Engineering Fracture Mechanics 129 (2014) 54–66

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Engineering Fracture Mechanics

journal homepage: www.elsevier .com/locate /engfracmech

Refinements on fracture toughness of PUR foams

http://dx.doi.org/10.1016/j.engfracmech.2013.12.0060013-7944/� 2013 Elsevier Ltd. All rights reserved.

⇑ Corresponding author.E-mail addresses: msvina@mec.upt.ro, lmarsavina@yahoo.com (L. Marsavina).

Liviu Marsavina a,⇑, Dan M. Constantinescu b, Emanoil Linul a, Dragos A. Apostol b,Tudor Voiconi a, Tomasz Sadowski c

a Politehnica University of Timisoara, Blvd. M. Viteazu, No. 1, Timisoara, Romaniab Politehnica University of Bucharest, Splaiul Independentei, No. 313, Bucharest, Romaniac Lublin University of Technology, 40 Nadbystrzycka Str, Lublin, Poland

a r t i c l e i n f o a b s t r a c t

Article history:Received 28 September 2013Received in revised form 5 December 2013Accepted 13 December 2013Available online 24 December 2013

Keywords:Polyurethane foamFracture toughnessDensitySize effectCell orientation

Many efforts have been made in recent years to determine the fracture toughness of differ-ent types of foams in static and dynamic loading conditions. Taking into account that thereis no standard method for the experimental determination of the fracture toughness ofplastic foams different procedures and specimens were used. This paper presents the poly-urethane foam fracture toughness results obtained for different foam densities. Two typesof specimens were used for determining fracture toughness in modes I, II and a mixed one,and also the size effect, loading speed and loading direction were investigated. The paperproposed correlations for density, cell orientation and mixed mode loading based on theexperimental testing results.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Polyurethane (PUR) foam materials are widely used as cores in sandwich composites, for packing and cushioning. Theyare made of interconnected networks of solid struts and cell walls incorporating voids with entrapped gas. The maincharacteristics of foams are lightweight, high porosity and good energy absorption capacity [1,2]. Foam materials crush incompression, while in tension fail by propagating of single crack [3]. Most of the rigid polymeric foams have a linear – elasticbehavior in tension up to fracture, and a brittle failure behavior. So, they can be treated using fracture criteria of LinearElastic Fracture Mechanics (LEFM).

Consequently, the fracture toughness of such foams became an important characteristic, because cracks weaken the foamstructures capacity of carrying load. Many experimental efforts have been made in recent years to determine the fracturetoughness of different types of foams: plastic [4–7], carbon [8] and metallic [9,10].

McIntyre and Anderson [11], using single edge notch bend specimens made of rigid closed-cell polyurethane foams, mea-sured the KIc for different densities. They found that the fracture toughness is independent of crack length and proposed alinear correlation between fracture toughness and density, for foam densities smaller than 200 kg/m3. At higher densities thecorrelation became non-linear. The same behavior was observed by Danielsson [12] on PVC Divinycell foams and Viana andCarlsson on Diab H foams [5]. Brittle fracture without yielding produced in mode I was observed in these experiments. It is tobe noted that a correlation between the static fracture toughness and relative density q/qs was proposed in [1]. Kabir et al.[7] used the procedure described by ASTM D5045 [13] for determining the fracture toughness of polyvinyl chloride (PVC) andpolyurethane (PUR) foams. They investigated the effects of density, specimen size, loading rate and of cell orientation.Density has a significant effect on fracture toughness, which increases more than 7 times when the foam density increases

Nomenclature

a crack length (mm)B specimen thickness (mm)cf effective size of fracture process zone (mm)E Young’s modulus (MPa)f (a/W) dimensionless stress intensity factors for SENB specimenGf energy release rate at fracture (N/mm)KI mode I stress intensity factor (MPa mm0.5)

KII mode II stress intensity factor (MPa mm0.5)

KIc mode I fracture toughness (MPa mm0.5)

