1999-damage mechanics of top-hat sti!eners used (2) copy

8/10/2019 1999-Damage Mechanics of Top-hat Sti!Eners Used (2) Copy

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* Corresponding author. Tel.: # 1-44-1703-592316; fax: # 1-44-1703-593299. E-mail address: r.a.shenoi @ship.soton.ac.uk (R.A. Shenoi)

Marine Structures 12 (1999) 1 }19

Damage mechanics of top-hat sti ! eners usedin FRP ship construction

H.J. Phillips , R.A. Shenoi *, C.E. Moss

Hamworthy Marine Technology Ltd., Poole, UK Department of Ship Science, Uni versity of Southampton, Southampton, High xeld, Hants SO17 1BJ, UK B.M.T. (Defence Ser vices) Ltd., Bath, UK

Received 29 May 1997; received in revised form 14 January 1999; accepted 18 January 1999

Abstract

This paper is concerned with the assessment of damage tolerance of a top-hat sti ! ener toplate connection in FRP marine structures. The subject is addressed in two parallel schemes,using stress-based and fracture-dependent criteria. Numerical modelling is used to determinethe internal load transfer characteristics and failure mechanisms in top-hat sti ! eners undertypical loadings seen in practice. The " nite element models are benchmarked against publishedtest results, which include phenomena such as delaminations. The models are then extended toinclude crack elements, which are employed to calculate the strain energy release rates in theform of G values. The result from this modelling is compared against typical experimentallyderived data pertaining to G values for the materials in question. Finally, an attempt is madeto compare the results of the studies using the two approaches and to judge the over-lap. 1999 Elsevier Science Ltd. All rights reserved.

Keywords: Fibre-reinforced plastic (FRP); Ship structures; Top-hat sti ! eners; Finite element analysis;Delamination; Strain energy release rates; Damage tolerance

1. Introduction

The sti ! ness of large unsupported panels constructed of " bre-reinforced plastic(FRP) materials is inherently low. Thus, it is necessary to sti ! en such panels by a

0951-8339/99/$- see front matter 1999 Elsevier Science Ltd. All rights reserved.PII: S 0 9 5 1 - 8 3 3 9 ( 9 9 ) 0 0 0 0 3 - 9


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Fig. 1. A typical top-hat sti ! ener.

suitable method. The most prevalent form is the use of top-hat sti ! eners. A typicalcon " guration of the sti ! ener is shown in Fig. 1.

The present fabrication method starts with the laying-up of the unsti ! ened baseplate panel. Rigid foam cores are then laid on these panels in the locations where theextra sti ! ness is desired. Then, an adequate amount of " lleting resin is injected into therecess between the foam and the plate panel and the required radius is scraped out.Next, a resin-impregnated cloth, or overlaminate, is laid across the crown (or table),down the web and around the " llet onto the base plate. A similar cloth run is carriedout for the opposite side. The process of overlaminating is repeated a number of times,frequently with as many as 24 plies, to achieve the desired sti ! ness. Occasionally,a limited number of unidirectional plies may be applied to the crown to obtain extrasti ! ness. The reinforcement material for the web, #ange and overlaminate is E-Glasswoven roving and chopped strand mat; the resin matrix is isophthalic polyester resin.

Although top-hats are a critical part of the ship 's structure, it has received surpris-ingly little attention in the open literature. Early reported work [1,2] was in connec-

tion with the development of the " rst GRP minehunter and dealt mainly with thegross problems of qualifying design concepts with regard to a speci " c application.This was extended to develop a more fundamental understanding of the top-hatbehaviour through theoretical modelling [3,4]. Such early modelling attempts werenecessarily restricted because of the relatively immature nature of the available " niteelement types. There was also some fundamental work on the use of novel " lletingmaterials, with large strain to failure capability, and their application to marine joints

2 H.J. Phillips et al. / Marine Structures 12 (1999) 1 }19


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and top-hat sti ! ening purposes [5]. E ! ort was also now being directed towardsvarious failure scenarios. One of the principal cases involved overall panel instabilityand sti ! ener-plate interaction under compressive loading [4,6]. The second approachfocused on the transfer of load at the top-hat sti ! ener to plate connection through the

orthogonal or out-of-plane direction under static loading conditions [7,8]. Guidanceon this subject in existing design regulations is minimal [9 }11]. This is all the moreimportant because many ships have now been in operation for over 20 years and areseeing sustained damage at the roots of the joints in the form of delaminations. It isthus essential that a systematic study is carried out with regard to the localisedbehaviour of a top-hat sti ! ener to plate connection and its response under thepresence of cracks or delaminations.

