Naik et al. [5]. This makes it difficult to obtain an es-timate of the true shear modulus. Naik et al. [5] providedan estimate on the lower bound of shear modulus by fittinga line between the origin and a point on the curve near peakstress. Naik et al. [5] also claimed that the values obtainedwith the tubular specimens are more representative of thetrue behaviour since notch effects are eliminated. Interest-ingly, this did not seem to have a significant effect on thelevel of scatter in their measurements. Scatter in propertiesmeasured using tubular specimens may be attributed to mi-cro cracks/damage induced from machining [5], specimengeometry (fillet radius, wall thickness) [5, 62], and layuporientation [62].

In summary, the effect of strain rate on shear modulus is notclearly understood. This is primarily due to mixed stressstates in the specimen leading to biased estimates of shearmodulus, as well as inherent limitations of the Hopkinson

10

10−2 100 102 104

Strain rate [s−1]

-40

-20

0

20

40

60

80




Figure 11: Summary of relative strain rate sensitivity for shear modulusstrain from the literature. ‘PP’ and ‘W’ denote pre-preg and plain weavereinforcement, respectively. Orange and purple symbols denote testing inthe 1-3 and 2-3 directions, respectively. White denotes that direction isnot specified. Error bars denote the range of reported sensitivity and notstandard deviation. Data taken from [5, 39, 40].

bar analysis as for the tensile modulus.

4.3.2. Shear strength

The through-thickness response of composites is partic-ularly sensitive to combined states of tension and shear.When tensile stresses are present, the interlaminar shearstrength has shown to decrease significantly [3, 63]. It isvery difficult to achieve the desired state of pure shear inquasi-static and high strain rate testing and therefore, moststudies are limited to reporting ‘apparent shear strength’ [2,7, 16]. The influence of strain rate on shear strength, basedon studies from the literature, is illustrated in Fig. 12.

Single and double lap specimens were initially the most pop-ular choices for high strain rate shear testing since they couldbe tested using a compressive SHPB. Bouette et al. [39],Harding and Li [64] and Harding and Dong [3] used doublelap specimens to extract the ILSS. These studies found thatlap joint specimens are unreliable since failure initiates nearthe ends of the overlap under a state of combined shear andnormal stresses. The same was found for single-lap speci-mens [3, 39, 40]. The work with single lap specimens showsthat the amplitude of stress concentration can be reduced ifthe overlap is kept small [39, 40]. While gauge region ge-ometry can be altered to reduce the combined stress state itcannot be eliminated. This is a likely contributor to the highlevels of experimental scatter on reported shear modulus andfailure stresses.

Other approaches to measuring the interlaminar shear prop-erties include the use of the double V-notch shear test(Iosipescu) [21], the out-of-plane off-axis tests [2], the dou-ble notched shear test in dynamic compression [65], shortbeam shear tests [65], and thin-walled tubular specimensloaded using a torsional SHPB [5, 62]. Yokoyama and Nakai[65] found that strengths obtained with the double-notchedshear specimens compared well with the short-beam sheartests. Further, measured ILSS values agree well with sim-

ulated stress levels in the centre of the specimens. Thislead them to conclude that the influences of the stress con-centrations from the notches were negligible. Further, thecompressive normal stresses at the notches acted to sup-press delamination. The result was much lower levels ofscatter compared to previous studies using a single or dou-ble lap specimen. Hufenbach et al. [21] used a lightweightIosipescu fixture for testing at intermediate strain rates up toapproximately 60 s−1 [21]. This appeared to work reason-ably well for testing in the 2-3 plane, but yielded unaccept-able levels of scatter in strength measurements for the 1-3plane and thus, the strain rate sensitivity could not be deter-mined. This was attributed to low stress and strain levels andmeasurement resolution of the load cell. Naik et al. [5] com-pared thin-walled tubular specimens, loaded with a torsionalSHPB, to single-lap specimens loaded in dynamic compres-sion using a SHPB. Tubular specimens were selected for de-tailed analysis as they created a purer state of shear stress.The level of scatter from single lap specimens was similarbut produced slightly lower strength values. This is likely aresult of the combined tension-shear stress state. The oppo-site was found by Gowtham et al. [62] who reported lowerstrengths measured using a torsional SHPB compared to asingle lap shear joint. This was attributed to stress concen-trations from the weave reinforcement in the failure planeof the tubular specimens. The weave reinforcement wasshown to create variations in stiffness and stress along theradial and circumferential directions, acting as stress con-centrations. This violates one of the primary assumptionsthat stress is uniform throughout the thickness.

A common characteristic to many of these studies is thehigh levels of scatter, which prohibits definitive claims frombeing made about the strain rate sensitivity [10, 21, 40].Qualitative trends may still be useful, and there appears tobe more of a general agreement between studies in thesetrends. Many studies report that the interlaminar shearstrength increases moderately with increasing strain rate[2, 3, 5, 62, 65]. The level of strain rate sensitivity hasyet to be determined reliably, with reports of strength in-creases ranging from 15% [62] to 200% [62]. There isalso a collection of studies that report a constant strength[39, 60, 65].

In summary, there is some indication of a positive influenceof strain rate on interlaminar shear strength. However, thepresence of combined tension and shear stresses, and stressconcentrations have prevented reliable characterisation ofthe high strain rate behaviour.

4.3.3. Ultimate shear strain

In the majority of cases, it appears that strain was eithernot reliably measured [21], or the focus of the study wason shear strength and thus, strains at failure were not re-ported [2, 62, 65]. Some fixtures and specimen geometriesmake shear strain measurements challenging or impossible[10]. Of the remaining studies, there is very little agreementas to the effect of strain rate on failure strain. The variationin strain rate sensitivity across the literature is presented in

11



2








2








2









―13―

10−2 100 102 104

Strain rate [s−1]

-100

-50

0

50

100

150

200

250


]

CFRP - PPGFRP - PPCFRP - WGFRP - WHYBRID - P3D - W

Shear: Strength

Figure 12: Summary of relative strain rate sensitivity for shear strengthfrom the literature. ‘PP’ and ‘W’ denote pre-preg and plain weave rein-forcement, respectively. Red symbol outline denotes that values are quotedwith respect to strain at lowest strain rate considered (260 S−1 for [2], 0.04s−1 for [21] and 300 s−1 for [62]). Orange and purple symbols denote test-ing in the 1-3 and 2-3 directions, respectively. White denotes that directionis not specified. Error bars denote the range of reported sensitivity and notstandard deviation. Data taken from [2, 3, 5, 10, 21, 39, 40, 60, 62, 64, 65].

Fig. 13. Two studies by Bouette et al. [39] and Hufenbachet al. [60] report that shear strain at failure is independent ofstrain rate, up to 1,000 s−1 and 400 s−1, respectively. Thelack of sensitivity to strain rate may be a shortcoming of lapspecimens with failure being heavily influenced by normalstresses at the ends of the overlap, similar to Hallett et al.[40]. In contrast, Gillespie et al. [2] reported an increasein peak strain up to a strain rate of 582 s−1, followed bya reduction at higher strain rates. These higher strain ratesapproach the upper limit for equilibrium, set by the ‘R crite-rion’, and are likely contaminated by inertia effects. Hardingand Li [64] found a significant increase (approx. 250 %) infailure strains with impact speed. Unfortunately, the strainrates at failure were not reported. Naik et al. [5] measured a38 % increase in failure strain between strain rates of 576 -1,000 s−1, but did not provide quasi-static reference valuesfor comparison.

Much like the cases of shear modulus and shear strength,ultimate shear strains presented in the literature are heavilyinfluenced by mixed stress states and stress concentrations.As a result the current literature cannot be used to determinethe influence of strain rate on ultimate shear strain.

5. Advanced Testing Approaches Using High Speed,Full-Field Measurements

A review of the literature highlights several key limita-tions with existing test methods that hinder the advancementof material characterisation for composites in the through-thickness direction. The assumptions required for a SHPBtest are particularly restrictive to the maximum strain ratethat can be obtained. In compression, strain rates are lim-ited generally to less than 1,500 s−1, and to an even greaterextent in tension (typically less than 100 s−1). This is dueto the assumption that the specimen is subjected to a state ofuniform stress. This is not the case, especially in early stages

10−2 100 102 104

Strain rate [s−1]

-100

-50

0

50

100

150

200


]

CFRP - PPCFRP - WGFRP - W3D - W

Shear: Ultimate Strain

Figure 13: Summary of relative strain rate sensitivity for ultimate shearstrain from the literature. ‘PP’ and ‘W’ denote pre-preg and plain weavereinforcement, respectively. Red symbol outline denotes that values arequoted with respect to strain at lowest strain rate considered (496 s−1 and576 s−1 for [5], and 0.04 s−1 for [21]). Orange and purple symbols denotetesting in the 1-3 and 2-3 directions, respectively. White denotes that direc-tion is not specified. Error bars denote the range of reported sensitivity andnot standard deviation. Data taken from [3, 5, 21, 40, 60].

of a test where inertia effects create heterogeneous deforma-tion [22, 27]. For example, Pankow et al. [27] used highspeed imaging in an attempt to resolve full-field strain pro-files on a specimen subjected to compression with a SHPB.Despite poor quality measurements and lack of temporalresolution, they found that the strain field was highly non-uniform. This was also found by Gilat et al. [22]. Gilat etal. [22] and Nakai and Yokoyama [35] note that SHPB the-ory overestimates strain for waisted specimens due to het-erogeneous deformation. Strain gauge measurements alsobecome highly sensitive to gauge position and are gener-ally unreliable for obtaining measurements of ultimate strain[58, 59].

Govender et al. [9] configured a Hopkinson bar into a spalltest in an attempt to remove some of the restrictive assump-tions of the SHPB and measure tensile strength. The spalltest, commonly used for concrete [37], is used sparingly inthe literature for through-thickness testing. The spall testapproach was also used by Gerlach et al. [46] for high strainrate tensile testing of epoxy resins. The approach of Goven-der et al. [9] utilised phase shifting of the waves measuredon the bar to infer the stress in the material at failure. Highspeed cameras were required to record the approximate timeand location of the failure. The major shortcoming of thespall test approach used by Govender et al. [9] is that theinput stress is inferred from measurements on the incidentbar. Tensile strength is also inferred based on measurementsof the global response (reflected pulse measured in the inputbar), which is affected by dispersion.

In the studies by Govender et al. [9], Pankow et al. [27] andGilat et al. [22], the temporal resolution is insufficient toproperly resolve the initial response of the material. In thesecases, common high speed cameras were used, which canachieve frame rates on the order of a 1-5 x 105 frames persecond. The advantage of these cameras is that they offer

12

relatively long record times, at the expense of frame rates(see Fig. 1 in [66]1). Moreover, as frame rate increases, thespatial resolution decreases due to memory read out limita-tions. Therefore, to achieve the necessary frame rates forquantitative imaging at high strain rates, ultra high speedcameras are required. These cameras use different strate-gies to overcome memory read out issues. An example ofthis is the ‘in-situ storage charge coupled device’ (IS-CCD),in which the memory for each pixel is located on the sen-sor [28]. These cameras offer significant opportunity for dy-namic material characterisation as they are simple to operateand trigger, can be used for stereo imaging, and offer fram-ing rates up to 5 x 106 frames per second.

An issue with testing brittle materials (i.e.: through-thickness tension for a composite) is small strains to failure.This requires high spatial/temporal resolution and low noise.With the development of ultra high speed cameras and full-field measurement techniques, such as DIC [67] or the gridmethod [68], some of the fundamental assumptions attachedto current test methods may be alleviated. This offers greatpotential to improve current test methods or develop newtechniques with kinematic fields that are not necessarily uni-form, or are intentionally non-uniform, as also proposedin [22]. With the ability to resolve the temporal evolutionin surface displacement, and hence acceleration, the speci-men’s acceleration field may be used as an embedded loadcell (see Eq. (1))). These full-field maps may be processedusing an inverse identification technique, such as the VirtualFields Method (VFM) [24, 25, 69] to reconstruct stress andextract material properties without need for measurement ofthe external force. This removes the requirement for stressequilibrium and uniform uniaxial strain states attached toSHPB testing. In fact, the presence of a heterogeneous strainfield during impact may be beneficial as multiple constitu-tive properties could be extracted from a single test usingthe VFM. This may be used to overcome some of the limita-tions of current test methods for shear characterisation as thecombined stress state could be characterised and potentiallyused for robust and accurate stiffness and strength identifi-cation.

Very encouraging results have been obtained recently,demonstrating the potential of this approach for identifyingthe in-plane strength and stiffness of composite laminates atvery high strain rates (> 2,000 s−1) [23, 29]. Moulart etal. [23] used the SHPB to generate a pulse with full-fieldmaps processed using the VFM to identify Young’s modu-lus and Poisson’s ratio for a quasi-isotropic laminate. Zhu[29], Pierron et al. [25], and Pierron and Forquin [24] havedemonstrated that this approach can be extended to spall testconfigurations to extract the stiffness and strength of brit-tle materials. This approach opens up a wide design spaceto design innovative tests to accurately determine the me-chanical response of materials at strain rates not achiev-able with any current technique, and in particular, offers a

1updated image can be found at http://photodyn.org/tools/ultra-high-speed-camera

very promising alternative for high strain rate testing in thethrough-thickness direction for polymer matrix fibre com-posites.

6. Conclusions

Understanding the influence of strain rate on the through-thickness mechanical properties of polymer matrix fibrecomposites is critical for the design of thick structures,or structures subjected to dynamic loading in the through-thickness direction. The split Hopkinson pressure bar hasserved as the primary tool for measuring high strain ratematerial properties. However, this approach relies on lim-ited experimental information and suffers from a num-ber of strong inherent assumptions. The result is poorconsistency across the literature regarding the high strainrate response of fibre-reinforced polymer composites in thethrough-thickness direction. Part of this can be attributed toinconsistency in the literature regarding material composi-tion (fibre and matrix materials, fibre volume fraction, rein-forcement architecture, etc.), and the way that strain rate isreported.

Available studies on the through-thickness properties sug-gest that a positive sensitivity to strain rate may be exhibitedby the compressive modulus, compressive ultimate strength,and tensile modulus. However, the magnitude of sensitiv-ity is uncertain due to large amounts of scatter between andwithin studies. Further, the degree to which inertia influ-ences the stress and strain measurements is difficult to de-termine and therefore, measurements of the modulus usingthe SHPB can only be regarded as ‘apparent’. Literatureshows that the influence of strain rate cannot be determinedwith certainty for ultimate strains in tension, compressionand shear. In the case of shear properties, reported valuesare heavily affected by combined states of tension and shearstress. The effect of tensile normal stresses are amplified bymanufacturing defects and geometric features, resulting inunreliable strength and strain values. Comparatively, greateruncertainty surrounds the influence of strain rate on tensileproperties. In this case, high scatter is problematic for bothhigh strain rate and quasi-static measurements. These testsare also particularly sensitive to load alignment, grippingtechnique and stress concentrations resulting from geomet-rical features of the specimen or machining defects.

The development of high speed cameras and full-field mea-surement techniques, such as DIC or the grid method, of-fer a promising outlook for high strain rate testing. Full-field measurements enable many fundamental assumptionsattached to current test methods to be alleviated. This cre-ates opportunity to improve current test methods and/or de-velop new techniques, which induce heterogeneous strains,to identify mechanical properties using inverse identificationprocedures. The authors believe that use of full-field mea-surements, in current or new test methods, will lead to amore consistent understanding of the effects of strain rateon the through-thickness properties of composites.

13


Shear: Strength CFRP - PPCFRP - WGFRP - W3D - W


2








2









―14―

10−2 100 102 104

Strain rate [s−1]

-100

-50

0

50

100

150

200

250


]


Shear: Strength

Figure 12: Summary of relative strain rate sensitivity for shear strengthfrom the literature. ‘PP’ and ‘W’ denote pre-preg and plain weave rein-forcement, respectively. Red symbol outline denotes that values are quotedwith respect to strain at lowest strain rate considered (260 S−1 for [2], 0.04s−1 for [21] and 300 s−1 for [62]). Orange and purple symbols denote test-ing in the 1-3 and 2-3 directions, respectively. White denotes that directionis not specified. Error bars denote the range of reported sensitivity and notstandard deviation. Data taken from [2, 3, 5, 10, 21, 39, 40, 60, 62, 64, 65].

Fig. 13. Two studies by Bouette et al. [39] and Hufenbachet al. [60] report that shear strain at failure is independent ofstrain rate, up to 1,000 s−1 and 400 s−1, respectively. Thelack of sensitivity to strain rate may be a shortcoming of lapspecimens with failure being heavily influenced by normalstresses at the ends of the overlap, similar to Hallett et al.[40]. In contrast, Gillespie et al. [2] reported an increasein peak strain up to a strain rate of 582 s−1, followed bya reduction at higher strain rates. These higher strain ratesapproach the upper limit for equilibrium, set by the ‘R crite-rion’, and are likely contaminated by inertia effects. Hardingand Li [64] found a significant increase (approx. 250 %) infailure strains with impact speed. Unfortunately, the strainrates at failure were not reported. Naik et al. [5] measured a38 % increase in failure strain between strain rates of 576 -1,000 s−1, but did not provide quasi-static reference valuesfor comparison.

Much like the cases of shear modulus and shear strength,ultimate shear strains presented in the literature are heavilyinfluenced by mixed stress states and stress concentrations.As a result the current literature cannot be used to determinethe influence of strain rate on ultimate shear strain.