KIIc mode II fracture toughness (MPa mm0.5)l, h cell dimensions (mm)Q ratio between cell dimensions (–)P load (N)R ASCB specimen radius (mm)S span (mm)S1, S2 support distances (mm)t cell wall thickness (mm)W specimen width (mm)W0 transition width (mm)YI, YII (S2/R) dimensionless stress intensity factors for ASCB specimenq foam density (kg/m3)qS solid material density (kg/m3)rf fracture stress (MPa)rN nominal stress (MPa)rN0 transition stress (MPa)m Poisson ratio (–)

L. Marsavina et al. / Engineering Fracture Mechanics 129 (2014) 54–66 55

3.5 times. They also presented the results of the established fracture toughness for H130 foams measured with crack orien-tation in two directions: rise and flow. The fracture toughness is higher with 27% when the crack is orientated parallel to therise direction. Burman [6] presented fracture toughness results for two commercial foams, Rohacell WF51 (density 52 kg/m3)and Divinycell H100 (density 100 kg/m3). The mode I fracture toughness KIc was obtained on Single Edge Notch Beam (SENB)specimens and has values 0.08 MPa m0.5 for WF51, respectively 0.21 MPa m0.5 for H100. He also determined the mode II frac-ture toughness using End-Notch Flexure (ENF) specimens, with values of 0.13 MPa m0.5 for WF51, respectively 0.21 MPa m0.5

for H100.Using the asymptotic matching, Bazant [14] derived a relative simple law bridging the classical plasticity and fracture

mechanics approaches. This law was experimentally validated for different types of materials, including PVC foams [15].Mixed mode fracture of polymeric foams is less investigated. Hallstrom and Grenestedt [16] investigated mixed mode

fracture of cracks and wedge shaped notches in expanded PVC foams. Different types of specimens made of DivinycellH100 were investigated and the non singular T-stress was considered in the formulation of fracture criteria. It was concludedthat for predominantly mode II the use of T-stress improved the facture predictions. Three different densities of PVC foamswere investigated using a Compact Tensile (CT) specimen with Arcan grips to produce mixed mode conditions [17]. The ratiobetween mode II and mode I fracture toughness KIIc/KIc was found to be between 0.4 and 0.65 depending on foam density. Formixed mode loading the Richard fracture criterion gives better predictions of fracture limit and crack initiation angle. Thesame fracture criterion was found by Marsavina et al. [18] to fit better the mixed mode fracture of PUR foams. The exper-imental investigations were carried out on Asymmetric Semi-Circular Bend (ASCB) specimens.

This paper presents the experimental results for the fracture toughness of three types of PUR foams. The effects of density,size, cell orientation, loading speed and mixed mode loading on fracture toughness are addressed.

2. Materials and methods

2.1. Foam materials

Experimental investigations were carried out on three types of closed cell PUR foams, manufactured by NECUMER GmbH,Germany. The densities of these foams are 100 (Necuron 100), 145 (Necuron 160) and 300 kg/m3 (Necuron 301), and themain properties (approximate values) provided by manufacturer are listed in Table 1. According to the manufacturer themain applications of these foams are test models, draw dies, large volume models, back filling of molds and patterns, andsubstructure for hard styling clay.

Fig. 1. Microstructure of investigated PUR foams.

Table 1Mechanical properties of investigated foams according to manufacturer.

Necuron 100 160 301

Density (kg/m3) 100 145 300Temperature resistance (�C) 120 120 65Compressive strength (MPa) 2 3 5Flexural strength (MPa) 1.5 2.5 6

56 L. Marsavina et al. / Engineering Fracture Mechanics 129 (2014) 54–66

The microstructures of the investigated foams (presented in Fig. 1 at 500�magnification) were obtained using QUANTA™FEG 250 SEM and are shown in Fig. 1. Based on the microstructure analysis the cell length and the cell wall thickness weredetermined using SigmaScanPro software. The results of the statistical analysis of the foams microstructure are shown inFig. 2. The medium size of cells on two directions and the wall thickness are presented in Table 2.