The purpose of this paper is three-fold: (a) to understand the behaviour of a top-hatsti ! ener under static loading and the mechanisms of load transfer and failure; (b) tostudy the in #uence of delamination cracks on strain energy release rates; and (c) topropose a uni " ed approach to categorise damage tolerance levels in FRP structures inthe regions of top-hat sti ! eners.

2. Strength-based assessment

2.1. Purpose of analysis

The main aim of this analysis is to identify how the load is transferred from anin-plane direction in the base panel to an orthogonal direction in the plane of the web.The transfer is achieved through the overlamination and " lleting material. It isessential to categorise the stress states within the di ! erent constituent elements of the joint. These stresses can then be used to assess the likely causes of failure in the joints.The three main possibilities are delamination in the overlaminate, cracking of the" lleting resin and braking of the " bre plies in the overlaminate.

2.2. Physical characterisation of joint beha viour

Three load con " gurations were adopted for the test programme [12]; these were thethree-point bend, reverse bend and straight pull-o ! , as shown schematically in Fig. 2.Both the three-point and reverse bend tests aim to simulate gross panel deformationand its e ! ect on the top-hat connection. The pull-o ! test is designed to simulateinertial loadings on the sti ! ener under impact and explosion loadings. In all cases theload-de #ection plots were linear up until failure. The structural sti ! nesses in the three

cases are listed in Table 1.In case of the three-point bend test, specimens " rst showed damage at about13.5 kN when the " llet-to-overlaminate interfaces failed. Subsequent loading causedprogressive through-thickness delamination in the inner region of the overlaminateand the onset of cracking along the overlaminate-to- #ange joints from the cracks inthe " llet. Final failure occurred by #exural failure on the tension surface under the topof the top-hat (see Fig. 3a).

H.J. Phillips et al. / Marine Structures 12 (1999) 1 }19 3


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Fig. 2. Loading con " gurations for the experiments: (a) three-point bend; (b) reverse bend; (c) pull-o ! .



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Table 1Experimental failure loads and de #ections

Loading con " guration Sti ! ness (kN/mm)

Experimental FEA

Three-point bend 909 750Reverse bend 600 458Pull-o ! 952 667

Fig. 3. Experimental failure modes: (a) three-point bend; (b) reverse bend; (c) pull-o ! .



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Fig. 4. A typical " nite element model for strength calculations.

In the reverse bend tests, " rst signs of damage were observed at a load of 5 kN atwhich point cracks appeared in the " llets on both sides. Final failure occurred ata load of 14 kN due to tensile action on the inner surface at the centre of the #ange, asshown in Fig. 3b.

In the pull-o ! tests, cracks appeared at the #ange-to- " llet interface at a load of about 5.5 kN. These cracks extended and joined together with increased load, until ata load of 7 kN overlaminate was severed completely from the #ange on one side (seeFig. 3c).

2.3. Features of the FE models

A series of models was generated in the ANSYS " nite element analysis packageusing two dimensional solid elements (which possess three translational degrees of freedom at each node); see Fig. 4 for a typical model. Each of the 12 layers in theoverlaminate was represented by one element through the thickness. The #ange plateof the top-hat sti ! ener has been represented by one element through the thickness.Conditions of plain strain have been assumed throughout.

The loads applied to the structural model attempt to mimic those in the experi-mental investigation. For each of the three test con " gurations, stress distributionshave been computed (i) at the load at which initial damage was noted and (ii) at thefailure load of the sti ! ener. The material properties used in the FE model generation

were obtained from previous work at Southampton [8] and from parallel work atDERA Rosyth [12]; the relevant properties are given in Table 2.