5. Advanced Testing Approaches Using High Speed,Full-Field Measurements

A review of the literature highlights several key limita-tions with existing test methods that hinder the advancementof material characterisation for composites in the through-thickness direction. The assumptions required for a SHPBtest are particularly restrictive to the maximum strain ratethat can be obtained. In compression, strain rates are lim-ited generally to less than 1,500 s−1, and to an even greaterextent in tension (typically less than 100 s−1). This is dueto the assumption that the specimen is subjected to a state ofuniform stress. This is not the case, especially in early stages

10−2 100 102 104

Strain rate [s−1]

-100

-50

0

50

100

150

200


]

CFRP - PPCFRP - WGFRP - W3D - W


Figure 13: Summary of relative strain rate sensitivity for ultimate shearstrain from the literature. ‘PP’ and ‘W’ denote pre-preg and plain weavereinforcement, respectively. Red symbol outline denotes that values arequoted with respect to strain at lowest strain rate considered (496 s−1 and576 s−1 for [5], and 0.04 s−1 for [21]). Orange and purple symbols denotetesting in the 1-3 and 2-3 directions, respectively. White denotes that direc-tion is not specified. Error bars denote the range of reported sensitivity andnot standard deviation. Data taken from [3, 5, 21, 40, 60].

of a test where inertia effects create heterogeneous deforma-tion [22, 27]. For example, Pankow et al. [27] used highspeed imaging in an attempt to resolve full-field strain pro-files on a specimen subjected to compression with a SHPB.Despite poor quality measurements and lack of temporalresolution, they found that the strain field was highly non-uniform. This was also found by Gilat et al. [22]. Gilat etal. [22] and Nakai and Yokoyama [35] note that SHPB the-ory overestimates strain for waisted specimens due to het-erogeneous deformation. Strain gauge measurements alsobecome highly sensitive to gauge position and are gener-ally unreliable for obtaining measurements of ultimate strain[58, 59].

Govender et al. [9] configured a Hopkinson bar into a spalltest in an attempt to remove some of the restrictive assump-tions of the SHPB and measure tensile strength. The spalltest, commonly used for concrete [37], is used sparingly inthe literature for through-thickness testing. The spall testapproach was also used by Gerlach et al. [46] for high strainrate tensile testing of epoxy resins. The approach of Goven-der et al. [9] utilised phase shifting of the waves measuredon the bar to infer the stress in the material at failure. Highspeed cameras were required to record the approximate timeand location of the failure. The major shortcoming of thespall test approach used by Govender et al. [9] is that theinput stress is inferred from measurements on the incidentbar. Tensile strength is also inferred based on measurementsof the global response (reflected pulse measured in the inputbar), which is affected by dispersion.

In the studies by Govender et al. [9], Pankow et al. [27] andGilat et al. [22], the temporal resolution is insufficient toproperly resolve the initial response of the material. In thesecases, common high speed cameras were used, which canachieve frame rates on the order of a 1-5 x 105 frames persecond. The advantage of these cameras is that they offer

12

relatively long record times, at the expense of frame rates(see Fig. 1 in [66]1). Moreover, as frame rate increases, thespatial resolution decreases due to memory read out limita-tions. Therefore, to achieve the necessary frame rates forquantitative imaging at high strain rates, ultra high speedcameras are required. These cameras use different strate-gies to overcome memory read out issues. An example ofthis is the ‘in-situ storage charge coupled device’ (IS-CCD),in which the memory for each pixel is located on the sen-sor [28]. These cameras offer significant opportunity for dy-namic material characterisation as they are simple to operateand trigger, can be used for stereo imaging, and offer fram-ing rates up to 5 x 106 frames per second.

An issue with testing brittle materials (i.e.: through-thickness tension for a composite) is small strains to failure.This requires high spatial/temporal resolution and low noise.With the development of ultra high speed cameras and full-field measurement techniques, such as DIC [67] or the gridmethod [68], some of the fundamental assumptions attachedto current test methods may be alleviated. This offers greatpotential to improve current test methods or develop newtechniques with kinematic fields that are not necessarily uni-form, or are intentionally non-uniform, as also proposedin [22]. With the ability to resolve the temporal evolutionin surface displacement, and hence acceleration, the speci-men’s acceleration field may be used as an embedded loadcell (see Eq. (1))). These full-field maps may be processedusing an inverse identification technique, such as the VirtualFields Method (VFM) [24, 25, 69] to reconstruct stress andextract material properties without need for measurement ofthe external force. This removes the requirement for stressequilibrium and uniform uniaxial strain states attached toSHPB testing. In fact, the presence of a heterogeneous strainfield during impact may be beneficial as multiple constitu-tive properties could be extracted from a single test usingthe VFM. This may be used to overcome some of the limita-tions of current test methods for shear characterisation as thecombined stress state could be characterised and potentiallyused for robust and accurate stiffness and strength identifi-cation.

Very encouraging results have been obtained recently,demonstrating the potential of this approach for identifyingthe in-plane strength and stiffness of composite laminates atvery high strain rates (> 2,000 s−1) [23, 29]. Moulart etal. [23] used the SHPB to generate a pulse with full-fieldmaps processed using the VFM to identify Young’s modu-lus and Poisson’s ratio for a quasi-isotropic laminate. Zhu[29], Pierron et al. [25], and Pierron and Forquin [24] havedemonstrated that this approach can be extended to spall testconfigurations to extract the stiffness and strength of brit-tle materials. This approach opens up a wide design spaceto design innovative tests to accurately determine the me-chanical response of materials at strain rates not achiev-able with any current technique, and in particular, offers a

1updated image can be found at http://photodyn.org/tools/ultra-high-speed-camera

very promising alternative for high strain rate testing in thethrough-thickness direction for polymer matrix fibre com-posites.

6. Conclusions

Understanding the influence of strain rate on the through-thickness mechanical properties of polymer matrix fibrecomposites is critical for the design of thick structures,or structures subjected to dynamic loading in the through-thickness direction. The split Hopkinson pressure bar hasserved as the primary tool for measuring high strain ratematerial properties. However, this approach relies on lim-ited experimental information and suffers from a num-ber of strong inherent assumptions. The result is poorconsistency across the literature regarding the high strainrate response of fibre-reinforced polymer composites in thethrough-thickness direction. Part of this can be attributed toinconsistency in the literature regarding material composi-tion (fibre and matrix materials, fibre volume fraction, rein-forcement architecture, etc.), and the way that strain rate isreported.

Available studies on the through-thickness properties sug-gest that a positive sensitivity to strain rate may be exhibitedby the compressive modulus, compressive ultimate strength,and tensile modulus. However, the magnitude of sensitiv-ity is uncertain due to large amounts of scatter between andwithin studies. Further, the degree to which inertia influ-ences the stress and strain measurements is difficult to de-termine and therefore, measurements of the modulus usingthe SHPB can only be regarded as ‘apparent’. Literatureshows that the influence of strain rate cannot be determinedwith certainty for ultimate strains in tension, compressionand shear. In the case of shear properties, reported valuesare heavily affected by combined states of tension and shearstress. The effect of tensile normal stresses are amplified bymanufacturing defects and geometric features, resulting inunreliable strength and strain values. Comparatively, greateruncertainty surrounds the influence of strain rate on tensileproperties. In this case, high scatter is problematic for bothhigh strain rate and quasi-static measurements. These testsare also particularly sensitive to load alignment, grippingtechnique and stress concentrations resulting from geomet-rical features of the specimen or machining defects.

The development of high speed cameras and full-field mea-surement techniques, such as DIC or the grid method, of-fer a promising outlook for high strain rate testing. Full-field measurements enable many fundamental assumptionsattached to current test methods to be alleviated. This cre-ates opportunity to improve current test methods and/or de-velop new techniques, which induce heterogeneous strains,to identify mechanical properties using inverse identificationprocedures. The authors believe that use of full-field mea-surements, in current or new test methods, will lead to amore consistent understanding of the effects of strain rateon the through-thickness properties of composites.

13


―15―

Acknowledgements

This material is based on research sponsored by theAir Force Research Laboratory, under agreement numberFA9550-17-1-0133. The U.S. Government is authorized toreproduce and distribute reprints for Governmental purposesnotwithstanding any copyright notation thereon. The viewsand conclusions contained herein are those of the authorsand should not be interpreted as necessarily representing theofficial policies or endorsements, either expressed or im-plied, of the Air Force Research Laboratory or the U.S. Gov-ernment.

Mr Jared Van Blitterswyk acknowledges the support of EP-SRC for funding through a Doctoral Training Grant. DrLloyd Fletcher and Prof. Fabrice Pierron acknowledge sup-port from EPSRC through grant EP/L026910/1. The authorsare also grateful to the grant programme manager, Dr DavidGarner from EOARD/AFOSR.

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14

3

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rate-dependent failure criteria for composites, Composites Science and Technology, 71-3 (2011), 357–364.

[2] Gillespie, J. W., Gama, B. A., Cichanowski, C. E. and Xiao, J. R.: Interlaminar shear strength of plain weave S2-glass/SC79 composites subjected to out-of-plane high strain rate compressive loadings, Composites Science and Technology, 65-11-12 (2005), 1891–1908.

[3] Harding, J. and Dong, L.: Effect of strain rate on the interlaminar shear strength of carbon-fibre-reinforced laminates, Composites Science and Technology, 51-3 (1994), 347–358.

[4] Yokoyama, T. and Nakai, K.: High strain-rate compressive characteristics of laminated composites in the through-thickness direction, CD-ROM Proc. SEM X International Congress & Exposition on Experimental & Applied Mechanics, (2004).

[5] Naik, N. K., Asmelash, A., Kavala, V. R. and Ch, V.: Interlaminar shear properties of polymer matrix composites: strain rate effect, Mechanics of Materials, 39-12 (2007), 1043–1052.

[6] Nakai, K. and Yokoyama, T.: Through-thickness tensile strength of carbon/epoxy laminated composites under impact loading, CD-ROM Proc. 16th International Conference on Experimental Mechanics, (2014).

[7] Olsson, R.: A survey of test methods for multiaxial and out-of-plane strength of composite laminates, Composites Science and Technology, 71-6 (2011), 773–783.

[8] Mespoulet, S.: Through-thickness test methods for laminated composite materials, PhD thesis, Imperial College of Science, Technology and Medicine, London, UK, (1998).

[9] Govender, R. A., Louca, L. A., Pullen, A., Fallah, A. S. and Nurick, G. N.: Determining the through-thickness properties of thick glass fiber reinforced polymers at high strain rates, Journal of Composite Materials, 46-10 (2012), 1219–1228.

[10] Gerlach, R., Siviour, C. R., Wiegand, J. and Petrinic, N.: In-plane and through-thickness properties, failure modes, damage and delamination in 3D woven carbon fibre composites subjected to impact loading, Composites Science and Technology, 72-3 (2012), 397–411.

[11] Field, J. E., Walley, S. M., Proud, W. G., Goldrein, H. T. and Siviour, C. R.: Review of experimental techniques for high rate deformation and shock studies, International Journal of Impact Engineering, 30-7 (2004), 725–775.

[12] Naik, N. K., Ch, V. and Kavala, V. R.: Hybrid composites under high strain rate compressive loading, Materials Science and Engineering A, 498-1-2 (2008), 87–99.

[13] Broughton, W. R.: Through-thickness testing, Mechanical Testing of Advanced Fibre Composites (Hodgkinson, J. M. ed.), Woodhead Publishing Limited (2000), chapter 8.

[14] He, Y., Makeev, A. and Shonkwiler, B.: Characterization of nonlinear shear properties for composite materials using digital image correlation and finite element analysis, Composites Science and Technology, 73 (2012), 64–71.

[15] Cui, W., Liu, T., Len, J. and Ruo, R.: Interlaminar tensile strength (ILTS) measurement of woven glass/polyester laminates using four-point curved beam specimen, Composites Part A: Applied Science and Manufacturing, 27-11 (1996), 1097–1105.

[16] Makeev, A., Carpentier, P. and Shonkwiler, B.: Methods to measure interlaminar tensile modulus of composites, Composites Part A: Applied Science and Manufacturing, 56 (2014), 256–261.

[17] Charrier, J. S., Laurin, F., Carrere, N. and Mahdi, S.: Determination of the out-of-plane tensile strength using four-point bending tests on laminated L-angle specimens with different stacking sequences and total thicknesses, Composites Part A: Applied Science and Manufacturing, 81 (2016), 243–253.

[18] Hufenbach, W., Hornig, A., Zhou, B., Langkamp, A. and Gude, M.: Determination of strain rate dependent through-thickness tensile properties of textile reinforced thermoplastic composites using L-shaped beam specimens, Composites Science and Technology, 71-8 (2011), 1110–1116.

[19] Gerlach, R., Siviour, C. R., Wiegand, J. and Petrinic, N.: The strain rate dependent material behavior of S-GFRP extracted from GLARE, Mechanics of Advanced Materials and Structures, 20-7 (2013), 505–514.

[20] Davis, J. R.: High strain rate tensile testing, Tensile Testing (2nd ed.), ASM International (2004), 251–263.

[21] Hufenbach, W., Langkamp, A., Hornig, A. and Ebert, C.: Experimental determination of the strain rate dependent out- of-plane shear properties of textile-reinforced composites, CD-ROM Proc. 17th European Conference on Composite Materials, (2009).

[22] Gilat, A., Schmidt, T. E. and Walker, A. L.: Full field strain measurement in compression and tensile split Hopkinson bar experiments, Experimental Mechanics, 49-2 (2009), 291–302.

3

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[3] Harding, J. and Dong, L.: Effect of strain rate on the interlaminar shear strength of carbon-fibre-reinforced laminates, Composites Science and Technology, 51-3 (1994), 347–358.

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[6] Nakai, K. and Yokoyama, T.: Through-thickness tensile strength of carbon/epoxy laminated composites under impact loading, CD-ROM Proc. 16th International Conference on Experimental Mechanics, (2014).

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[22] Gilat, A., Schmidt, T. E. and Walker, A. L.: Full field strain measurement in compression and tensile split Hopkinson bar experiments, Experimental Mechanics, 49-2 (2009), 291–302.

4

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[44] Ravichandran, R. and Ghatuparthi, S.: Critical appraisal of limiting strain rates for compression testing of ceramics in a split Hopkinson pressure bar, Journal of the American Ceramic Society, 77-1 (1994), 263–267.

[45] Gama, B. A., Gillespie, J. W., Mahfuz, H., Raines, R. P., Haque, A., Jeelani, S., Bogetti, T. A. and Fink, B. K.: High strain-rate behavior of plain-weave S-2 glass/vinyl ester composites, Journal of Composite Materials, 35-13 (2001), 1201–1228.

[46] Gerlach, R., Siviour, C. R., Petrinic, N. and Wiegand, J.: Experimental characterisation and constitutive modelling of RTM-6 resin under impact loading, Polymer, 49-11 (2008), 2728–2737.

[47] Song, Z., Wang, Z., Ma, H. and Xuan, H.: Mechanical behavior and failure mode of woven carbon/epoxy laminate composites under dynamic compressive loading, Composites: Part B, 60 (2014), 531–536.

[48] Gorham, D. A., Griffiths, L. J., Martin, D. J., Billington, E. W., Brissenden, C., Signoret, C., Pouyet, J. M. and Lataillade, J.-L.: Specimen inertia in high strain-rate compression, Journal of Physics D: Applied Physics, 22-12 (1989), 1888–1893.

[49] Zhao, H. and Gary, G.: On the use of SHPB techniques to determine the dynamic behavior of materials in the range of small strains, International Journal of Solids and Structures, 33-23 (1996), 3363–3375.

[50] Shah Khan, M. Z. and Simpson, G.: Mechanical properties of a glass reinforced plastic naval composite material under increasing compressive strain rates, Materials Letters, 45-3-4 (2000), 167–174.

[51] Shen, L., Li, Y. and Wang, Z.: Experimental


―16―

Acknowledgements

This material is based on research sponsored by theAir Force Research Laboratory, under agreement numberFA9550-17-1-0133. The U.S. Government is authorized toreproduce and distribute reprints for Governmental purposesnotwithstanding any copyright notation thereon. The viewsand conclusions contained herein are those of the authorsand should not be interpreted as necessarily representing theofficial policies or endorsements, either expressed or im-plied, of the Air Force Research Laboratory or the U.S. Gov-ernment.

Mr Jared Van Blitterswyk acknowledges the support of EP-SRC for funding through a Doctoral Training Grant. DrLloyd Fletcher and Prof. Fabrice Pierron acknowledge sup-port from EPSRC through grant EP/L026910/1. The authorsare also grateful to the grant programme manager, Dr DavidGarner from EOARD/AFOSR.

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[45] Gama, B. A., Gillespie, J. W., Mahfuz, H., Raines, R. P., Haque, A., Jeelani, S., Bogetti, T. A. and Fink, B. K.: High strain-rate behavior of plain-weave S-2 glass/vinyl ester composites, Journal of Composite Materials, 35-13 (2001), 1201–1228.

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[48] Gorham, D. A., Griffiths, L. J., Martin, D. J., Billington, E. W., Brissenden, C., Signoret, C., Pouyet, J. M. and Lataillade, J.-L.: Specimen inertia in high strain-rate compression, Journal of Physics D: Applied Physics, 22-12 (1989), 1888–1893.

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[51] Shen, L., Li, Y. and Wang, Z.: Experimental


―17―

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175

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[66] Reu, P. L. and Miller, T. J.: The application of high-speed digital image correlation, The Journal of Strain Analysis for Engineering Design, 43-8 (2008), 673–688.