2.2. Determination of foam density

The determination of the density of the investigated foams was performed according with ASTM D 1622-03 [19].Sartorius GD 503 Class Balance was used for the mass measurement, and the dimensions of the specimens were measuredusing a digital caliper Mitutoyo Digimatic. Specimens used for establishing the density had the approximate dimensions84 � 35 � 10 mm.

2.3. Tensile testing tests

Tensile tests were performed using dog bone specimens with a gage length of 50 mm and a cross section in the calibratedzone with 10 mm width and 4 mm thickness, according to EN ISO 527 [20]. The test specimens were cut from foam panels (of50 mm thickness, for the foams Necuron 100 and 160, respectively 25 mm for Necuron 301), both in the rise direction (inplane) and in the flow direction (out of plane). Four specimens were tested for each kind of foam material at room temper-ature and with a loading rate of 2 mm/min. Specimens were placed inside the wedge grips and a tensile load was appliedquasi-statically in a Zwick/Roell Zwicky line testing machine with a 2.5 kN loading cell. A laserXtens extensometer was usedfor monitoring the strains and to obtain the Young’s modulus, Fig. 3.

Fig. 2. Statistical analysis of the cell dimensions.

Table 2Cell dimensions.

Necuron 100 160 301

Cell length in plane, l (lm) 104.5 ± 9.4a 83.8 ± 9.6a 68.5 ± 33.9a

Cell length out of plane, h (lm) 120.2 ± 14.5a 88.1 ± 11.2a 67.8 ± 32.1a

Cell wall thickness, t (lm) 2.9–5.8 5.1–13.1 3.8–21.8

a Standard deviation values.

Fig. 3. Tensile tests set-up.

L. Marsavina et al. / Engineering Fracture Mechanics 129 (2014) 54–66 57

2.4. Fracture toughness tests

Two types of specimens were adopted for estimating the fracture toughness of PUR foams.The three point bend tests were performed on a 5 kN Zwick Proline testing machine, Fig. 4. The SENB specimens were cut

in the two main directions, Fig. 5, and loaded with 2 mm/min. The load–displacement curve was recorded and the maximumforce Pmax was used for calculation of fracture toughness, as in Murakami [21]:

KIc ¼3PmaxS

2BW2

ffiffiffiffiffiffipap

f ða=WÞ; ðMPa mm0:5Þ ð1Þ

Fig. 4. Three point bend tests.

Fig. 5. The single edge notch bend specimen.

58 L. Marsavina et al. / Engineering Fracture Mechanics 129 (2014) 54–66

where Pmax is the maximum load in (N), a, B and W are specimen dimensions in (mm). The function f(a/W) is given by [21]:

f ða=WÞ ¼ 1:122� 1:40ða=WÞ þ 7:33ða=WÞ2 � 13:08ða=WÞ3 þ 14:0ða=WÞ4 ð2Þ

Evaluation of fracture toughness under mixed mode was carried out on Asymmetric Semi-Circular Bend (ASCB) speci-mens, Fig. 6. This ASCB specimen with radius R, which contains an edge crack of length a oriented normal to the specimenedge, loaded with a three point bend fixture, was proved to give a wide range of mixed modes, from pure mode I (S1 = S2),mixed modes I and II (S1 – S2), to pure mode II, only by changing the position of one support [22–24]. The considered geom-etry of the specimen has: R = 40 mm, a = 20 mm, t = 10 mm, S1 = 30 mm and S2 = 30, 12, 8, 6, 4, 2.66 mm. The Stress IntensityFactors (SIFs) of the ASCB specimen are expressed in the form [23]:

Ki ¼Pmax

2Rt

ffiffiffiffiffiffipap

Yiða=R; S1=R; S2=RÞ; i ¼ I; II ð3Þ

where the non-dimensional SIFs Yi(a/R, S1/R, S2/R) were determined by finite element analysis [18] for a/R = 0.5 and S1/R = 0.75:

YIðS2=RÞ ¼ 6:235ðS2=RÞ3 � 15:069ðS2=RÞ2 þ 17:229ðS2=RÞ � 1:062

YIIðS2=RÞ ¼ 1:884ðS2=RÞ5 � 7:309ðS2=RÞ4 þ 5:037ðS2=RÞ3 þ 2:77ðS2=RÞ2 � 5:075ðS2=RÞ þ 1:983ð4Þ

The tests were performed on a Zwick/Roell 5 kN testing machine at room temperature with a loading rate of 2 mm/min,except of the studies investigating the effect of loading rate. Fig. 7 presents a picture with the ASCB specimen in the bendingfixture. For each position of support S2 four specimens were tested.