2.4. Sti w ness characterisation

The " rst step is to validate the FE models by comparing the model sti ! ness withthat of the equivalent tested specimen. The FE model and experimental initial



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Table 2Material properties used in the FE modelling

Material Location Property Value

Polyester/woven Sti ! ener, #ange Ex 13,060 MParoving glass and overlaminate

Ey 7770 MPanuxy 0.25

Urethane acrylate Fillet Ex 1500 MPaEy 1500 MPanuxy 0.25

Core material Ex 10 MPaGxy 10 MPanuxy 0.25

Table 3Comparison of sti ! nesses } experimental versus FEA

Three point bending Reverse bending Straight pull o ! (3PB) (RB) (PO)

FE Expt. FE Expt. FE Expt.(N/mm) (N/mm) (N/mm) (N/mm) (N/mm) (N/mm)

731.2 696.8 713.0 384.6 930.0 1000

sti ! nesses of the top-hat under each of the three loading con " gurations are shown inTable 3. It is evident that for the three-point bend and the straight pull-o ! tests there isquite good correlation between the two sets of values. There is however a discrepancyas far as the reverse bend results are concerned.

2.5. Stress patterns

The stress distributions of interest are the " llet principal stress, overlaminatethrough-thickness and in-plane stresses, #ange plate through-thickness and in-planestresses. It is also necessary to compare the load transfer mechanisms predicted fromthe FE models with some experimentally derived failure modes. Table 4 shows thevalue and location of the maximum stress for each load level and load con " guration

for the top-hat sti ! ener.2.5.1. Three-point bending

The most signi " cant stress patterns for the top-hat at the experimental initial loadof 13.5 kN are shown in Fig. 5a for the overlaminate through-thickness stresses andFig. 5b for the #ange in-plane stresses. The magnitude of the " llet principal stress is thegreatest in the central region in the " llet as shown in Table 4 but is less than the



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Fig. 5. Stress distributions in three-point bend con " guration: (a) overlaminate through-thickness stress;(b) #ange in-plane stress.



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T a b l e 4

L o c a t i o n s a n d v a

l u e s o f m a x i m u m s t r e s s e s



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ultimate value. Thus, the " llet is unlikely to fail at this load. The region under thegreatest in-plane stress in the #ange is in the inner central part below the core; thishowever is unlikely to cause failure. The region of the #ange under the highestthrough-thickness stress is in the outer central part as shown in Table 4. The region of

the overlaminate which is subject to both the highest in-plane and through-thicknessstresses is the outer region in the curved part above the " llet as shown in Fig. 5a.Delaminations are likely to form here due to high through-thickness stresses.

The value of the maximum principal stress in the " llet at the sti ! ener experimentalfailure load of 16.5 kN is 18.09 MPa. The ultimate tensile strength (UTS) of the " lletmaterial in the literature [13] is quoted at about 26 MPa, so the " llet would remainintact at this load. This corresponds to the failure mode in the experiments in whichthe " llet itself did not crack. The initial damage was seen along the interface of the" llet with the overlaminate. The through-thickness stress at the initial failure load of 13.5 kN, however, is greater than the quoted interlaminar tensile strength (ILTS) of 7 MPa for the woven roving/polyester [14]. Hence, the FE model predicts thatdelaminations would occur near to the outer surface of the overlaminate at 13.5 kNdue to through-thickness stresses greater than the ILTS of the material. This exactlymatches the experimental " ndings. A similar match is obtained for the #ange failurecause. At 16.5 kN the in-plane stress in the #ange is 208 MPa which is greater than theUTS of the material. The FE model predicts that the #ange plate would fail in thecentre of the upper surface at a load of 16.5 kN, which again mirrors the experimental

" ndings.

2.5.2. Re verse bending At a load of 5 kN, the " llet principal stress is 4.8 MPa which is much less than the

UTS of 26 MPa. The FE model, therefore, does not predict " llet failure at this loadlevel. The initial failure mode in the experiments, however, was that of " llet cracking.The presence of voids within the " llet would cause higher stresses which could havecaused premature failure. This indicates that large voids may have been present in the" llets prior to loading which opened out due to the nature of the load but did notcause any further damage within the " llets. The experimental load/de #ection curveshowed no sudden loss of sti ! ness and an FE model containing a void in the resinexhibits an almost identical value of sti ! ness as the model not containing voids. Thus,it seems likely that the cracks in the " llet were due to the voids opening out under loadwith no loss of top-hat sti ! ness.