[67] Sutton, M. A., Orteu, J.-J. and Schreier, H. W.: Image Correlation for Shape, Motion and Deformation Measurements, Springer (2009).

[68] Grédiac, M., Sur, F. and Blaysat, B.: The grid method for in-plane displacement and strain measurement: a review and analysis, Strain, 52-3 (2016), 205–243.

[69] Pierron, F. and Grédiac, M.: The Virtual Fields Method: Extracting Constitutive Mechanical Parameters from Full-Field Deformation Measurements, Springer (2012).


―18―

App

endi

xA

:Lite

ratu

reSu

rvey

Tabl

es

Tabl

e1:

Sum

mar

yof

publ

ishe

dst

udie

son

stra

inra

teef

fect

sof

inte

rlam

inar

com

pres

sive

prop

ertie

sof

fibre

-rei

nfor

ced

poly

mer

com

posi

tes.

Not

es:C

onst

ituen

tmat

eria

lslis

ted

inth

efo

rmat

:‘fib

re/m

atri

x’.M

ater

iall

abel

sar

ein

clud

edin

‘()’

for

asso

ciat

ion

with

Fig.

5-

Fig.

7.Q

uasi

-sta

tic:

italic

type

face

;hig

hst

rain

rate

:re

gula

rty

pefa

ce;t

estm

etho

d:el

ectr

o-m

echa

nica

lloa

dfr

ame

(EM

LF)

,hyd

raul

iclo

adfr

ame

(HL

F),h

igh-

spee

dlo

adfr

ame

(HSL

F),s

plit

Hop

kins

onpr

essu

reba

r(SH

PB);

spec

imen

geom

etry

(in

‘[]’

):R

=re

ctan

gula

r/cu

bic

spec

imen

s,C

=cy

lindr

ical

spec

imen

s.

Ref

eren

ceM

ater

ial

Test

[Spe

cim

en]

Stra

inR

ate

(s−

1 )N

otes

Yok

oyam

aT.

&N

akai

K.(

2004

)[4

]ca

rbon

/epo

xypr

e-pr

eg.(

[0/9

0]s)

:T70

0S/2

500

(CFR

P-PP

)

carb

on/e

poxy

2Dpl

ain

wea

ve:T

300B

/250

0(C

FPR

-W)

glas

s/ep

oxy

2Dpl

ain

wea

ve:E

-2/2

500

(GFR

P-W

)

EM

LF(I

nstr

on45

05)

[C-s

tack

]

Com

pres

sion

SHPB

[C]

0.00

2–

1,51

0D

ynam

icst

ress

equi

libri

umis

not

achi

eved

duri

ngth

eea

rly

stag

esof

the

test

.A

utho

rsst

udy

influ

ence

ofst

rain

rate

onse

cant

mod

ulus

inst

ead.

Rei

nfor

cem

ent

arch

itect

ure

has

agr

eate

rin

fluen

ceon

the

com

pres

sive

prop

ertie

sw

ithex

cept

ion

toco

mpr

essi

vest

reng

th.

Stra

inra

tese

nsiti

vity

attr

ibut

edto

visc

oela

stic

natu

reof

the

epox

yre

sin.

carb

on/e

poxy

pre-

preg

:inc

reas

ein

elas

ticm

odul

us(+

105%

),de

crea

sein

fail-

ure

stre

ngth

(-30

%),

and

failu

rest

rain

(-11

%)a

t1,5

10s−

1 ;

carb

on/e

poxy

2Dw

eave

:in

crea

sein

elas

ticm

odul

us(+

143%

),de

crea

sein

stre

ngth

(-6%

),an

dde

crea

sein

ultim

ate

stra

in(-

17%

)at1

,510

s−1 ;

glas

s/ep

oxy

2Dw

eave

:in

crea

sein

elas

ticm

odul

us(+

60%

),in

crea

sein

stre

ngth

(+15

%),

and

decr

ease

inul

timat

est

rain

(-9%

)at1

,510

s−1 .

Song

Z.e

tal.

(201

4)[4

7]ca

rbon

/epo

xy2D

satin

wea

ve:T

300-

3/–

(GFR

P-W

)H

LF(M

TS81

0)[C

]

Com

pres

sion

SHPB

[C]

500

–1,

100

Hig

hst

rain

rate

stre

ss-s

trai

ncu

rves

are

affe

cted

bydi

sper

sion

.C

onsi

sten

cyof

test

ques

tiona

ble

asst

reng

thde

crea

ses

sign

ifica

ntly

only

at80

0s−

1 .N

oex

plan

atio

nfo

rthi

sbe

havi

ouri

spr

ovid

ed.

Ela

stic

mod

ulus

incr

ease

s(q

ualit

ativ

ely)

upto

1,10

0s−

1 ,an

dst

reng

thde

-cr

ease

sup

to80

0s−

1(-

37%

)be

fore

incr

easi

ngat

1,10

0s−

1(+

11%

).U

ltim

ate

stra

ins

decr

ease

betw

een

-62%

at80

0s−

1an

d-4

2%at

1,10

0s−

1 .

Nai

kN

.K.e

tal.

(200

8)[1

2]ca

rbon

/epo

xy2D

satin

wea

ve:–

/–(C

FRP-

W)

E-g

lass

/epo

xy2D

plai

nw

eave

:–/–

(GFR

P-W

)

E-g

lass

/epo

xy2D

satin

wea

ve:–

/–(G

FRP-

W)

carb

on2D

satin

wea

ve&

E-g

lass

2Dpl

ain

wea

ve/e

poxy

:–/–

(HY

BR

ID-W

)

Com

pres

sion

SHPB

[C]

1,27

5&

1,50

3Q

uasi

-sta

ticpr

oper

ties

not

prov

ided

.St

ress

wav

eat

tenu

atio

nat

trib

uted

toof

fset

info

rce

betw

een

inpu

tand

tran

smitt

erba

r.In

ertia

effe

cts

pres

entd

ur-

ing

entir

elo

adin

gse

quen

ce.

Tran

smitt

erba

rpea

kfo

rce

used

asco

nser

vativ

ees

timat

efo

rco

mpu

ting

stre

ssin

spec

imen

.E

last

icm

odul

uses

timat

edus

ing

stra

inan

dst

ress

atpe

akst

ress

.

Slig

htin

crea

sein

elas

ticm

odul

us(+

7%),

stre

ngth

incr

ease

s(+

46%

),an

dul

-tim

ate

stra

inin

crea

ses

(+25

%)a

t1,5

03s−

1re

lativ

eto

1,27

5s−

1 .

Hos

urM

.V.e

tal.

(200

1)[5

4]ca

rbon

/epo

xypr

e-pr

eg.([

0/90

] s):

PAN

EX

33/A

PCM

LL

C(D

A45

18)(

CFR

P-PP

)LF

nots

pec.

[R]

Com

pres

sion

SHPB

[R]

82,1

64,8

17Q

uasi

-sta

ticst

rain

estim

ated

usin

gcr

ossh

ead

disp

lace

men

tco

rrec

ted

for

com

plia

nce.

Hig

her

quas

i-st

atic

ultim

ate

stra

ins

attr

ibut

edto

grea

ter

time

for

stre

ssre

dist

ribu

tion.

Inci

dent

puls

ege

nera

ted

bySH

PBis

high

lyno

n-un

ifor

m(s

igni

fican

tdi

sper

sion

susp

ecte

d).

Sam

ples

at82

s−1

did

not

fail

with

SHPB

,th

eref

ore,

stre

ngth

atqu

asi-

stat

icco

nditi

ons

cann

otbe

com

pare

d.

Ela

stic

mod

ulus

incr

ease

sat

82s−

1(+

30%

),fo

llow

edby

ade

crea

sew

ithin

crea

sing

stra

inra

teto

817

s−1

(+12

%).

Stre

ngth

incr

ease

s(+1

9%at

817

s−1

rela

tive

to82

s−1 ),

butl

ower

com

pare

dto

quas

i-st

atic

valu

es.

Failu

rest

rain

incr

ease

s(+

19%

at81

7s−

1re

lativ

eto

82s−

1 ),bu

tare

low

erth

anqu

asi-

stat

icva

lues

.

175

[51] Shen, L., Li, Y. and Wang, Z.: Experimental investigation of the effect of strain rate on the compression behavior of 3D E-glass fiber-reinforced composites, Applied Mechanics and Materials, 174-177 (2012), 1528–1532.

[52] Akil, Ö, Yldrm, U., Güden, M. and Hall, I. W.: Effect of strain rate on the compression behaviour of a woven fabric S2-glass fiber reinforced vinyl ester composite, Polymer Testing, 22-8 (2003), 883–887.

[53] Güden, M., Yldrm, U. and Hall, I. W.: Effect of strain rate on the compression behavior of a woven glass fiber/SC-15 composite, Polymer Testing, 23-6 (2004), 719–725.

[54] Hosur, M. V., Alexander, J., Vaidya, U. K. and Jeelani, S.: High strain rate compression response of carbon/epoxy laminate composites, Composite Structures, 52-3-4 (2001), 405–417.

[55] Woo, S.-C. and Kim, T.-W.: High strain-rate failure in carbon/Kevlar hybrid woven composites via a novel SHPB-AE coupled test, Composites Part B, 97 (2016), 317–328.

[56] Tagarielli, V. L., Minisgallo, G., Mcmillan, A. J. and Petrinic, N.: The response of a multi-directional composite laminate to through-thickness loading, Composites Science and Technology, 70-13 (2010), 1950–1957.

[57] Kapoor, R., Pangeni, L., Bandaru, A. K., Ahmad, S. and Bhatnagar, N.: High strain rate compression response of woven Kevlar reinforced polypropylene composites, Composites Part B, 89 (2016), 374–382.

[58] Lifshitz, J. M. and Leber, H.: Response of fiber-reinforced polymers to high strain-rate loading in interlaminar tension and combined tension/shear, Composites Science and Technology, 58-6 (1998), 987–996.

[59] Medina, J. L. and Harding, J.: The effect of strain rate on the through-thickness tensile stiffness and strength properties of fibre-reinforced epoxy composites, Journal de Physique IV France, 10 (2000), 275–280.

[60] Hufenbach, W., Langkamp, A., Gude, M., Ebert, C., Hornig, A., Nitschke, S. and Böhm, H.:

Characterisation of strain rate dependent material properties of textile reinforced thermoplastics for crash and impact analysis, Procedia Materials Science, 2 (2013), 204–211.

[61] Naik, N. K., Yernamma, P., Thoram, N. M., Gadipatri, R. and Kavala, V. R.: High strain rate tensile behavior of woven fabric E-glass/epoxy composite, Polymer Testing, 29-1 (2010), 14–22.

[62] Gowtham, H. L., Pothnis, J. R., Ravikumar, G. and Naik, N. K.: Dependency of dynamic interlaminar shear strength of composites on test technique used, Polymer Testing, 42 (2015), 151–159.

[63] Cui, G. Y. and Ruiz, C.: Through-thickness failure of laminated carbon/epoxy composites under combined stresses, Composites Science and Technology, 53-3 (1995), 253–258.

[64] Harding, J. and Li, Y. L.: Determination of interlaminar shear strength for glass/epoxy and carbon/epoxy laminates at impact rates of strain, Composites Science and Technology, 45-2 (1992), 161–171.

[65] Yokoyama, T. and Nakai, K.: Evaluation of interlaminar shear strength of a unidirectional carbon/epoxy laminated composite under impact loading, Journal de Physique IV France, 134 (2006), 797–804.

[66] Reu, P. L. and Miller, T. J.: The application of high-speed digital image correlation, The Journal of Strain Analysis for Engineering Design, 43-8 (2008), 673–688.

[67] Sutton, M. A., Orteu, J.-J. and Schreier, H. W.: Image Correlation for Shape, Motion and Deformation Measurements, Springer (2009).

[68] Grédiac, M., Sur, F. and Blaysat, B.: The grid method for in-plane displacement and strain measurement: a review and analysis, Strain, 52-3 (2016), 205–243.

[69] Pierron, F. and Grédiac, M.: The Virtual Fields Method: Extracting Constitutive Mechanical Parameters from Full-Field Deformation Measurements, Springer (2012).


―19―

Woo

S.-C

.&

Kim

T.-W

.(2

016)

[55]

carb

on&

kevl

ar/e

poxy

2Dtw

illw

eave

:T

300/

Kev

lar4

9/–

(HY

BR

ID-W

)C

ompr

essi

onSH

PB[C

]1,

007,

1,48

5,1,

941

Low

tran

smis

sion

ofth

ein

putp

ulse

thro

ugh

the

spec

imen

(10-

12%

at1,

485

s−1

and

1,94

1s−

1 ).T

here

fore

,low

sign

al-t

o-no

ise

ratio

onst

ress

mea

sure

-m

ent(

nois

ein

stre

ss-s

trai

ncu

rves

).M

ater

ialb

ehav

esin

am

ore

britt

lem

anne

rat

high

stra

inra

tes.

Aco

ustic

emis

sion

sign

als

wer

ean

alys

edto

iden

tify

the

onse

toff

ailu

re,a

ndda

mag

epr

ogre

ssio

nw

ithin

the

spec

imen

.

Eff

ecto

fst

rain

rate

onm

odul

usw

asno

trep

orte

d.St

reng

thin

crea

ses

(+80

%at

1,94

1s−

1 ),an

dul

timat

est

rain

decr

ease

(-15

%at

1,94

1s−

1 ).

Kap

oorR

.eta

l.(2

016)

[57]

kevl

ar/p

olyp

ropy

lene

2Dpl

ain

wea

ve:K

evla

r29

/MA

g-PP

(Not

incl

uded

infig

ures

)

Com

pres

sion

SHPB

[C]

1,37

0,2,

005,

2,53

8,3,

239,

3,44

0,4,

264

Poss

ibly

the

first

pape

rto

repo

rton

the

high

stra

inra

teth

roug

h-th

ickn

ess

prop

ertie

sfo

rke

vlar

/ther

mop

last

icre

sin

com

posi

tes.

Spec

imen

sha

veve

rylo

was

pect

ratio

(L/D

=0.

1-0.

3).

Rel

iabl

em

easu

rem

ents

wer

eno

tpo

ssib

lew

ithth

eth

inne

stsp

ecim

ens.

Ela

stic

mod

ulus

incr

ease

s(+2

45%

at4,

264

s−1

rela

tive

to1,

370

s−1 ),

stre

ngth

incr

ease

s(+

196%

at4,

264

s−1

rela

tive

to1,

370

s−1 ),

and

ultim

ate

stra

inin

-cr

ease

s(+

134%

).Si

gnifi

cant

incr

ease

inul

timat

est

rain

due

todu

ctile

be-

havi

ouro

fthe

rmop

last

icm

atri

x.To

ughn

ess

incr

ease

sin

ano

n-lin

earm

anne

r(+

808%

at4,

264

s−1

rela

tive

to1,

370

s−1 ).

Gam

aB

.eta

l.(2

001)

[45]

S-2

glas

s/vi

nyle

ster

2Dpl

ain

wea

ve:–

/–(G

FRP-

W)

LSLF

(Ins

tron

-not

spec

.)[R

]

Com

pres

sion

SHPB

[R]

200

-160

0St

rain

sm

easu

red

dire

ctly

from

spec

imen

sus

ing

stra

inga

uges

.In

put

puls

efr

omSH

PBhi

ghly

non-

unif

orm

.St

rain

mea

sure

dby

stra

inga

uges

mou

nted

onth

esp

ecim

enis

used

until

unlo

adin

g,th

enSH

PBth

eory

used

.Hig

hle

vels

ofdi

sper

sion

mak

est

ress

-str

ain

curv

esun

info

rmat

ive.

‘Non

-lin

ear’

stra

ins

are

defin

edto

acco

untf

orpa

rasi

ticst

rain

sfr

omdi

sper

sion

.Sp

ecim

ens

may

notr

each

quas

i-st

atic

stre

sseq

uilib

rium

prio

rto

failu

re.

Eff

ect

ofst

rain

rate

onm

odul

usno

tre

port

ed.

Stre

ngth

incr

ease

s(+

38%

at1,

125

s−1 )b

efor

ere

achi

ngan

appr

oxim

atel

yas

ympt

otic

valu

eat

high

erst

rain

rate

s.U

ltim

ate

stra

inin

crea

ses

(+98

%at

1,12

5s−

1 ),bu

tw

ithhi

ghun

cer-

tain

ty.

Gov

ende

rR.e

tal.

(201

1)[9

]gl

ass/

viny

lest

er2D

plai

nw

eave

:E-g

lass

24oz

./Der

akan

e80

84(G

FRP-

W)

EM

LF(Z

wic

kU

nive

rsal

)[C

]

Com

pres

sion

SHPB

[C]

510

Cro

sshe

addi

spla

cem

entu

sed

toes

timat

est

rain

due

toco

ncer

nsab

outs

trai

nga

uge

alig

nmen

t.Sm

alls

peci

men

spr

even

ted

the

use

ofex

tens

omet

ers.

Eff

ecto

fstr

ain

rate

onm

odul

usno

trep

orte

das

quas

i-st

atic

stre

sseq

uilib

rium

was

nota

chie

ved

until

late

inth

ete

st.

Stre

ngth

initi

ally

incr

ease

s(+

13%

at51

0s−

1 )but

decr

ease

sw

ithin

crea

sing

stra

inra

te(+

4%at

1,80

0s−

1 ).Sl

ight

redu

ctio

nin

ultim

ate

stra

in(-

5%).