3. Results and discussions

3.1. Density and tensile property results

The results of density for the investigated foams are shown in Table 3 and are in agreement with the results indicated bymanufacturer.

Typical tensile stress–strain curves obtained for the investigated PUR are shown in Fig. 8 for in plane loading. Theobtained results are shown in Table 3. Young’s modulus and tensile strength increase with the density.

Fig. 6. The ASCB specimen.

Fig. 7. Test set-up for ASCB specimens.

Table 3Experimental results for density and tensile properties for investigated foams.

Necuron 100 160 301

Density (kg/m3) 100.37 ± 0.25a 145.53 ± 0.22a 300.28 ± 1.38a

Young’s modulus (MPa) 30.18 ± 1.75a 66.89 ± 1.07a 281.39 ± 2.92a

Tensile strength (MPa) 1.16 ± 0.024a 1.87 ± 0.036a 3.86 ± 0.092a

a Standard deviation values.

Fig. 8. Typical stress–strain curves from tensile tests.

L. Marsavina et al. / Engineering Fracture Mechanics 129 (2014) 54–66 59

3.2. Fracture toughness test results

3.2.1. Effect of densityIt was shown that the density plays the most important role on the mechanical properties of foams [1,5,7]. The fracture

toughness results obtained on SENB and ASCB are presented in Table 4. As we expected with the increase of density threetimes the fracture toughness of PUR foams increases more than four times. It can be also observed that the fracture tough-ness values determined on ASCB specimens are higher than those on SENB, with 20% for Necuron 100 and with 0.8% forNecuron 301. In Fig. 9 the fracture toughness results are plotted versus relative density together with other values from lit-erature. It can be observed that the obtained fracture toughness values determined on PVC foams are lower than those fromthe literatures [5–7].

Table 4Experimental results of fracture toughness for investigated foams.

Necuron 100 160 301

Fracture toughness (MPa m0.5) SENB 0.072 ± 0.003a 0.121 ± 0.003a 0.369 ± 0.071a

ASCB 0.087 ± 0.003a 0.131 ± 0.003a 0.372 ± 0.014a

a Standard deviation values.

Fig. 9. Fracture toughness results versus foam relative density.

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Based on the experimental values obtained for fracture toughness, it is possible to propose a correlation between fracture

toughness of PUR foams and the relative density: KIc ¼ 2:5 qqS

� �1:413, which has a correlation coefficient r2 = 0.99, which means

that 99% of the experimental data fit the proposed correlation.Brittle fracture was observed for all tested specimens. The linear elastic behavior was confirmed during the tests when no

cushioning occurs and no plastic deformations remain after the test, Fig. 10.

3.2.2. Size effectThe size effect was investigated using SENB specimens. The size effect is defined as the dependence of the nominal stress

rN = (3PmaxS)/(2BW2) as a function of the characteristic size of the specimen, considered the width of the specimen W. Thesize effect is best highlighted in a plot of Log(rN) versus Log(W), Fig. 11. If the failure of the foam obeys Linear Elastic FractureMechanics (LEFM), the logarithmic size effect plot would have to be a straight line with the slope �1/2 [14], shown dotted inFig. 11. A ductile behavior following the strength of material criteria (SC) with no size effect would be a horizontal line rN = -rf, with rf fracture or yield stress. The obtained experimental results are asymptotic to these approaches having the form[15]:

rN ¼rN0ffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ W

W0

q ð5Þ

where rN0 and W0 (represents the transitional size) are fitting parameters. Having determined rN0 and W0 the following frac-ture parameters can be identified [15]:

Fig. 10. SEM images of initial notch surface and fractured surface after test.

Fig. 11. Schematic of size effect.

L. Marsavina et al. / Engineering Fracture Mechanics 129 (2014) 54–66 61

– energy release rate at fracture:

Gf ¼r2

N0g0ða0Þcf

E0ð6Þ

and

– effective size of fracture process zone:

cf ¼W0gða0Þ

g0ða0Þð7Þ

where g(a0) = [f(a0)]2, with a0 = a/W = 0.5 for all considered cracked specimens, E0 = E for plane stress and E0 = E/(1 � m2) forplane strain, with E – Young’s modulus and m – Poisson’s ratio.

The plane strain condition a, B, (W � a) > 2.5 (KIc/ry)2 was not satisfied for all specimens sizes, so E0 = E was used in Eq. (6).All the specimens were cut from the same plate and had the same thickness B of approximately 53 mm for Necuron 100

and 160, respectively 25 mm for Necuron 301, which corresponds to plate thickness. To determine the size effect of mode Ifracture toughness, specimens geometrically similar in two dimensions with length-to-width ratio 4 were selected. Typicalload–displacement curves for different types of specimens are shown in Fig. 12 together with a picture of specimens. Themean values of the specimens dimensions and obtained experimental results are shown in Table 5.

Fig. 13 presents the experimental data and the fitting done according to Eq. (5), while Table 6 presents the fitting param-eters and the values of the energy release rate Gf at fracture and effective size of fracture process zone cf. It can be seen thatfor all specimen sizes, the LEFM fits better the experimental results, preponderantly for the highest density foam (Fig. 13c).This can be also seen from the plot of fracture toughness versus specimen width W, Fig. 14.

The results show that all tested specimens (width W from 5 mm to 226 mm) are closer in behavior to linear elastic frac-ture mechanics, Fig. 13. All fitting parameters from Table 6, as rN0, W0, Gf, cf increase with foam density. The size of the frac-ture process zone is approximately 4 times cell size for Necuron 100 and increases to 17 times cell size for Necuron 301.

The size effect results of PUR foams show that the design of such structures based on strength or plasticity criteria is gen-erally valid only for small structural parts. In the case of large components, the size effect must be taken into account.

3.2.3. Effect of cell orientationThe effect of cell orientation on fracture toughness as a measure of anisotropy was pointed out by Gibson and Ashby [1].

Identifying three directions: two in the rise direction – in plane (1), (2) and one out of plane corresponding to flow direction

Fig. 12. Load–displacement curves for different specimen sizes.

Table 5Specimen dimensions and experimental results (mean values and standard deviation).

Specimen type Extra small Small Medium Large Extra large

Necuron100

B (mm) 53.125 53.302 53.310 53.687 53.275W (mm) 5.385 10.106 25.452 100.187 224.500S (mm) 20.00 40.00 100.00 400.00 900.00a (mm) 2.50 5.00 12.50 50.00 112.50rN (MPa) 0.567 ± 0.0586a 0.491 ± 0.044a 0.317 ± 0.016a 0.171 ± 0.0021a 0.110 ± 0.0002a

KIc (MPa m0.5) 0.071 ± 0.0074a 0.087 ± 0.0076a 0.089 ± 0.0046a 0.096 ± 0.0012a 0.093 ± 0.0001a

160B (mm) 52.173 52.296 52.232 51.725 51.83W (mm) 5.55 10.792 25.946 100.838 226.6S (mm) 20 40 100 400 900a (mm) 2.5 5.0 12.5 50.0 112.5rN (MPa) 0.834 ± 0.0179a 0.759 ± 0.039a 0.475 ± 0.0309a 0.244 ± 0.0071a 0.155 ± 0.0095a

KIc (MPa m0.5) 0.105 ± 0.0016a 0.135 ± 0.0071a 0.133 ± 0.0087a 0.137 ± 0.0039a 0.131 ± 0.0079a

301B (mm) 25.37 25.33 25.312 25.27 25.295W (mm) 5.655 10.584 25.57 87.9725 173.65S (mm) 20 40 100 350 700a (mm) 2.5 5 12.5 43.75 87.5rN (MPa) 2.957 ± 0.2768a 2.211 ± 0.0557a 1.367 ± 0.0723a 0.688 ± 0.010a 0.476 ± 0.0119a

KIc (MPa m0.5) 0.375 ± 0.034a 0.392 ± 0.0101a 0.383 ± 0.0203a 0.361 ± 0.0192a 0.354 ± 0.0164a

a Standard deviation values.