Ger

lach

R.e

tal.

(201

2)[1

0]ca

rbon

/epo

xy3D

wea

ve:(

Tena

xH

TS/

HTA

)/R

TM

-6(3

D-W

)E

MLF

(not

spec

.)H

LF(I

tm.s

−1 )[

R]

Com

pres

sion

SHPB

[R]

0.00

4-6

,000

Stra

inw

asm

easu

red

usin

ga

lase

rex

tens

omet

erfo

rqu

asi-

stat

icte

sts.

At

inte

rmed

iate

stra

ins

digi

tal

spec

kle

phot

ogra

phy

was

used

.M

odifi

eddi

rect

impa

ctSH

PBus

edfo

rhi

ghst

rain

rate

test

ing.

Com

pres

sion

stre

ss-s

trai

nre

spon

seat

high

stra

inra

tes

show

sso

me

wav

ines

sdu

eto

disp

ersi

on.S

tren

gth

mea

sure

das

max

imum

stre

ssbe

fore

unst

able

failu

re.

Tang

ent

mod

ulus

(mea

sure

dat

300

MPa

)in

crea

ses

(+43

%at

6,00

0s−

1 ).N

eglig

ible

stra

inra

teef

fect

onst

reng

th.

18

Shah

Kha

nM

.Z.&

Sim

pson

G.

(200

0)[5

0]ca

rbon

/epo

xy2D

plai

nw

eave

:DF1

400/

Syno

lite

0288

-T1

resi

n(C

FRP-

W)

HLF

[R]

0.00

1-1

0Q

uasi

-sta

ticst

rain

ses

timat

edus

ing

cros

shea

ddi

spla

cem

ent

corr

ecte

dfo

rco

mpl

ianc

e.H

ydra

ulic

load

fram

eus

edto

load

atin

term

edia

test

rain

rate

s.St

reng

than

dul

timat

est

rain

take

nat

poin

tof

max

imum

stre

ss.

Inco

nsis

tent

failu

rem

odes

thou

ghtt

oco

ntri

bute

tosc

atte

rin

mea

sure

dul

timat

epa

ram

e-te

rs.

Ela

stic

mod

ulus

incr

ease

s(+

25%

at10

s−1 ),

stre

ngth

incr

ease

s(+

21%

at10

s−1 ),

and

stra

inin

crea

ses(

+11%

at10

s−1 ).

Sign

ifica

ntsc

atte

rin

allm

easu

red

para

met

ers

(up

to±

25%

,12

%an

d33

%fo

rel

astic

mod

ulus

,st

reng

than

dul

timat

est

rain

,res

pect

ivel

y).

Shen

etal

.(20

12)[

51]

glas

s/vi

nyle

ster

3Dw

eave

:E

-gla

ss/M

L-5

06(3

D-

W)

HLF

(MTS

810)

[R]

Com

pres

sion

SHPB

[R]

0.00

1-1

,200

Hyd

raul

iclo

adfr

ame

used

tote

stat

quas

i-st

atic

and

inte

rmed

iate

stra

inra

tes.

Stre

ssst

rain

curv

esar

eve

ryno

n-lin

eara

ndex

hibi

tver

yla

rge

incr

ease

inth

eta

ngen

tmod

ulus

(defi

ned

abov

e0.

025

stra

in).

Unc

lear

how

man

ysp

ecim

ens

wer

ete

sted

.U

nrea

listic

ally

high

effe

ctof

stra

inra

teon

the

tang

entm

odul

ussu

gges

tssp

ecim

ens

are

noti

na

stat

eof

stre

sseq

uilib

rium

.

Tang

entm

odul

usin

crea

ses

(+35

0%at

1,20

0s−

1 )with

very

high

unce

rtai

nty

(±79

%).

Stre

ngth

incr

ease

s(+

8%at

1,20

0s−

1 )and

ultim

ate

stra

inde

crea

ses

(-50

%1,

200

s−1 ).

Aki

leta

l.(2

003)

[52]

glas

s/vi

nyle

ster

2Dw

eave

:S-2

glas

s/–

(GFR

P-W

)H

LF(n

otsp

ec.)

[R,C

]

Com

pres

sion

SHPB

[C]

0.00

1-9

00Ta

ngen

tm

odul

us,

fitte

dto

late

rre

gion

of’li

near

’re

spon

sean

dus

edto

estim

ate

elas

ticm

odul

us.

Stra

inra

tese

nsiti

vebe

havi

our

attr

ibut

edto

visc

oela

stic

prop

ertie

sof

the

mat

rix.

Con

sist

ents

hear

failu

rem

ode

betw

een

quas

i-st

atic

and

high

stra

inra

tete

sts.

Tang

entm

odul

usin

crea

ses(

+79%

at90

0s−

1 )with

high

unce

rtai

nty

(±26

%),

stre

ngth

incr

ease

s(+

29%

at90

0s−

1 ),an

dul

timat

est

rain

decr

ease

ssl

ight

ly(-

6%at

900

s−1 ).

Pank

owet

al.(

2011

)[27

]gl

ass/

epox

y3D

wea

ve:Z

-fibr

e/SC

-15

HLF

(not

spec

.)[R

]

Com

pres

sion

SHPB

[C]

QS

-175

0U

sed

2DD

ICpe

rfor

med

with

high

spee

dca

mer

ato

mea

sure

stra

inon

the

spec

imen

.Po

orsp

atia

land

tem

pora

lres

olut

ion

resu

ltsin

high

erro

r(>

5%st

rain

).N

ode

tails

prov

ided

onth

eD

ICse

tup.

Hig

hst

rain

rate

test

ssu

ffer

from

high

leve

lsof

disp

ersi

on(o

scill

atio

nsin

stre

ss-s

trai

nre

spon

se).

Thi

sin

trod

uces

unce

rtai

nty

inst

reng

than

dul

timat

est

rain

mea

sure

men

ts.

Eff

ect

ofst

rain

rate

onm

odul

usno

tre

port

edqu

antit

ativ

ely.

Stra

inra

teap

-pe

ars

toha

vene

glig

ible

effe

cton

elas

ticm

odul

us.S

tren

gth

incr

ease

sre

lativ

eto

quas

i-st

atic

valu

es(+

11%

at1,

750

s−1 )b

utno

tstr

ain

rate

sens

itive

(with

insc

atte

r).

Ulti

mat

est

rain

sin

crea

sere

lativ

eto

quas

i-st

atic

valu

es(+

20%

at1,

750

s−1 )b

utal

sono

tstr

ain

rate

sens

itive

(with

insc

atte

r).

Gud

enet

al.(

2004

)[53

]gl

ass/

epox

y2D

wea

ve:S

-2gl

ass/

SC-1

5E

MLF

(Shi

mad

zuAG

-I)[

C]

Com

pres

sion

SHPB

[C]

0.00

01-1

,100

Com

pres

sive

mod

ulus

com

pute

dus

ing

linea

rre

gion

ofst

ress

-str

ain

curv

eat

4%st

rain

.St

rain

rate

limite

dto

1,10

0s−

1 ,ab

ove

whi

chqu

asi-

stat

icst

ress

equi

libri

umco

uld

not

beac

hiev

edpr

ior

failu

re.

Con

sist

ent

shea

rfa

ilure

mod

ebe

twee

nqu

asi-

stat

ican

dhi

ghst

rain

rate

test

s.

Ela

stic

mod

ulus

incr

ease

s(+

70%

at1,

100

s−1 ),

stre

ngth

incr

ease

s(+

53%

at1,

100

s−1 ),

ultim

ate

stra

inde

crea

ses

slig

htly

with

incr

easi

ngst

rain

rate

(-3%

at1,

100

s−1 ).

19


―20―

Woo

S.-C

.&

Kim

T.-W

.(2

016)

[55]

carb

on&

kevl

ar/e

poxy

2Dtw

illw

eave

:T

300/

Kev

lar4

9/–

(HY

BR

ID-W

)C

ompr

essi

onSH

PB[C

]1,

007,

1,48

5,1,

941

Low

tran

smis

sion

ofth

ein

putp

ulse

thro

ugh

the

spec

imen

(10-

12%

at1,

485

s−1

and

1,94

1s−

1 ).T

here

fore

,low

sign

al-t

o-no

ise

ratio

onst

ress

mea

sure

-m

ent(

nois

ein

stre

ss-s

trai

ncu

rves

).M

ater

ialb

ehav

esin

am

ore

britt

lem

anne

rat

high

stra

inra

tes.

Aco

ustic

emis

sion

sign

als

wer

ean

alys

edto

iden

tify

the

onse

toff

ailu

re,a

ndda

mag

epr

ogre

ssio

nw

ithin

the

spec

imen

.

Eff

ecto

fst

rain

rate

onm

odul

usw

asno

trep

orte

d.St

reng

thin

crea

ses

(+80

%at

1,94

1s−

1 ),an

dul

timat

est

rain

decr

ease

(-15

%at

1,94

1s−

1 ).

Kap

oorR

.eta

l.(2

016)

[57]

kevl

ar/p

olyp

ropy

lene

2Dpl

ain

wea

ve:K

evla

r29

/MA

g-PP

(Not

incl

uded

infig

ures

)

Com

pres

sion

SHPB

[C]

1,37

0,2,

005,

2,53

8,3,

239,

3,44

0,4,

264

Poss

ibly

the

first

pape

rto

repo

rton

the

high

stra

inra

teth

roug

h-th

ickn

ess

prop

ertie

sfo

rke

vlar

/ther

mop

last

icre

sin

com

posi

tes.

Spec

imen

sha

veve

rylo

was

pect

ratio

(L/D

=0.

1-0.

3).

Rel

iabl

em

easu

rem

ents

wer

eno

tpo

ssib

lew

ithth

eth

inne

stsp

ecim

ens.

Ela

stic

mod

ulus

incr

ease

s(+2

45%

at4,

264

s−1

rela

tive

to1,

370

s−1 ),

stre

ngth

incr

ease

s(+

196%

at4,

264

s−1

rela

tive

to1,

370

s−1 ),

and

ultim

ate

stra

inin

-cr

ease

s(+

134%

).Si

gnifi

cant

incr

ease

inul

timat

est

rain

due

todu

ctile

be-

havi

ouro

fthe

rmop

last

icm

atri

x.To

ughn

ess

incr

ease

sin

ano

n-lin

earm

anne

r(+

808%

at4,

264

s−1

rela

tive

to1,

370

s−1 ).

Gam

aB

.eta

l.(2

001)

[45]

S-2

glas

s/vi

nyle

ster

2Dpl

ain

wea

ve:–

/–(G

FRP-

W)

LSLF

(Ins

tron

-not

spec

.)[R

]

Com

pres

sion

SHPB

[R]

200

-160

0St

rain

sm

easu

red

dire

ctly

from

spec

imen

sus

ing

stra

inga

uges

.In

put

puls

efr

omSH

PBhi

ghly

non-

unif

orm

.St

rain

mea

sure

dby

stra

inga

uges

mou

nted

onth

esp

ecim

enis

used

until

unlo

adin

g,th

enSH

PBth

eory

used

.Hig

hle

vels

ofdi

sper

sion

mak

est

ress

-str

ain

curv

esun

info

rmat

ive.

‘Non

-lin

ear’

stra

ins

are

defin

edto

acco

untf

orpa

rasi

ticst

rain

sfr

omdi

sper

sion

.Sp

ecim

ens

may

notr

each

quas

i-st

atic

stre

sseq

uilib

rium

prio

rto

failu

re.

Eff

ect

ofst

rain

rate

onm

odul

usno

tre

port

ed.

Stre

ngth

incr

ease

s(+

38%

at1,

125

s−1 )b

efor

ere

achi

ngan

appr

oxim

atel

yas

ympt

otic

valu

eat

high

erst

rain

rate

s.U

ltim

ate

stra

inin

crea

ses

(+98

%at

1,12

5s−

1 ),bu

tw

ithhi

ghun

cer-

tain

ty.

Gov

ende

rR.e

tal.

(201

1)[9

]gl

ass/

viny

lest

er2D

plai

nw

eave

:E-g

lass

24oz

./Der

akan

e80

84(G

FRP-

W)

EM

LF(Z

wic

kU

nive

rsal

)[C

]

Com

pres

sion

SHPB

[C]

510

Cro

sshe

addi

spla

cem

entu

sed

toes

timat

est

rain

due

toco

ncer

nsab

outs

trai

nga

uge

alig

nmen

t.Sm

alls

peci

men

spr

even

ted

the

use

ofex

tens

omet

ers.

Eff

ecto

fstr

ain

rate

onm

odul

usno

trep

orte

das

quas

i-st

atic

stre

sseq

uilib

rium

was

nota

chie

ved

until

late

inth

ete

st.

Stre

ngth

initi

ally

incr

ease

s(+

13%

at51

0s−

1 )but

decr

ease

sw

ithin

crea

sing

stra

inra

te(+

4%at

1,80

0s−

1 ).Sl

ight

redu

ctio

nin

ultim

ate

stra

in(-

5%).

Ger

lach

R.e

tal.

(201

2)[1

0]ca

rbon

/epo

xy3D

wea

ve:(

Tena

xH

TS/

HTA

)/R

TM

-6(3

D-W

)E

MLF

(not

spec

.)H

LF(I

tm.s

−1 )[

R]

Com

pres

sion

SHPB

[R]

0.00

4-6

,000

Stra

inw

asm

easu

red

usin

ga

lase

rex

tens

omet

erfo

rqu

asi-

stat

icte

sts.

At

inte

rmed

iate

stra

ins

digi

tal

spec

kle

phot

ogra

phy

was

used

.M

odifi

eddi

rect

impa

ctSH

PBus

edfo

rhi

ghst

rain

rate

test

ing.

Com

pres

sion

stre

ss-s

trai

nre

spon

seat

high

stra

inra

tes

show

sso

me

wav

ines

sdu

eto

disp

ersi

on.S

tren

gth

mea

sure

das

max

imum

stre

ssbe

fore

unst

able

failu

re.

Tang

ent

mod

ulus

(mea

sure

dat

300

MPa

)in

crea

ses

(+43

%at

6,00

0s−

1 ).N

eglig

ible

stra

inra

teef

fect

onst

reng

th.

18

Shah

Kha

nM

.Z.&

Sim

pson

G.

(200

0)[5

0]ca

rbon

/epo

xy2D

plai

nw

eave

:DF1

400/

Syno

lite

0288

-T1

resi

n(C

FRP-

W)

HLF

[R]

0.00

1-1

0Q

uasi

-sta

ticst

rain

ses

timat

edus

ing

cros

shea

ddi

spla

cem

ent

corr

ecte

dfo

rco

mpl

ianc

e.H

ydra

ulic

load

fram

eus

edto

load

atin

term

edia

test

rain

rate

s.St

reng

than

dul

timat

est

rain

take

nat

poin

tof

max

imum

stre

ss.

Inco

nsis

tent

failu

rem

odes

thou

ghtt

oco

ntri

bute

tosc

atte

rin

mea

sure

dul

timat

epa

ram

e-te

rs.

Ela

stic

mod

ulus

incr

ease

s(+

25%

at10

s−1 ),

stre

ngth

incr

ease

s(+

21%

at10

s−1 ),

and

stra

inin

crea

ses(

+11%

at10

s−1 ).

Sign

ifica

ntsc

atte

rin

allm

easu

red

para

met

ers

(up

to±

25%

,12

%an

d33

%fo

rel

astic

mod

ulus

,st

reng

than

dul

timat

est

rain

,res

pect

ivel

y).

Shen

etal

.(20

12)[

51]

glas

s/vi

nyle

ster

3Dw

eave

:E

-gla

ss/M

L-5

06(3

D-

W)

HLF

(MTS

810)

[R]

Com

pres

sion

SHPB

[R]

0.00

1-1

,200

Hyd

raul

iclo

adfr

ame

used

tote

stat

quas

i-st

atic

and

inte

rmed

iate

stra

inra

tes.

Stre

ssst

rain

curv

esar

eve

ryno

n-lin

eara

ndex

hibi

tver

yla

rge

incr

ease

inth

eta

ngen

tmod

ulus

(defi

ned

abov

e0.

025

stra

in).

Unc

lear

how

man

ysp

ecim

ens

wer

ete

sted

.U

nrea

listic

ally

high

effe

ctof

stra

inra

teon

the

tang

entm

odul

ussu

gges

tssp

ecim

ens

are

noti

na

stat

eof

stre

sseq

uilib

rium

.

Tang

entm

odul

usin

crea

ses

(+35

0%at

1,20

0s−

1 )with

very

high

unce

rtai

nty

(±79

%).

Stre

ngth

incr

ease

s(+

8%at

1,20

0s−

1 )and

ultim

ate

stra

inde

crea

ses

(-50

%1,

200

s−1 ).

Aki

leta

l.(2

003)

[52]

glas

s/vi

nyle

ster

2Dw

eave

:S-2

glas

s/–

(GFR

P-W

)H

LF(n

otsp

ec.)

[R,C

]

Com

pres

sion

SHPB

[C]

0.00

1-9

00Ta

ngen

tm

odul

us,

fitte

dto

late

rre

gion

of’li

near

’re

spon

sean

dus

edto

estim

ate

elas

ticm

odul

us.

Stra

inra

tese

nsiti

vebe

havi

our

attr

ibut

edto

visc

oela

stic

prop

ertie

sof

the

mat

rix.

Con

sist

ents

hear

failu

rem

ode

betw

een

quas

i-st

atic

and

high

stra

inra

tete

sts.

Tang

entm

odul

usin

crea

ses(

+79%

at90

0s−

1 )with

high

unce

rtai

nty

(±26

%),

stre

ngth

incr

ease

s(+

29%

at90

0s−

1 ),an

dul

timat

est

rain

decr

ease

ssl

ight

ly(-

6%at

900

s−1 ).

Pank

owet

al.(

2011

)[27

]gl

ass/

epox

y3D

wea

ve:Z

-fibr

e/SC

-15

HLF

(not

spec

.)[R

]

Com

pres

sion

SHPB

[C]

QS

-175

0U

sed

2DD

ICpe

rfor

med

with

high

spee

dca

mer

ato

mea

sure

stra

inon

the

spec

imen

.Po

orsp

atia

land

tem

pora

lres

olut

ion

resu

ltsin

high

erro

r(>

5%st

rain

).N

ode

tails

prov

ided

onth

eD

ICse

tup.

Hig

hst

rain

rate

test

ssu

ffer

from

high

leve

lsof

disp

ersi

on(o

scill

atio

nsin

stre

ss-s

trai

nre

spon

se).

Thi

sin

trod

uces

unce

rtai

nty

inst

reng

than

dul

timat

est

rain

mea

sure

men

ts.

Eff

ect

ofst

rain

rate

onm

odul

usno

tre

port

edqu

antit

ativ

ely.

Stra

inra

teap

-pe

ars

toha

vene

glig

ible

effe

cton

elas

ticm

odul

us.S

tren

gth

incr

ease

sre

lativ

eto

quas

i-st

atic

valu

es(+

11%

at1,

750

s−1 )b

utno

tstr

ain

rate

sens

itive

(with

insc

atte

r).

Ulti

mat

est

rain

sin

crea

sere

lativ

eto

quas

i-st

atic

valu

es(+

20%

at1,

750

s−1 )b

utal

sono

tstr

ain

rate

sens

itive

(with

insc

atte

r).

Gud

enet

al.(

2004

)[53

]gl

ass/

epox

y2D

wea

ve:S

-2gl

ass/

SC-1

5E

MLF

(Shi

mad

zuAG

-I)[

C]

Com

pres

sion

SHPB

[C]

0.00

01-1

,100

Com

pres

sive

mod

ulus

com

pute

dus

ing

linea

rre

gion

ofst

ress

-str

ain

curv

eat

4%st

rain

.St

rain

rate

limite

dto

1,10

0s−

1 ,ab

ove

whi

chqu

asi-

stat

icst

ress

equi

libri

umco

uld

not

beac

hiev

edpr

ior

failu

re.

Con

sist

ent

shea

rfa

ilure

mod

ebe

twee

nqu

asi-

stat

ican

dhi

ghst

rain

rate

test

s.

Ela

stic

mod

ulus

incr

ease

s(+

70%

at1,

100

s−1 ),

stre

ngth

incr

ease

s(+

53%

at1,

100

s−1 ),

ultim

ate

stra

inde

crea

ses

slig

htly

with

incr

easi

ngst

rain

rate

(-3%

at1,

100

s−1 ).

19


―21―

Tabl

e2:

Sum

mar

yof

publ

ishe

dst

udie

son

stra

inra

teef

fect

sof

inte

rlam

inar

tens

ilepr

oper

ties

offib

re-r

einf

orce

dpo

lym

erco

mpo

site

s.N

otes

:C

onst

ituen

tmat

eria

lslis

ted

inth

efo

rmat

:‘fi

bre/

mat

rix’

.M

ater

iall

abel

sar

ein

clud

edin

‘()’

for

asso

ciat

ion

with

Fig.

8-

Fig.

10.

Qua

si-s

tatic

:ita

licty

pefa

ce;h

igh

stra

inra

te:

regu

lar

type

face

;tes

tmet

hod:

elec

tro-

mec

hani

call

oad

fram

e(E

ML

F),h

ydra

ulic

load

fram

e(H

LF)

,hig

h-sp

eed

load

fram

e(H

SLF)

,spl

itH

opki

nson

pres

sure

bar(

SHPB

);sp

ecim

enge

omet

ry(i

n‘[

]’):

W=

wai

sted

,D=

dog-

bone

,L=

L-s

hape

d/cu

rve

beam

,O=

off-

axis

,C=

cylin

dric

alsp

ecim

ens.

Ref

eren

ceM

ater

ial

Test

[Spe

cim

en]

Stra

inR

ate

(s−

1 )N

otes

Nak

aiK

.&Y

okoy

ama

T.(2

014)

,(2

016)

[6,3

5]ca

rbon

/epo

xypr

e-pr

eg.(

[0],

[0/9

0]s)

:T

700S

/252

1,T

700S

/250

0(C

FRP-

PP)

EM

LF(I

nstr

on55

00R

)[W

]

Tens

ion

SHPB

[C-W

]

0.02

–60

Wai

sted

spec

imen

sw

ere

bond

edto

mag

nesi

umal

loy

end

caps

usin

gD

P-46

0ep

oxy.

Stra

ins

unde

rqu

asi-

stat

ican

dhi

ghst

rain

rate

load

ing

wer

em

easu

red

usin

gst

rain

gaug

es.

Spec

imen

appe

ars

tobe

ina

stat

eof

quas

i-st

atic

stre

sseq

uilib

rium

for

muc

hof

the

test

.St

rain

sco

mpu

ted

usin

gSH

PBov

eres

timat

etr

uest

rain

sdue

tono

n-un

ifor

mde

form

atio

nof

the

gaug

ere

gion

.

Eff

ecto

fstr

ain

rate

onel

astic

mod

ulus

notr

epor

ted.

Stre

ngth

incr

ease

sm

ore

for

the

cros

s-pl

yla

yup

com

pare

dto

the

unid

irec

tiona

lla

yup

(+13

0%at

50s−

1([

0/90

] s),

+77%

at50

s−1

([0]

s)),

and

ultim

ate

stra

inin

crea

ses

mor

efo

rth

ecr

oss-

ply

layu

pco

mpa

red

toth

eun

idir

ectio

nal

layu

p(+

31%

at50

s−1

([0/

90] s

),-1

0%at

50s−

1([

0]s)

).L

arge

unce

rtai

nty

inst

reng

th(u

pto

±51

%fo

r[0

/90]

san

d±

18%

for

[0] s

at50

s−1 )

and

ultim

ate

stra

ins

(up

to±

61%

for[

0/90

] san

d±

43%

for[

0]s

at50

s−1 ).

Lif

shitz

J.&

Leb

erH

.(1

998)

[58]

carb

on/e

poxy

pre-

preg

.:A

S4/3

502

([0]

s)(C

FRP-

PP)

glas

s/ep

oxy

2Dpl

ain

wea

ve:N

EM

A/A

STM

G-1

0(G

FRP-

W)

Tens

ion

SHPB

[C-W

-O

]12

7-19

5Te

nsio

n,sh

ear

and

com

bine

dte

nsio

n-sh

ear

beha

viou

rw

asst

udie

dus

ing

two

type

sof

spec

imen

s.W

aist

edsp

ecim

ens

wer

eus

edfo

rte

nsio

n,an

dof

f-ax

isw

aist

edsp

ecim

ens

wer

eus

edfo

rte

nsio

n/sh

ear

load

ing.

Off

-axi

ssp

ecim

ens

wer

efo

rmed

bybo

ndin

gtw

oha

lves

toge

ther

.B

onde

dsp

ecim

ens

very

diffi

cult

tom

achi

nefr

omC

FRP

and

the

resu

ltsha

dto

om

uch

scat

ter

tobe

mea

ning

ful.

Spec

imen

sbo

nded

toin

cide

ntan

dtr

ansm

itter

bars

(Hys

onad

hesi

ve).

Osc

illat

ions

inst

ress

-str

ain

resp

onse

and

erra

ticsh

ape

clos

eto

failu

reth

ough

tto

bea

resu

ltof

mic

rocr

ack

form

atio

n.St

rain

sm

easu

red

usin

gst

rain

gaug

es.N

oqu

asi-

stat

icul

timat

est

rain

sre

port

ed.

Ela

stic

mod

ulus

incr

ease

s(+

41%

for

carb

on/e

poxy

at19

5s−

1 ,+7

%fo

rgl

ass/

epox

yat

127

s−1 ).

Stre

ngth

incr

ease

sfo

rth

eca

rbon

/epo

xyla

min

ate

(+36

%at

195

s−1 ),

butd

ecre

ases

for

the

glas

s/ep

oxy

lam

inat

e(-

14%

at12

7s−

1 ).

Nai

kN

.K.e

tal.

(201

0)[6

1]gl

ass/

epox

y2D

plai

nw

eave

:E

-gla

ss/L

Y55

6(G

FRP-

W)

LFno

tspe

c.[C

-W]

Tens

ion

SHPB

[C-W

]

140

–40

0Sp

ecim

ens

bond

edto

end

tabs

whi

chfit

insi

dein

cide

ntan

dtr

ansm

itter

bars

.A

utho

rscl

aim

spec

imen

reac

hqu

asi-

stat

icst

ress

equi

libri

um;h

owev

er,p

lots

ofre

actio

nfo

rces

dono

tapp

eare

qual

duri

nglo

adin

g.

Stre

ngth

incr

ease

ssi

gnifi

cant

lyw

hen

com

pare

dto

quas

i-st

atic

valu

es(+

88%

at39

0s−

1 ).T

hein

fluen

ceof

stra

inra

teon

stre

ngth

ism

uch

low

erw

ithin

the

rang

eof

high

stra

inra

tes

cons

ider

ed(+

11%

at39

0s−

1re

lativ

eto

145

s−1 ).

Ger

lach

R.e

tal.

(201

3)[1

9]S2

-gla

ss/e

poxy

pre-

preg

.:–/

FM94

(cut

from

GL

AR

Esh

eets

)(G

FRP-

PP)

EM

LF(n

otsp

ec.)

[C-W

]

Tens

ion

SHPB

[C-W

]

5x

10−

4 ,10,

200

Atte

mpt

sto

mea

sure

inte

rlam

inar

stre

ngth

from

GL

AR

Epl

ates

.Sp

ecim

ens

bond

eddi

rect

lyto

inci

dent

and

tran

smitt

erba

rs.

Due

toth

esm

all

effe

ctiv

ega

uge

leng

th(2

mm

),no

mea

ning

fuls

trai

nm

easu

rem

ents

coul

dbe

perf

orm

edus

ing

digi

tals

peck

leph

otog

raph

y.L

arge

scat

ter

inth

roug

h-th

ickn

ess

dire

c-tio

nat

trib

uted

toin

cons

iste

ntfa

ilure

mod

esan

dva

riat

ion

inm

anuf

actu

ring

the

GL

AR

Epl

ates

.

Eff

ect

ofst

rain

rate

onel

astic

mod

ulus

and

ultim

ate

stra

inno

tre

port

ed.

Stre

ngth

incr

ease

d(+

45%

(±10

5%))

at20

0s−

1 .

20

Huf

enba

chW

.eta

l.(2

013)

[60]

glas

s/ep

oxy

2Dw

eave

:(M

KF

&Tw

inte

x)(G

FRP)

Tens

ion

SHPB

[D,L

]5

x10

−4

-400

Lar

gesc

atte

rin

SHPB

tens

ion

test

sat

trib

uted

tore

info

rcem

enta

rchi

tect

ure.

Aut

hors

conc

lude

that

SHPB

isno

tsu

itabl

efo

rte

stin

gco

arse

text

ilear

chi-

tect

ures

.Var

ying

leve

lsof

com

pact

ion

inL

-sha

ped

beam

spec

imen

sre

sulte

din

unac

cept

able

scat

ter(

resu

ltsno

trep

orte

d).

Eff

ects

ofst

rain

rate

onm

odul

usno

trep

orte

d.In

crea

sing

stre

ngth

(+93

%at

400

s−1 )w

ithap

prox

imat

ely

cons

tant

stra

inat

failu

re(w

ithin

scat

ter:

-75%

–+8

7%at

44s−

1to

-87%

–+63

9%at

400

s−1 ).

Gov

ende

rR.e

tal.

(201

1)[9

]gl

ass/

viny

lest

er2D

plai

nw

eave

:E-g

lass

24oz

./Der

akan

e80

84(G

FRP-

W)

Com

pres

sion

SHPB

-sp

all[

C]

1,80

0N

oqu

asi-

stat

icva

lues

repo

rted

due

toco

nsis

tent

failu

rew

ithin

the

grip

s.A

spal

lte

stw

asus

edto

mea

sure

tens

ilest

reng

th.

Puls

etim

e-sh

iftin

gus

edto

estim

ate

forc

esin

the

spec

imen

atfa

ilure

.A

high

spee

dca

mer

aw

asus

edto

qual

itativ

ely

mon

itort

hefa

ilure

.

The

effe

ctof

stra

inra

teon

the

elas

ticm

odul

usan

dul

timat

est

rain

wer

eno

tre

port

ed.T

heav

erag

est

reng

thw

as12

5M

Pa(s

td.d

ev.=

21.2

MPa

).A

utho

rsco

mpa

reth

isto

the

stre

ngth

quot

edby

the

epox

ym

anuf

actu

rer

(76

MPa

)to

conc

lude

that

the

mat

eria

llik

ely

exhi

bits

asi

gnifi

cant

sens

itivi

tyto

stra

inra

te.

Ger

lach

R.e

tal.

(201

2)[1

0]ca

rbon

/epo

xy3D

wea

ve(T

enax

HT

S/H

TA)/

RT

M-6

(3D

-W)

EM

LF(n

otsp

ec.)

[cro

ss]

HLF

(Itm

.s−

1 )[C

ROSS

]

Com

pres

sion

SHPB

[CR

OSS

]

0.00

4-1

1,00

0C

ross

-spe

cim

ens

used

toin

trod

uce

load

with

out

edge

effe

cts

for

3Dre

in-

forc

emen

t.Sp

ecim

ens

load

edin

com

pres

sion

with

aSH

PBus

ing

U-s

hape

dfix

ture

.Sp

ecim

enge

omet

ryan

dfix

ture

mad

eno

n-co

ntac

tm

easu

rem

ents

proh

ibiti

ve.S

tres

sst

ate

notu

nifo

rmdu

eto

smal

lfille

tsbe

twee

ncr

oss

arm

s.

Influ

ence

ofst

rain

rate

onel

astic

mod

ulus

and

ultim

ate

stra

inno

tre

port

ed.

Stre

ngth

gene

rally

incr

ease

s(+

84%

–+9

4%)

with

incr

easi

ngst

rain

rate

,but

with

high

scat

ter(±

60%

).

Huf

enba

chW

.(20

11)[

18]

glas

s/po

lypr

opyl

ene

2Dpl

ain

wea

ve:T

win

tex

TPP

6074

5(G

FRP-

W)

EM

LF(Z

WIC

KZ2

50)[

L]

HSL

F(I

NST

RO

NV

HS

160/

20)[

L]

10−

4-7

3DD

ICus

edon

L-s

hape

dbe

amsp

ecim

ens.

Sign

ifica

ntsc

atte

rin

the

optic

alm

easu

rem

ents

attr

ibut

edto

the

coar

sete

xtile

surf

ace

patte

rn.

Het

erog

eneo

usst

rain

field

sth

roug

hth

ickn

ess.

Stra

ins

aver

aged

over

subs

ets.

Lim

ited

mea

sure

men

tres

olut

ion

atin

term

edia

test

rain

rate

s(H

Sca

mer

are

solu

tion)

.

Eff

ect

ofst

rain

rate

onm

odul

usan

dul

timat

est

rain

not

repo

rted

.St

reng

thin

crea

ses

sign

ifica

ntly

(+20

4%at

1s−

1an

d+1

71%

at7

s−1 ).

21


―22―

Tabl

e2:

Sum

mar

yof

publ

ishe

dst

udie

son

stra

inra

teef

fect

sof

inte

rlam

inar

tens

ilepr

oper

ties

offib

re-r

einf

orce

dpo

lym

erco

mpo

site

s.N

otes

:C

onst

ituen

tmat

eria

lslis

ted

inth

efo

rmat

:‘fi

bre/

mat

rix’

.M

ater

iall

abel

sar

ein

clud

edin

‘()’

for

asso

ciat

ion

with

Fig.

8-

Fig.

10.

Qua

si-s

tatic

:ita

licty

pefa

ce;h

igh

stra

inra

te:

regu

lar

type

face

;tes

tmet

hod:

elec

tro-

mec

hani

call

oad

fram

e(E

ML

F),h

ydra

ulic

load

fram

e(H

LF)

,hig

h-sp

eed

load

fram

e(H

SLF)

,spl

itH

opki

nson

pres

sure

bar(

SHPB

);sp

ecim

enge

omet

ry(i

n‘[

]’):

W=

wai

sted

,D=

dog-

bone

,L=

L-s

hape

d/cu

rve

beam

,O=

off-

axis

,C=

cylin

dric

alsp

ecim

ens.

Ref

eren

ceM

ater

ial

Test

[Spe

cim

en]

Stra

inR

ate

(s−

1 )N

otes

Nak

aiK

.&Y

okoy

ama

T.(2

014)

,(2

016)

[6,3

5]ca

rbon

/epo

xypr

e-pr

eg.(

[0],

[0/9

0]s)

:T

700S

/252

1,T

700S

/250

0(C

FRP-

PP)

EM

LF(I

nstr

on55

00R

)[W

]

Tens

ion

SHPB

[C-W

]

0.02

–60

Wai

sted

spec

imen

sw

ere

bond

edto

mag

nesi

umal

loy

end

caps

usin

gD

P-46

0ep

oxy.