Fig. 13. Results of size effect investigations on PUR foams.

Table 6Fitting parameters and fracture parameters according with size effect analysis.

Necuron rN0 (MPa) W0 (mm) Gf (N/mm) cf (mm)

100 1.275 1.542 0.830 0.394160 1.651 2.232 0.902 0.570301 3.297 4.545 1.747 1.160

Fig. 14. PUR foams fracture toughness versus the specimen width.

62 L. Marsavina et al. / Engineering Fracture Mechanics 129 (2014) 54–66

Fig. 15. Effect of cell orientation.

Fig. 16. Ratio between out of plane and in plane fracture toughness versus ration between cell dimensions.

Fig. 17. Results of mixed mode fracture of PUR foams and fracture curves.

L. Marsavina et al. / Engineering Fracture Mechanics 129 (2014) 54–66 63

perpendicular to the cell growth (3), Fig 15a. They correlate the ratio between fracture toughness on different direction to theratio of cell dimensions Q = h/l:

ðKIcÞiðKIcÞj

¼ Q n ð8Þ

with i, j = 1, 2, 3 direction in which the crack front lies, n = 0.5 (i=2, j=3), 1 (i=2, j=1), 1.5 (i=3, j=1).Fig. 15b presents the influence of cell orientation on fracture toughness for investigated PUR foams, obtained using SENB

specimens. It can be observed that for low densities the fracture toughness is higher out of plane comparing with in plane

Fig. 18. Crack paths for different positions of S2 support.

Fig. 19. Fracture limit curve KI/KIc versus KII/KIIc based on eq. (9), with p = q = 1.75, and experimental data.

Fig. 20. Fracture toughness of PUR foams versus loading speed.

64 L. Marsavina et al. / Engineering Fracture Mechanics 129 (2014) 54–66

direction with 5.7% for Necuron 100, and with 4.2% for Necuron 160, while for Necuron 301 the in plane fracture toughness ishigher with approximately 8%. This can be explained by the dimensions of the cellular structure. The dimensions h and l ofcells were measured on the SEM images and the mean values from approximately 25 cells were obtained. Fig. 16 presents theresults of the ratio KIc_out of plane/KIc_in plane for SENB specimens (yellow1 circle for Necuron 100, blue circle for Necuron 160 andblack circle for Necuron 301) versus h/l and the predictions given by Eq. (8). In Fig. 16 are also presented the mode I fracturetoughness values obtained on ASCB specimens for Necuron 100 (yellow square) and 160 (blue square), resulting the same ten-dency KIc_out of plane > KIc_ in plane. For Necuron 301 the out of plane mode I fracture toughness could not be determined becausethe thickness of plate is 25 mm and the radius of ASCB specimen is 40 mm.

1 For interpretation of color in Fig. 16, the reader is referred to the web version of this article.

Fig. 21. Radar diagrams on factors influencing the PUR fracture toughness.

L. Marsavina et al. / Engineering Fracture Mechanics 129 (2014) 54–66 65

3.2.4. Effect of mixed mode loadingAn extensive study on the assessment of mixed mode fracture criteria for PUR foams was presented by Marsavina et al.

[18] using ASCB specimens. Here only the main results will be presented. Four fracture criteria were considered Maximumcircumferential tensile stress (MTS) of Erdogan and Sih [25], Minimum Strain Energy Density (SED) of Sih [26], Maximumenergy release rate criterion (Gmax) of Hussain et al. [27] and Equivalent stress intensity factor (ESIF) of Richard [28,29].Fig. 17 presents the mean values of the ratio between KII/KIc versus KI/KIc, together with the fracture curves predicted by theconsidered criteria. For Necuron 100 and 160 the effect of cell orientation was also investigated. The mixed mode fracture isslightly different on the two considered cell orientations Fig. 17a and b.