Stra

ins

unde

rqu

asi-

stat

ican

dhi

ghst

rain

rate

load

ing

wer

em

easu

red

usin

gst

rain

gaug

es.

Spec

imen

appe

ars

tobe

ina

stat

eof

quas

i-st

atic

stre

sseq

uilib

rium

for

muc

hof

the

test

.St

rain

sco

mpu

ted

usin

gSH

PBov

eres

timat

etr

uest

rain

sdue

tono

n-un

ifor

mde

form

atio

nof

the

gaug

ere

gion

.

Eff

ecto

fstr

ain

rate

onel

astic

mod

ulus

notr

epor

ted.

Stre

ngth

incr

ease

sm

ore

for

the

cros

s-pl

yla

yup

com

pare

dto

the

unid

irec

tiona

lla

yup

(+13

0%at

50s−

1([

0/90

] s),

+77%

at50

s−1

([0]

s)),

and

ultim

ate

stra

inin

crea

ses

mor

efo

rth

ecr

oss-

ply

layu

pco

mpa

red

toth

eun

idir

ectio

nal

layu

p(+

31%

at50

s−1

([0/

90] s

),-1

0%at

50s−

1([

0]s)

).L

arge

unce

rtai

nty

inst

reng

th(u

pto

±51

%fo

r[0

/90]

san

d±

18%

for

[0] s

at50

s−1 )

and

ultim

ate

stra

ins

(up

to±

61%

for[

0/90

] san

d±

43%

for[

0]s

at50

s−1 ).

Lif

shitz

J.&

Leb

erH

.(1

998)

[58]

carb

on/e

poxy

pre-

preg

.:A

S4/3

502

([0]

s)(C

FRP-

PP)

glas

s/ep

oxy

2Dpl

ain

wea

ve:N

EM

A/A

STM

G-1

0(G

FRP-

W)

Tens

ion

SHPB

[C-W

-O

]12

7-19

5Te

nsio

n,sh

ear

and

com

bine

dte

nsio

n-sh

ear

beha

viou

rw

asst

udie

dus

ing

two

type

sof

spec

imen

s.W

aist

edsp

ecim

ens

wer

eus

edfo

rte

nsio

n,an

dof

f-ax

isw

aist

edsp

ecim

ens

wer

eus

edfo

rte

nsio

n/sh

ear

load

ing.

Off

-axi

ssp

ecim

ens

wer

efo

rmed

bybo

ndin

gtw

oha

lves

toge

ther

.B

onde

dsp

ecim

ens

very

diffi

cult

tom

achi

nefr

omC

FRP

and

the

resu

ltsha

dto

om

uch

scat

ter

tobe

mea

ning

ful.

Spec

imen

sbo

nded

toin

cide

ntan

dtr

ansm

itter

bars

(Hys

onad

hesi

ve).

Osc

illat

ions

inst

ress

-str

ain

resp

onse

and

erra

ticsh

ape

clos

eto

failu

reth

ough

tto

bea

resu

ltof

mic

rocr

ack

form

atio

n.St

rain

sm

easu

red

usin

gst

rain

gaug

es.N

oqu

asi-

stat

icul

timat

est

rain

sre

port

ed.

Ela

stic

mod

ulus

incr

ease

s(+

41%

for

carb

on/e

poxy

at19

5s−

1 ,+7

%fo

rgl

ass/

epox

yat

127

s−1 ).

Stre

ngth

incr

ease

sfo

rth

eca

rbon

/epo

xyla

min

ate

(+36

%at

195

s−1 ),

butd

ecre

ases

for

the

glas

s/ep

oxy

lam

inat

e(-

14%

at12

7s−

1 ).

Nai

kN

.K.e

tal.

(201

0)[6

1]gl

ass/

epox

y2D

plai

nw

eave

:E

-gla

ss/L

Y55

6(G

FRP-

W)

LFno

tspe

c.[C

-W]

Tens

ion

SHPB

[C-W

]

140

–40

0Sp

ecim

ens

bond

edto

end

tabs

whi

chfit

insi

dein

cide

ntan

dtr

ansm

itter

bars

.A

utho

rscl

aim

spec

imen

reac

hqu

asi-

stat

icst

ress

equi

libri

um;h

owev

er,p

lots

ofre

actio

nfo

rces

dono

tapp

eare

qual

duri

nglo

adin

g.

Stre

ngth

incr

ease

ssi

gnifi

cant

lyw

hen

com

pare

dto

quas

i-st

atic

valu

es(+

88%

at39

0s−

1 ).T

hein

fluen

ceof

stra

inra

teon

stre

ngth

ism

uch

low

erw

ithin

the

rang

eof

high

stra

inra

tes

cons

ider

ed(+

11%

at39

0s−

1re

lativ

eto

145

s−1 ).

Ger

lach

R.e

tal.

(201

3)[1

9]S2

-gla

ss/e

poxy

pre-

preg

.:–/

FM94

(cut

from

GL

AR

Esh

eets

)(G

FRP-

PP)

EM

LF(n

otsp

ec.)

[C-W

]

Tens

ion

SHPB

[C-W

]

5x

10−

4 ,10,

200

Atte

mpt

sto

mea

sure

inte

rlam

inar

stre

ngth

from

GL

AR

Epl

ates

.Sp

ecim

ens

bond

eddi

rect

lyto

inci

dent

and

tran

smitt

erba

rs.

Due

toth

esm

all

effe

ctiv

ega

uge

leng

th(2

mm

),no

mea

ning

fuls

trai

nm

easu

rem

ents

coul

dbe

perf

orm

edus

ing

digi

tals

peck

leph

otog

raph

y.L

arge

scat

ter

inth

roug

h-th

ickn

ess

dire

c-tio

nat

trib

uted

toin

cons

iste

ntfa

ilure

mod

esan

dva

riat

ion

inm

anuf

actu

ring

the

GL

AR

Epl

ates

.

Eff

ect

ofst

rain

rate

onel

astic

mod

ulus

and

ultim

ate

stra

inno

tre

port

ed.

Stre

ngth

incr

ease

d(+

45%

(±10

5%))

at20

0s−

1 .

20

Huf

enba

chW

.eta

l.(2

013)

[60]

glas

s/ep

oxy

2Dw

eave

:(M

KF

&Tw

inte

x)(G

FRP)

Tens

ion

SHPB

[D,L

]5

x10

−4

-400

Lar

gesc

atte

rin

SHPB

tens

ion

test

sat

trib

uted

tore

info

rcem

enta

rchi

tect

ure.

Aut

hors

conc

lude

that

SHPB

isno

tsu

itabl

efo

rte

stin

gco

arse

text

ilear

chi-

tect

ures

.Var

ying

leve

lsof

com

pact

ion

inL

-sha

ped

beam

spec

imen

sre

sulte

din

unac

cept

able

scat

ter(

resu

ltsno

trep

orte

d).

Eff

ects

ofst

rain

rate

onm

odul

usno

trep

orte

d.In

crea

sing

stre

ngth

(+93

%at

400

s−1 )w

ithap

prox

imat

ely

cons

tant

stra

inat

failu

re(w

ithin

scat

ter:

-75%

–+8

7%at

44s−

1to

-87%

–+63

9%at

400

s−1 ).

Gov

ende

rR.e

tal.

(201

1)[9

]gl

ass/

viny

lest

er2D

plai

nw

eave

:E-g

lass

24oz

./Der

akan

e80

84(G

FRP-

W)

Com

pres

sion

SHPB

-sp

all[

C]

1,80

0N

oqu

asi-

stat

icva

lues

repo

rted

due

toco

nsis

tent

failu

rew

ithin

the

grip

s.A

spal

lte

stw

asus

edto

mea

sure

tens

ilest

reng

th.

Puls

etim

e-sh

iftin

gus

edto

estim

ate

forc

esin

the

spec

imen

atfa

ilure

.A

high

spee

dca

mer

aw

asus

edto

qual

itativ

ely

mon

itort

hefa

ilure

.

The

effe

ctof

stra

inra

teon

the

elas

ticm

odul

usan

dul

timat

est

rain

wer

eno

tre

port

ed.T

heav

erag

est

reng

thw

as12

5M

Pa(s

td.d

ev.=

21.2

MPa

).A

utho

rsco

mpa

reth

isto

the

stre

ngth

quot

edby

the

epox

ym

anuf

actu

rer

(76

MPa

)to

conc

lude

that

the

mat

eria

llik

ely

exhi

bits

asi

gnifi

cant

sens

itivi

tyto

stra

inra

te.

Ger

lach

R.e

tal.

(201

2)[1

0]ca

rbon

/epo

xy3D

wea

ve(T

enax

HT

S/H

TA)/

RT

M-6

(3D

-W)

EM

LF(n

otsp

ec.)

[cro

ss]

HLF

(Itm

.s−

1 )[C

ROSS

]

Com

pres

sion

SHPB

[CR

OSS

]

0.00

4-1

1,00

0C

ross

-spe

cim

ens

used

toin

trod

uce

load

with

out

edge

effe

cts

for

3Dre

in-

forc

emen

t.Sp

ecim

ens

load

edin

com

pres

sion

with

aSH

PBus

ing

U-s

hape

dfix

ture

.Sp

ecim

enge

omet

ryan

dfix

ture

mad

eno

n-co

ntac

tm

easu

rem

ents

proh

ibiti

ve.S

tres

sst

ate

notu

nifo

rmdu

eto

smal

lfille

tsbe

twee

ncr

oss

arm

s.

Influ

ence

ofst

rain

rate

onel

astic

mod

ulus

and

ultim

ate

stra

inno

tre

port

ed.

Stre

ngth

gene

rally

incr

ease

s(+

84%

–+9

4%)

with

incr

easi

ngst

rain

rate

,but

with

high

scat

ter(±

60%

).

Huf

enba

chW

.(20

11)[

18]

glas

s/po

lypr

opyl

ene

2Dpl

ain

wea

ve:T

win

tex

TPP

6074

5(G

FRP-

W)

EM

LF(Z

WIC

KZ2

50)[

L]

HSL

F(I

NST

RO

NV

HS

160/

20)[

L]

10−

4-7

3DD

ICus

edon

L-s

hape

dbe

amsp

ecim

ens.

Sign

ifica

ntsc

atte

rin

the

optic

alm

easu

rem

ents

attr

ibut

edto

the

coar

sete

xtile

surf

ace

patte

rn.

Het

erog

eneo

usst

rain

field

sth

roug

hth

ickn

ess.

Stra

ins

aver

aged

over

subs

ets.

Lim

ited

mea

sure

men

tres

olut

ion

atin

term

edia

test

rain

rate

s(H

Sca

mer

are

solu

tion)

.

Eff

ect

ofst

rain

rate

onm

odul

usan

dul

timat

est

rain

not

repo

rted

.St

reng

thin

crea

ses

sign

ifica

ntly

(+20

4%at

1s−

1an

d+1

71%

at7

s−1 ).

21


―23―

Med

ina

J.&

Har

ding

J.(2

000)

[59]

carb

on/e

poxy

pre-

preg

.:T

300/

924

(CFR

P-PP

)

carb

on/e

poxy

2Dpl

ain

wea

ve:F

ibre

dux

924C

/833

(CFR

P-W

)

R-g

lass

/epo

xy2D

plai

nw

eave

:Fib

redu

x92

4G/2

0982

(GFR

P-W

)

LFno

tspe

c.[W

-C]

Tens

ion

SHPB

[W-C

]

5-9

40W

aist

edsp

ecim

ens

bond

edto

stee

len

dca

ps.

Stra

inga

uges

occa

sion

ally

faile

dbe

fore

the

spec

imen

,or

wer

epo

sitio

ned

off

ofth

efa

ilure

plan

e.L

ongi

tudi

nal

stra

inga

uge

show

spe

rsis

tent

osci

llatio

nsin

stra

in.

Res

ults

show

that

rein

forc

emen

tarc

hite

ctur

eha

sla

rger

influ

ence

than

fibre

mat

eria

l.Po

isso

n’s

ratio

doub

led

whe

ngl

ass

fibre

sus

edco

mpa

red

toca

rbon

fibre

s.

carb

on/e

poxy

pre-

preg

:Te

nsile

mod

ulus

incr

ease

sw

ithst

rain

rate

(+31

%),

tens

ilest

reng

thin

crea

ses

(+12

%),

and

tens

ilest

rain

also

incr

ease

s(+

22%

);

carb

on/e

poxy

2Dpl

ain

wea

ve:

Tens

ilem

odul

usin

crea

ses

with

stra

inra

te(+

7%),

tens

ilest

reng

thin

crea

ses

(+37

%),

and

tens

ilest

rain

also

incr

ease

s(+

63%

);

glas

s/ep

oxy

2Dpl

ain

wea

ve:

Tens

ilem

odul

usde

crea

ses

with

stra

inra

te(-

13%

),te

nsile

stre

ngth

incr

ease

s(+

40%

),an

dte

nsile

stra

inal

soin

crea

ses

(+65

%).

22

Tabl

e3:

Sum

mar

yof

publ

ishe

dst

udie

son

stra

inra

teef

fect

sof

inte

rlam

inar

shea

rpr

oper

ties

offib

re-r

einf

orce

dpo

lym

erco

mpo

site

s.N

otes

:C

onst

ituen

tmat

eria

lslis

ted

inth

efo

rmat

:‘fi

bre/

mat

rix’

.M

ater

iall

abel

sar

ein

clud

edin

‘()’

for

asso

ciat

ion

with

Fig.

11-

Fig.

13.

Qua

si-s

tatic

:ita

licty

pefa

ce;h

igh

stra

inra

te:

regu

lar

type

face

;tes

tmet

hod:

elec

tro-

mec

hani

call

oad

fram

e(E

ML

F),h

ydra

ulic

load

fram

e(H

LF)

,hig

h-sp

eed

load

fram

e(H

SLF)

,spl

itH

opki

nson

pres

sure

bar(

SHPB

);sp

ecim

enge

omet

ry(i

n‘[

]’):

SBS

=sh

ortb

eam

shea

r(3

poin

tben

d),I

=no

tche

d/un

notc

hed

shea

rtes

t,R

=re

ctan

gula

r/cu

bic

spec

imen

s,O

=of

f-ax

is,T

=th

in-w

alle

dtu

be,S

L=

sing

lela

p-sh

earj

oint

,DL

=do

uble

lap-

shea

rjoi

nt.

Ref

eren

ceM

ater

ial

Test

[Spe

cim

en]

Stra

inR

ate

(s−

1 )N

otes

Nai

kN

.K.e

tal.

(200

7)[5

]ca

rbon

/epo

xy2D

plai

n-w

eave

:–/–

(CFR

P-W

),E

-gla

ss/e

poxy

2Dpl

ain

wea

ve:–

/–(G

FRP-

W)

LFno

tspe

c.[S

L]

Tors

ion

SHPB

[T]

Com

pres

sion

SHPB

[SL

]

496

–1,

000

Sing

lela

pan

dtu

bula

rspe

cim

ens

cons

ider

edat

high

stra

inra

tes.

Vis

coel

astic

beha

viou

rof

mat

rix

and

less

time

for

dam

age

prop

agat

ion

resp

onsi

ble

for

incr

ease

insh

ear

stre

ngth

.Po

stfa

ilure

mic

rosc

opy

oftu

bula

rsp

ecim

ens

reve

als

feat

ures

asso

ciat

edw

itha

pure

shea

rst

ress

stat

e.Sh

ear

stre

ssm

ayno

tbe

cons

tant

due

toth

efa

bric

and

diff

eren

tpro

pert

ies

with

inth

esp

ecim

enth

ickn

ess.

Wal

lthi

ckne

ssse

tat3

mm

sinc

eth

inne

rw

alls

gave

inco

nsis

tent

resu

lts(t

houg

htto

bea

resu

ltof

man

ufac

turi

ngde

fect

s).

No

quas

i-st

atic

ultim

ate

stra

ins

prov

ided

.M

odul

uses

timat

edby

stre

ssan

dst

rain

atpo

int

whe

nqu

asi-

stat

icst

ress

equi

libri

umw

asth

ough

tto

beac

hiev

ed.

carb

on/e

poxy

2Dpl

ain

wea

ve:

Incr

ease

inm

odul

us(+

38%

),in

crea

sein

stre

ngth

(+69

%)

and

incr

ease

inul

timat

est

rain

(+41

%)

at1,

000

s−1

rela

-tiv

eto

496

s−1 ;

glas

s/ep

oxy

2Dpl

ain

wea

ve:

Incr

ease

inm

odul

us(+

29%

),in

crea

sein

stre

ngth

(+67

%)

and

incr

ease

inul

timat

est

rain

(+35

%)

at1,

000

s−1

rela

tive

to57

6s−

1 .

Har

ding

J.&

Don

gL

.(19

94)[

3]ca

rbon

/epo

xypr

e-pr

eg.:

T80

0/92

4([

0],[

0/90

],[±

45])

(CFR

P-PP

)LF

nots

pec.

[DL]

Tens

ion

SHPB

[DL

]

275

–33

2Sc

atte

ris

sola

rge

that

the

expe

rim

ents

cann

otbe

cons

ider

edas

proo

fof

ast

rain

rate

depe

nden

ce.I

mpr

oved

spec

imen

desi

gnre

quir

edif

stre

ngth

valu

esar

eto

beac

cept

edw

ithco

nfide

nce.

Nor

mal

stre

sspl

ays

asi

gnifi

cant

role

inth

efa

ilure

proc

ess

assh

own

bym

icro

grap

hsof

failu

resu

rfac

es.

Influ

ence

ofst

rain

rate

onsh

earm

odul

usno

trep

orte

d.

carb

on/e

poxy

pre-

preg

.[0]

(1-3

):sh

ear

stre

ngth

incr

ease

s(+

26%

)an

dul

timat

esh

ears

trai

nde

crea

ses

(-16

%)a

t275

s−1 .

carb

on/e

poxy

pre-

preg

.[0/

90](

2-3)

:sh

ear

stre

ngth

incr

ease

s(+

39%

)an

dul

timat

esh

ears

trai

nde

crea

ses

(-16

%)a

t332

s−1 .

carb

on/e

poxy

pre-

preg

.[±

45](

1-3)

:sh

ear

stre

ngth

incr

ease

s(+

38%

)an

dul

timat

esh

ear

stra

inde

crea

ses

(-22

%)

at28

1s−

1 .

23


―24―

Med

ina

J.&

Har

ding

J.(2

000)

[59]

carb

on/e

poxy

pre-

preg

.:T

300/

924

(CFR

P-PP

)

carb

on/e

poxy

2Dpl

ain

wea

ve:F

ibre

dux

924C

/833

(CFR

P-W

)

R-g

lass

/epo

xy2D

plai

nw

eave

:Fib

redu

x92

4G/2

0982

(GFR

P-W

)

LFno

tspe

c.[W

-C]

Tens

ion

SHPB

[W-C

]

5-9

40W

aist

edsp

ecim

ens

bond

edto

stee

len

dca

ps.

Stra

inga

uges

occa

sion

ally

faile

dbe

fore

the

spec

imen

,or

wer

epo

sitio

ned

off

ofth

efa

ilure

plan

e.L

ongi

tudi

nal

stra

inga

uge

show

spe

rsis

tent

osci

llatio

nsin

stra

in.

Res

ults

show

that

rein

forc

emen

tarc

hite

ctur

eha

sla

rger

influ

ence

than

fibre

mat

eria

l.Po

isso

n’s

ratio

doub

led

whe

ngl

ass

fibre

sus

edco

mpa

red

toca

rbon

fibre

s.

carb

on/e

poxy

pre-

preg

:Te

nsile

mod

ulus

incr

ease

sw

ithst

rain

rate

(+31

%),

tens

ilest

reng

thin

crea

ses

(+12

%),

and

tens

ilest

rain

also

incr

ease

s(+

22%

);

carb

on/e

poxy

2Dpl

ain

wea

ve:

Tens

ilem

odul

usin

crea

ses

with

stra

inra

te(+

7%),

tens

ilest

reng

thin

crea

ses

(+37

%),

and

tens

ilest

rain

also

incr

ease

s(+

63%

);

glas

s/ep

oxy

2Dpl

ain

wea

ve:

Tens

ilem

odul

usde

crea

ses

with

stra

inra

te(-

13%

),te

nsile

stre

ngth

incr

ease

s(+

40%

),an

dte

nsile

stra

inal

soin

crea

ses

(+65

%).

22

Tabl

e3:

Sum

mar

yof

publ

ishe

dst

udie

son

stra

inra

teef

fect

sof

inte

rlam

inar

shea

rpr

oper

ties

offib

re-r

einf

orce

dpo

lym

erco

mpo

site

s.N

otes

:C

onst

ituen

tmat

eria

lslis

ted

inth

efo

rmat

:‘fi

bre/

mat

rix’

.M

ater

iall

abel

sar

ein

clud

edin

‘()’

for

asso

ciat

ion

with

Fig.

11-

Fig.

13.

Qua

si-s

tatic

:ita

licty

pefa

ce;h

igh

stra

inra

te:

regu

lar

type

face

;tes

tmet

hod:

elec

tro-

mec

hani

call

oad

fram

e(E

ML

F),h

ydra

ulic

load

fram

e(H

LF)

,hig

h-sp

eed

load

fram

e(H

SLF)

,spl

itH

opki

nson

pres

sure

bar(

SHPB

);sp

ecim

enge

omet

ry(i

n‘[

]’):

SBS

=sh

ortb

eam

shea

r(3

poin

tben

d),I

=no

tche

d/un

notc

hed

shea

rtes

t,R

=re

ctan

gula

r/cu

bic

spec

imen

s,O

=of

f-ax

is,T

=th

in-w

alle

dtu

be,S

L=

sing

lela

p-sh

earj

oint

,DL

=do

uble

lap-

shea

rjoi

nt.

Ref

eren

ceM

ater

ial

Test

[Spe

cim

en]

Stra

inR

ate

(s−

1 )N

otes

Nai

kN

.K.e

tal.

(200

7)[5

]ca

rbon

/epo

xy2D

plai

n-w

eave

:–/–

(CFR

P-W

),E

-gla

ss/e

poxy

2Dpl

ain

wea

ve:–

/–(G

FRP-

W)

LFno

tspe

c.[S

L]

Tors

ion

SHPB

[T]

Com

pres

sion

SHPB

[SL

]

496

–1,

000

Sing

lela

pan

dtu

bula

rspe

cim

ens

cons

ider

edat

high

stra

inra

tes.

Vis

coel

astic

beha

viou

rof

mat

rix

and

less

time

for

dam

age

prop

agat

ion

resp

onsi

ble

for

incr

ease

insh

ear

stre

ngth

.Po

stfa

ilure

mic

rosc

opy

oftu

bula

rsp

ecim

ens

reve

als

feat

ures

asso

ciat

edw

itha

pure

shea

rst

ress

stat

e.Sh

ear

stre

ssm

ayno

tbe

cons

tant

due

toth

efa

bric

and

diff

eren

tpro

pert

ies

with

inth

esp

ecim

enth

ickn

ess.

Wal

lthi

ckne

ssse

tat3

mm

sinc

eth

inne

rw

alls

gave

inco

nsis

tent

resu

lts(t

houg

htto

bea

resu

ltof

man

ufac

turi

ngde

fect

s).

No

quas

i-st

atic

ultim

ate

stra

ins

prov

ided

.M

odul

uses

timat

edby

stre

ssan

dst

rain

atpo

int

whe

nqu

asi-

stat

icst

ress

equi

libri

umw

asth

ough

tto

beac

hiev

ed.

carb

on/e

poxy

2Dpl

ain

wea

ve:

Incr

ease

inm

odul

us(+

38%

),in

crea

sein

stre

ngth

(+69

%)

and

incr

ease

inul

timat

est

rain

(+41

%)

at1,

000

s−1

rela

-tiv

eto

496

s−1 ;

glas

s/ep

oxy

2Dpl

ain

wea

ve:

Incr

ease

inm

odul

us(+

29%

),in

crea

sein

stre

ngth

(+67

%)

and

incr

ease

inul

timat

est

rain

(+35

%)

at1,

000

s−1

rela

tive

to57

6s−

1 .

Har

ding

J.&

Don

gL

.(19

94)[

3]ca

rbon

/epo

xypr

e-pr

eg.:

T80

0/92

4([

0],[

0/90

],[±

45])

(CFR

P-PP

)LF

nots

pec.

[DL]

Tens

ion

SHPB

[DL

]

275

–33

2Sc

atte

ris

sola

rge

that

the

expe

rim

ents

cann

otbe

cons

ider

edas

proo

fof

ast

rain

rate

depe

nden

ce.I

mpr

oved

spec

imen

desi

gnre

quir

edif

stre

ngth

valu

esar

eto

beac

cept

edw

ithco

nfide

nce.

Nor

mal

stre

sspl

ays

asi

gnifi

cant

role

inth

efa

ilure

proc

ess

assh

own

bym

icro

grap

hsof

failu

resu

rfac

es.

Influ

ence

ofst

rain

rate

onsh

earm

odul

usno

trep

orte

d.

carb

on/e

poxy

pre-

preg

.[0]

(1-3

):sh

ear

stre

ngth

incr

ease

s(+

26%

)an

dul

timat

esh

ears

trai

nde

crea

ses

(-16

%)a

t275

s−1 .

carb

on/e

poxy

pre-

preg

.[0/

90](

2-3)

:sh

ear

stre

ngth

incr

ease

s(+

39%

)an

dul

timat

esh

ears

trai

nde

crea

ses

(-16

%)a

t332

s−1 .

carb

on/e

poxy

pre-

preg

.[±

45](

1-3)

:sh

ear

stre

ngth

incr

ease

s(+

38%

)an

dul

timat

esh

ear

stra

inde

crea

ses

(-22

%)

at28

1s−

1 .

23


―25―

Huf

enba

chW

.eta

l.(2

009)

[21]

glas

s/po

lypr

opyl

ene

hybr

idya

rn:M

KF

3Dw

eave

(3D

-W)&

Twin

tex

2Dw

eave

(GFR

P-W

)H

SLF

(IN

STRO

NV

HS

160/

20)[

I]6

x10

−3

-60

Lig

htw

eigh

tIo

sipe

scu

fixtu

reus

edto

redu

ceth

eef

fect

sof

fram

ein

ertia

l.H

igh

spee

dca

mer

asus

edfo

rvi

sual

anal

ysis

ofda

m-

age

and

failu

repr

oces

ses.

App

roxi

mat

ely

equa

lin

terl

amin

arsh

ear

stre

ngth

for

both

com

posi

tes.

Low

failu

rest

ress

and

stra

inle

vels

(Tw

inte

xin

1-3

plan

e)m

ake

the

mea

sure

men

tsno

isy

and

unre

liabl

e.

Influ

ence

ofst

rain

rate

onsh

earm

odul

usno

trep

orte

d.

MK

F(2

-3) :

shea

rst

reng

thin

crea

ses

(+6%

)up

to6

s−1 ,

follo

wed

bya

de-

crea

se(-

18%

)at6

0s−

1 ,and

ultim

ate

shea

rstr

ain

decr

ease

s(-

13%

)at6

0s−

1 .

Twin

tex

(2-3

) :sh

ear

stre

ngth

incr

ease

s(+

41%

)an

dul

timat

esh

ear

stra

inin

-cr

ease

s(+

18%

)at6

0s−

1 .

Twin

tex

(1-3

):sh

ear

stre

ngth

tren

dsun

clea

r(r

ange

betw

een

-35%

at6

s−1

and

+35%

at60

s−1 )a

ndul

timat

esh

ears

trai

nin

crea

ses

(+11

8%)a

t60

s−1 .

Huf

enba

chW

.eta

l.(2

013)

[60]

glas

s/po

lypr

opyl

ene

hybr

idya

rn:M

KF

3Dw

eave

(3D

-W)

HSL

F(I

NST

RON

VH

S16

0/20

)[I]

5x

10−

4-6

0L

ight

wei

ght

Iosi

pesc

ufix

ture

used

tore

duce

the

effe

cts

offr

ame

iner

tial.

Use

dpr

evio

usly

upto

60s−

1[2

1].

Hig

hly

non-

linea

rsh

ear

resp

onse

atal

lst

rain

rate

s.

Influ

ence

ofst

rain

rate

onsh

ear

mod

ulus

not

repo

rted

.Sh

ear

stre

ngth

in-

crea

ses

(+83

%at

3s−

1 ),an

dne

glig

ible

effe

cton

ultim

ate

shea

rstr

ain

(with

insc

atte

r:+2

1%±

57%

).

Gow

tham

H.L

.eta

l.(2

015)

[62]

E-g

lass

/epo

xy2D

plai

nw

eave

:–/L

Y55

6(H

Y95

1H

arde

ner)

(GFR

P-W

)To

rsio

nSH

PB[T

]

Com

pres

sion

SHPB

[SL

]

192

–45

7(T

)30

0–

1500

(SL

)Q

uasi

-sta

ticte

stin

gpe

rfor

med

only

for

tors

ion

spec

imen

s(d

etai

lsno

tre

port

ed).

Qua

si-s

tatic

tors

iona

lsi

mul

atio

nspe

rfor

med

toas

sess

poss

ible

stre

ssco

ncen

trat

ions

intu

bula

rspe

cim

ens.

Sing

le-l

apan

dtu

bula

rspe

cim

ens

com

pare

dus

ing

two

SHPB

s.L

ower

stre

ngth

mea

sure

dw

ithth

in-w

alle

dsp

ecim

ens

thou

ghtt

obe

are

sult

ofva

riat

ions

inst

iffne

ssan

dst

ress

alon

gth

era

dial

,and

circ

umfe

rent

iald

irec

tions

.

Eff

ecto

fst

rain

rate

onsh

ear

mod

ulus

and

ultim

ate

shea

rst

rain

notr

epor

ted.

Inte

rlam

inar

shea

rstr

engt

hin

crea

ses(

+56%

at45

7s−

1 )for

tubu

lars

peci

men

san

din

crea

ses

(+11

%at

1,50

0s−

1 )for

sing

le-l

apsp

ecim

ens.

Ger

lach

R.e

tal.

(201

2)[1

0]ca

rbon

/epo

xy3D

wea

ve:(

Tena

xH

TS/

HTA

)/R

TM

-6(3

D-W

)E

MLF

(not

spec

.)[I

-db

l.no

tch]

Com

pres

sion

SHPB

[I-d

bl.n

otch

)]

0.00

4-1

1,00

0Tw

obi

nder

volu

me

frac

tions

cons

ider

ed(3

%an

d6%

).Tu

bula

rsp

ecim

ens

not

prac

tical

for

3Dw

eave

sdu

eto

the

arra

ngem

ent

and

wid

esp

acin

gof

rein

forc

emen

t.A

doub

le-n

otch

shea

rsp

ecim

enw

asad

opte

d.A

vera

gesh

ear

stre

ngth

ishi

gher

inth

e2-

3pl

ane

com

pare

dto

the

1-3

plan

e.In

adeq

uate

reso

lutio

nan

dac

cura

cyof

optic

alsh

ear

stra

inm

easu

rem

ents

(dig

ital

spec

kle

phot

ogra

phy)

.L

arge

scat

ter

inst

reng

thm

easu

rem

ent

attr

ibut

edto

stre

ssco

ncen

trat

ions

atno

tche

s.

Influ

ence

ofst

rain

rate

onsh

ear

mod

ulus

and

ultim

ate

stra

inno

tre

port

ed.

Shea

rstr

engt

hin

crea

ses

inth

e1-

3pl

ane

(+52

%(3

%bi

nder

)and

+37%

(6%

bind

er))

and

incr

ease

sin

the

2-3

plan

e(+

34%

(3%

bind

er)

and

+31%

(6%

bind

er))

at11

,000

s−1 .

24

Yok

oyam

aT.

&N

akai

K.(

2006

)[6

5]ca

rbon

/epo

xypr

e-pr

eg.:

T70

0/25

21([

0])

(CFR

P-PP

)E

MLF

(Ins

tron

5500

R)[

I,SB

S]

Com

pres

sion

SHPB

[I-d

bl.n

otch

)]

0.02

-780

Sim

ilar

resu

ltsar

eob

tain

edw

hen

the

notc

hed

shea

rsp

ecim

ens

are

load

edin

tens

ion

and

com

pres

sion

.St

reng

thva

lues

from

notc

hed

spec

imen

sag

ree

wel

lw

ithth

esh

ort

beam

shea

r(S

BS)

test

s.C

ompr

essi

veno

rmal

stre

sses

arou

ndno

tche

sth

ough

tto

redu

ceef

fect

ofst

ress

conc

entr

atio

ns.

Eff

ecto

fst

rain

rate

onsh

ear

mod

ulus

and

ultim

ate

shea

rst

rain

notr

epor

ted.

Neg

ligib

leef

fect

ofst

rain

rate

onin

terl

amin

arsh

ears

tren

gth

upto

780

s−1 .

Bou

ette

B.e

tal.

(199

2)[3

9]ca

rbon

/epo

xypr

e-pr

eg.:

T30

0/52

08([

0])(

CFR

P-PP

)E

MLF

(LF

nots

pec.

)[S

L]

HLF

(LF

nots

pec.

)(I

tm.s

−1 )[

SL]

Tens

ion

SHPB

[SL

,D

L]

0.00

1-1

,000

Two

spec

imen

sw

ere

desi

gned

usin

gFE

A:

one

perm

ittin

gth

ede

term

i-na

tion

ofth

esh

ear

mod

ulus

,an

dth

eot

her

(dou

ble

lap

shea

rsp

ecim

en)

perm

ittin

gm

easu

rem

ent

ofth

esh

ear

stre

ngth

(1-3

plan

e).

Onl

yva

l-ue

sfo

rsi

ngle

-lap

spec

imen

sre

port

ed.

Stra

inm

easu

red

usin

gst

rain

gaug

eson

the

spec

imen

.A

utho

rsem

phas

ize

that

stre

ngth

valu

esm

ust

bein

terp

rete

dw

ithca

utio

ndu

eto

tens

ileno

rmal

stre

sses

ends

ofth

eov

erla

p.M

aint

aini

ngsh

orte

rov

erla

ple

ngth

redu

ces

peel

stre

sses

.

Eff

ecto

fst

rain

rate

onul

timat

esh

ear

stra

inno

trep

orte

d.N

eglig

ible

chan

gein

shea

rm

odul

usor

inte

rlam

inar

shea

rst

reng

thup

to1,

000

s−1

(with

inex

-pe

rim

enta

lsca

tter)

.