ESIF appears to predict better the mixed mode fracture of polyurethane foams, this being probably due to the fact thattakes into account the ratio between mode I and mode II fracture toughness KIc/KIIc. This was also observed by Nouryet al. [17] for PVC foams in the density range 90–200 kg/m3. However, for the low density foams the Gmax criterion canbe also considered, while for Necuron 301 the SED criterion provides a good prediction of fracture.

The obtained crack paths for three different support position S2 are shown in Fig. 18.Empirical relationships between ratios KII/KIIc and KI/KIc were proposed in the literature to assess mixed mode fracture

[22,30]. A general relation can be expressed in the form:

KI

KIc

� �p

þ KII

KIIc

� �q

¼ 1 ð9Þ

where p and q are fitting parameters. The parameters can be p = q or p – q according to Lim et al. [22], or p = 1 and q = 2 [30].Such an empirical prediction was fitted with our experimental fracture toughness results and indicate a good correlation forp = q = 1.75 for all foam densities and indicate a good agreement with those experimental data, Fig. 19.

3.2.5. Effect of loading speedThe influence of loading speed on the mode I and mode II fracture toughness was investigated for Necuron 100 and 160

foams using ASCB specimen. Three loading speeds were considered as being 2, 50 and 500 mm/min. Fig. 20 shows a decreaseof mode I fracture toughness with increasing loading speed from 2 to 500 mm/min with 37% for Necuron 100, respectivelywith 43% for Necuron 160. Apparently, there is no influence of loading speed on mode II fracture toughness.

However, it was shown that the mode I dynamic fracture toughness is two times higher than the static one for PUR foams,Marsavina et al. [31,32], respectively 3.75 times for PVC foams, Kabir et al. [7].

4. Conclusions

Radar diagrams plotted for Necuron 100 and 160 in Fig. 21 summarize different effects on the fracture toughness of PURfoams. For both foams a greater influence was given by the loading speed (from 2 to 500 mm/min) notated as KIc_2/KIc_500

determined on ASCB specimens, than that of the ratio between mode I and mode II fracture toughness KIc/KIIc. Another issueis the influence of the specimen type, as KIc_ASCB/KIc_SENB; on the contrary the cell orientation KIc_out of plane/KIc_in plane looks tohave the minor influence, for both specimen types SENB and ASCB.

The main conclusions of this study are:

� The order of magnitude for fracture toughness of PUR foams is between 0.07 MPa m0.5 for density of 100 kg/m3 to0.37 MPa m0.5 for density of 300 kg/m3. Fracture toughness is strongly dependent on foam density increasing withincreasing density, Fig. 9.� Cell orientation and dimensions influence also the fracture toughness, as presented in Figs. 15 and 16.

66 L. Marsavina et al. / Engineering Fracture Mechanics 129 (2014) 54–66

� Experimental results show that the Equivalent Stress Intensity Factor Criterion of Richard [28] predicts better the fracturetoughness under mixed mode conditions. Also, an empirical formulation based on ratios KII/KIIc and KI/KIc was proposed todescribe the mixed mode fracture of investigated PUR foams, Fig. 19 and Eq. (9).� An increase of the loading speed produces a decreasing of mode I fracture toughness and appears to have no effect on

mode II fracture toughness, Fig. 20.� The fracture of polyurethane foams is brittle, as no plastic deformations remains after the test and no cushioning occurs

during tests, Fig. 10.

Acknowledgments

This work was supported by the grant PN-II-ID-PCE-2011-3-0456. Part of experimental results were obtained at LublinUniversity of Technology, in the facilities of the Center of Excellence for Modern Composites Applied in Aerospace and SurfaceTransport Infrastructure (European Union Seventh Framework Programme (FP7/2007 – 2013), FP7 - REGPOT – 2009 – 1, un-der grant agreement No: 245479 and ILK from Technische Universität Dresden.

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