Hal

lett

S.R

.eta

l.(1

999)

[40]

carb

on/e

poxy

pre-

preg

.:T

300/

914

([0/

90] s

)(C

FRP-

PP)

LFno

tspe

c.[S

L(Z

)]

Com

pres

sion

SHPB

[SL

(Z)]

5x

10−

4-8

00Z

-sha

ped

sing

le-l

apsp

ecim

ens

used

.Sh

ear

stra

inm

easu

red

dire

ctly

usin

g±

45◦

rose

ttest

rain

gaug

e.H

igh

spee

dph

otog

raph

y(C

ordi

n)us

edto

obse

rve

failu

rem

echa

nism

s.L

inea

rre

gres

sion

fitus

edto

estim

ate

shea

rm

odul

usfr

omst

ress

-str

ain

curv

e(n

oise

and

osci

lla-

tions

incu

rve)

.To

om

uch

scat

ter

onsh

ear

stre

ngth

valu

esto

reso

lve

stra

inra

tede

pend

ency

.Fa

ilure

foun

dto

initi

ate

near

the

notc

hes,

sugg

estin

gth

atth

est

ress

conc

entr

atio

nm

aydo

min

ate

the

failu

re.

Shea

rm

odul

usin

crea

ses

(+41

%at

700

s−1 )

butw

ithhi

ghsc

atte

r(±

34%

).N

eglig

ible

effe

cton

shea

rst

reng

th(w

ithin

expe

rim

enta

lsc

atte

r)at

450

s−1

and

700

s−1 .U

ltim

ate

shea

rstr

ain

incr

ease

s(+

27%

at70

0s−

1 )but

with

high

scat

ter(±

20%

at45

0s−

1an

d±

12%

at70

0s−

1 ).

Gill

espi

eJ.

etal

(200

5)[2

]S-

2gl

ass/

epox

y2D

wea

ve(1

5x15

and

5x5)

–/S

C79

(GFR

P-W

)LF

nots

pec.

[R-O

]

Com

pres

sion

SHPB

[R-O

]

QS

-1,0

00O

ut-o

f-pl

ane

off-

axis

spec

imen

slo

aded

inco

mpr

essi

onto

obta

insh

ear

stre

ngth

.O

ff-a

xis

angl

esco

nsid

ered

incl

ude:

0◦,

15◦ ,

30◦ ,

45◦ ,

60◦ ,

75◦ ,

and

90◦ .

An

‘R-v

alue

’cr

iteri

on(b

ased

onre

lativ

edi

ffer

ence

betw

een

reac

tion

forc

es)

was

tode

term

ine

whi

chte

sts

wer

elik

ely

cont

ami-

nate

dby

iner

tial

effe

ct(l

imits

stra

inra

teto

<60

0s−

1 ).A

stra

inra

tede

pend

ent

failu

recr

iteri

onw

asid

entifi

edba

sed

onex

peri

men

tal

resu

lts.

Eff

ecto

fst

rain

rate

onsh

ear

mod

ulus

and

ultim

ate

shea

rst

rain

notr

epor

ted.

Inte

rlam

inar

shea

rstr

engt

hfo

und

toin

crea

se(+

134%

)at9

85s−

1 .

25


―26―

Huf

enba

chW

.eta

l.(2

009)

[21]

glas

s/po

lypr

opyl

ene

hybr

idya

rn:M

KF

3Dw

eave

(3D

-W)&

Twin

tex

2Dw

eave

(GFR

P-W

)H

SLF

(IN

STRO

NV

HS

160/

20)[

I]6

x10

−3

-60

Lig

htw

eigh

tIo

sipe

scu

fixtu

reus

edto

redu

ceth

eef

fect

sof

fram

ein

ertia

l.H

igh

spee

dca

mer

asus

edfo

rvi

sual

anal

ysis

ofda

m-

age

and

failu

repr

oces

ses.

App

roxi

mat

ely

equa

lin

terl

amin

arsh

ear

stre

ngth

for

both

com

posi

tes.

Low

failu

rest

ress

and

stra

inle

vels

(Tw

inte

xin

1-3

plan

e)m

ake

the

mea

sure

men

tsno

isy

and

unre

liabl

e.

Influ

ence

ofst

rain

rate

onsh

earm

odul

usno

trep

orte

d.

MK

F(2

-3):

shea

rst

reng

thin

crea

ses

(+6%

)up

to6

s−1 ,

follo

wed

bya

de-

crea

se(-

18%

)at6

0s−

1 ,and

ultim

ate

shea

rstr

ain

decr

ease

s(-

13%

)at6

0s−

1 .

Twin

tex

(2-3

):sh

ear

stre

ngth

incr

ease

s(+

41%

)an

dul

timat

esh

ear

stra

inin

-cr

ease

s(+

18%

)at6

0s−

1 .

Twin

tex

(1-3

):sh

ear

stre

ngth

tren

dsun

clea

r(r

ange

betw

een

-35%

at6

s−1

and

+35%

at60

s−1 )a

ndul

timat

esh

ears

trai

nin

crea

ses

(+11

8%)a

t60

s−1 .

Huf

enba

chW

.eta

l.(2

013)

[60]

glas

s/po

lypr

opyl

ene

hybr

idya

rn:M

KF

3Dw

eave

(3D

-W)

HSL

F(I

NST

RON

VH

S16

0/20

)[I]

5x

10−

4-6

0L

ight

wei

ght

Iosi

pesc

ufix

ture

used

tore

duce

the

effe

cts

offr

ame

iner

tial.

Use

dpr

evio

usly

upto

60s−

1[2

1].

Hig

hly

non-

linea

rsh

ear

resp

onse

atal

lst

rain

rate

s.

Influ

ence

ofst

rain

rate

onsh

ear

mod

ulus

not

repo

rted

.Sh

ear

stre

ngth

in-

crea

ses

(+83

%at

3s−

1 ),an

dne

glig

ible

effe

cton

ultim

ate

shea

rstr

ain

(with

insc

atte

r:+2

1%±

57%

).

Gow

tham

H.L

.eta

l.(2

015)

[62]

E-g

lass

/epo

xy2D

plai

nw

eave

:–/L

Y55

6(H

Y95

1H

arde

ner)

(GFR

P-W

)To

rsio

nSH

PB[T

]

Com

pres

sion

SHPB

[SL

]

192

–45

7(T

)30

0–

1500

(SL

)Q

uasi

-sta

ticte

stin

gpe

rfor

med

only

for

tors

ion

spec

imen

s(d

etai

lsno

tre

port

ed).

Qua

si-s

tatic

tors

iona

lsi

mul

atio

nspe

rfor

med

toas

sess

poss

ible

stre

ssco

ncen

trat

ions

intu

bula

rspe

cim

ens.

Sing

le-l

apan

dtu

bula

rspe

cim

ens

com

pare

dus

ing

two

SHPB

s.L

ower

stre

ngth

mea

sure

dw

ithth

in-w

alle

dsp

ecim

ens

thou

ghtt

obe

are

sult

ofva

riat

ions

inst

iffne

ssan

dst

ress

alon

gth

era

dial

,and

circ

umfe

rent

iald

irec

tions

.

Eff

ecto

fst

rain

rate

onsh

ear

mod

ulus

and

ultim

ate

shea

rst

rain

notr

epor

ted.

Inte

rlam

inar

shea

rstr

engt

hin

crea

ses(

+56%

at45

7s−

1 )for

tubu

lars

peci

men

san

din

crea

ses

(+11

%at

1,50

0s−

1 )for

sing

le-l

apsp

ecim

ens.

Ger

lach

R.e

tal.

(201

2)[1

0]ca

rbon

/epo

xy3D

wea

ve:(

Tena

xH

TS/

HTA

)/R

TM

-6(3

D-W

)E

MLF

(not

spec

.)[I

-db

l.no

tch]

Com

pres

sion

SHPB

[I-d

bl.n

otch

)]

0.00

4-1

1,00

0Tw

obi

nder

volu

me

frac

tions

cons

ider

ed(3

%an

d6%

).Tu

bula

rsp

ecim

ens

not

prac

tical

for

3Dw

eave

sdu

eto

the

arra

ngem

ent

and

wid

esp

acin

gof

rein

forc

emen

t.A

doub

le-n

otch

shea

rsp

ecim

enw

asad

opte

d.A

vera

gesh

ear

stre

ngth

ishi

gher

inth

e2-

3pl

ane

com

pare

dto

the

1-3

plan

e.In

adeq

uate

reso

lutio

nan

dac

cura

cyof

optic

alsh

ear

stra

inm

easu

rem

ents

(dig

ital

spec

kle

phot

ogra

phy)

.L

arge

scat

ter

inst

reng

thm

easu

rem

ent

attr

ibut

edto

stre

ssco

ncen

trat

ions

atno

tche

s.

Influ

ence

ofst

rain

rate

onsh

ear

mod

ulus

and

ultim

ate

stra

inno

tre

port

ed.

Shea

rstr

engt

hin

crea

ses

inth

e1-

3pl

ane

(+52

%(3

%bi

nder

)and

+37%

(6%

bind

er))

and

incr

ease

sin

the

2-3

plan

e(+

34%

(3%

bind

er)

and

+31%

(6%

bind

er))

at11

,000

s−1 .

24

Yok

oyam

aT.

&N

akai

K.(

2006

)[6

5]ca

rbon

/epo

xypr

e-pr

eg.:

T70

0/25

21([

0])

(CFR

P-PP

)E

MLF

(Ins

tron

5500

R)[

I,SB

S]

Com

pres

sion

SHPB

[I-d

bl.n

otch

)]

0.02

-780

Sim

ilar

resu

ltsar

eob

tain

edw

hen

the

notc

hed

shea

rsp

ecim

ens

are

load

edin

tens

ion

and

com

pres

sion

.St

reng

thva

lues

from

notc

hed

spec

imen

sag

ree

wel

lw

ithth

esh

ort

beam

shea

r(S

BS)

test

s.C

ompr

essi

veno

rmal

stre

sses

arou

ndno

tche

sth

ough

tto

redu

ceef

fect

ofst

ress

conc

entr

atio

ns.

Eff

ecto

fst

rain

rate

onsh

ear

mod

ulus

and

ultim

ate

shea

rst

rain

notr

epor

ted.

Neg

ligib

leef

fect

ofst

rain

rate

onin

terl

amin

arsh

ears

tren

gth

upto

780

s−1 .

Bou

ette

B.e

tal.

(199

2)[3

9]ca

rbon

/epo

xypr

e-pr

eg.:

T30

0/52

08([

0])(

CFR

P-PP

)E

MLF

(LF

nots

pec.

)[S

L]

HLF

(LF

nots

pec.

)(I

tm.s

−1 )[

SL]

Tens

ion

SHPB

[SL

,D

L]

0.00

1-1

,000

Two

spec

imen

sw

ere

desi

gned

usin

gFE

A:

one

perm

ittin

gth

ede

term

i-na

tion

ofth

esh

ear

mod

ulus

,an

dth

eot

her

(dou

ble

lap

shea

rsp

ecim

en)

perm

ittin

gm

easu

rem

ent

ofth

esh

ear

stre

ngth

(1-3

plan

e).

Onl

yva

l-ue

sfo

rsi

ngle

-lap

spec

imen

sre

port

ed.

Stra

inm

easu

red

usin

gst

rain

gaug

eson

the

spec

imen

.A

utho

rsem

phas

ize

that

stre

ngth

valu

esm

ust

bein

terp

rete

dw

ithca

utio

ndu

eto

tens

ileno

rmal

stre

sses

ends

ofth

eov

erla

p.M

aint

aini

ngsh

orte

rov

erla

ple

ngth

redu

ces

peel

stre

sses

.

Eff

ecto

fst

rain

rate

onul

timat

esh

ear

stra

inno

trep

orte

d.N

eglig

ible

chan

gein

shea

rm

odul

usor

inte

rlam

inar

shea

rst

reng

thup

to1,

000

s−1

(with

inex

-pe

rim

enta

lsca

tter)

.

Hal

lett

S.R

.eta

l.(1

999)

[40]

carb

on/e

poxy

pre-

preg

.:T

300/

914

([0/

90] s

)(C

FRP-

PP)

LFno

tspe

c.[S

L(Z

)]

Com

pres

sion

SHPB

[SL

(Z)]

5x

10−

4-8

00Z

-sha

ped

sing

le-l

apsp

ecim

ens

used

.Sh

ear

stra

inm

easu

red

dire

ctly

usin

g±

45◦

rose

ttest

rain

gaug

e.H

igh

spee

dph

otog

raph

y(C

ordi

n)us

edto

obse

rve

failu

rem

echa

nism

s.L

inea

rre

gres

sion

fitus

edto

estim

ate

shea

rm

odul

usfr

omst

ress

-str

ain

curv

e(n

oise

and

osci

lla-

tions

incu

rve)

.To

om

uch

scat

ter

onsh

ear

stre

ngth

valu

esto

reso

lve

stra

inra

tede

pend

ency

.Fa

ilure

foun

dto

initi

ate

near

the

notc

hes,

sugg

estin

gth

atth

est

ress

conc

entr

atio

nm

aydo

min

ate

the

failu

re.

Shea

rm

odul

usin

crea

ses

(+41

%at

700

s−1 )

butw

ithhi

ghsc

atte

r(±

34%

).N

eglig

ible

effe

cton

shea

rst

reng

th(w

ithin

expe

rim

enta

lsc

atte

r)at

450

s−1

and

700

s−1 .U

ltim

ate

shea

rstr

ain

incr

ease

s(+

27%

at70

0s−

1 )but

with

high

scat

ter(±

20%

at45

0s−

1an

d±

12%

at70

0s−

1 ).

Gill

espi

eJ.

etal

(200

5)[2

]S-

2gl

ass/

epox

y2D

wea

ve(1

5x15

and

5x5)

–/S

C79

(GFR

P-W

)LF

nots

pec.

[R-O

]

Com

pres

sion

SHPB

[R-O

]

QS

-1,0

00O

ut-o

f-pl

ane

off-

axis

spec

imen

slo

aded

inco

mpr

essi

onto

obta

insh

ear

stre

ngth

.O

ff-a

xis

angl

esco

nsid

ered

incl

ude:

0◦,

15◦ ,

30◦ ,

45◦ ,

60◦ ,

75◦ ,

and

90◦ .

An

‘R-v

alue

’cr

iteri

on(b

ased

onre

lativ

edi

ffer

ence

betw

een

reac

tion

forc

es)

was

tode

term

ine

whi

chte

sts

wer

elik

ely

cont

ami-

nate

dby

iner

tial

effe

ct(l

imits

stra

inra

teto

<60

0s−

1 ).A

stra

inra

tede

pend

ent

failu

recr

iteri

onw

asid

entifi

edba

sed

onex

peri

men

tal

resu

lts.

Eff

ecto

fst

rain

rate

onsh

ear

mod

ulus

and

ultim

ate

shea

rst

rain

notr

epor

ted.

Inte

rlam

inar

shea

rstr

engt

hfo

und

toin

crea

se(+

134%

)at9

85s−

1 .

25


―27―

Fluid and Thermal Engineering

Har

ding

J.&

LiY

.L.(

1992

)[64

]ca

rbon

/epo

xypr

e-pr

eg.(

[0])

:T

300-

3000

A/C

iba-

Gei

gyX

D92

7(C

FRP-

PP)

E-g

lass

/epo

xy2D

plai

nw

eave

:–/C

iba-

Gei

gyX

D92

7(C

FPR

-W)

hybr

idca

rbon

-gla

ss/e

poxy

:T

300-

3000

A/C

iba-

Gei

gyX

D92

7,–/

Cib

a-G

eigy

XD

927

(GFR

P-W

)

LFno

tspe

c.(I

nstr

on)[

DL]

Tens

ion

SHPB

[DL

]

QS

-1,6

00Sh

ears

trai

nsan

dsh

earm

odul

usw

ere

notm

easu

red.

Loa

dce

lldi

spla

cem

ent

used

toin

fera

nap

pare

ntsh

ears

trai

n.N

ose

nsiti

vity

tofib

revo

lum

efr

actio

nor

ply

layu

pfo

rthe

sam

em

ater

ial.

Prob

lem

sar

ose

with

hybr

idsp

ecim

ens

asa

resu

ltof

adi

scon

tinui

tyin

elas

ticpr

oper

ties

(diff

eren

ttyp

esof

rein

forc

ing

plie

s)on

eith

ersi

deof

the

failu

repl

ane.

Fini

teel

emen

tsi

mul

atio

nssh

owsi

gnifi

cant

norm

alst

ress

esat

the

ends

ofth

eov

erla

p.St

ress

conc

entr

atio

nsth

ough

tto

dom

inat

efa

ilure

initi

atio

nin

the

spec

imen

s.

carb

on/e

poxy

pre-

preg

:in

crea

sein

failu

rest

reng

th(+

73%

)at

1,60

0s−

1bu

tw

ithhi

ghsc

atte

r(±

27%

);

glas

s/ep

oxy

2Dw

eave

:in

crea

sein

stre

ngth

(+11

1%)

at1,

600

s−1

but

with

high

scat

ter(±

56%

);

hybr

idgl

ass/

epox

y:in

crea

sein

stre

ngth

(+37

%)

at1,

600

s−1

butw

ithhi

ghsc

atte

r(±

31%

).

26


―28―

characterisation of the interlaminar properties of

Documents