The in-plane stresses in the overlaminate are lower than the in-plane failure stressbut the through-thickness stresses in the overlaminate predicted by the FE model are

21 MPa along the interface of the overlaminate and the " llet. This is about three timesthe ILTS so delaminations would be predicted in this location. No delaminations,however, were visible in the experiments in this location. The high through-thicknessstresses may have caused a debond between the overlaminate and the " llet which inturn caused the " llet crack. The FE model predicts maximum in-plane and through-thickness stresses in the #ange plate which are not high enough to cause failure ata load of 5 kN. This is consistent with the experimental initial failure mode at 5 kN.



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2.5.3. Straight pull-o w The maximum values of stress for the " llet principal stress, overlaminate in-plane

and through-thickness and #ange in-plane and through-thickness stresses are given inthe lower two rows of Table 4. The " llet maximum principal stress at the sti ! ener

experimental failure load of 7 kN is 7.8 MPa. This is much lower than the UTS of the" llet material of 26 MPa. The FE model would not, therefore, predict " llet failure atthis load. This corresponds to the experimental failure mode in which no " llet crackswere visible.

The maximum in-plane stresses in the overlaminate and in the #ange are less thanthe UTS (in-plane) stress of 207 MPa at a load of 7 kN. Therefore, no failure ispredicted at this load from the FE model as a result of high in-plane stresses. Themaximum through-thickness stress of 2.8 MPa in the #ange is lower than 7 MPawhich is the ILTS. The maximum through-thickness stress in the overlaminate,however, is higher than the ILTS. The FE model predicts delamination of theoverlaminate in the curved region close to the " llet due to high through-thicknessstresses.

3. Energy-based assessment

3.1. Fracture mechanics criteria used in the approach

Two dimensional linear elastic fracture mechanics (LEFM) models have been usedto calculate mode I and mode II stress intensity factors which, in turn, have been usedto evaluate strain energy release rates, G. The theoretical basis is outlined in AppendixA. The load }de#ection characteristics of the top-hat sti ! ener under the three modes of loading discussed in the previous section are almost linear. Furthermore, in theprevious section, it was shown that the curved region of the overlaminate is one of themost sensitive areas prone to delamination. The material in this location is linearelastic up to failure. For this reason, there is no need to evaluate non-linear para-meters such as the J -integral: only the strain energy release rate has been calculated ineach case.

3.2. Modelling details

The FE model used in the strength analyses has been adapted so as to includea region containing cracks. The crack elements are six-noded triangular elementswith their mid-side nodes at the quarter point. The general scheme was similar to the

pattern shown in Fig. 4 except for the region containing the crack; this is shownin Fig. 6.Investigations showed that under certain conditions the two crack faces crossed

over each other, i.e. under a tensile load, the vertical displacement of the top crack facewas in fact less than the vertical displacement of the lower crack face. The problem of crack faces overlapping has been discussed in the literature [15,16]. Four methodsexist which can be used to overcome this problem: (a) application of displacement



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Fig. 6. Finite element detail in the region of cracks.

constraints on the crack face nodes, (b) application of nodal loads on the crack face, (c)application of gap elements at the crack interface or (d) to assume that the overlappinge! ect is negligible. In this particular case, a number of gap elements were insertedalong the crack face. The gap elements behave as linear springs in compression but intension their sti ! ness drops to zero thus not inhibiting the crack face should it open. Inaddition, the unloaded crack face is generated using nodes at the same location sincethe gap element allows connection of two nodes which are initially coincident. A checkhas been made to con " rm that the presence of the gap elements does not a ! ect thecalculated values of the strain energy release rate. This has been done by comparingthe results from two models with and without the gap elements present. The two setsof results are identical indicating that the presence of the gap elements has no e ! ect onthe calculations.

3.3. Loads , material properties and boundary conditions

The material properties used in the " nite element model are given in Table 2.Boundary conditions chosen were consistent with the strength analyses for the threecases of three-point bend, reverse bend and straight pull-o ! . The applied load in eachcase is chosen as 10 kN. The signi " cance of this load is that it is below any



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delamination damage which occurred in the three-point bend and reverse bend tests,implying that any cracks simulating delaminations observed in the tests and appro-priately inserted in the model should be stable at this load. Additionally, since thestrain energy release rates are proportional to the square of the applied load, it is

simple to interpolate values for di ! erent load values.

3.4. Results

The study focused on cracks in the overlaminate region only, despite the fact thatthe limited tests showed up some ultimate failures within the #ange laminate. This isbecause the strength analysis showed the region of high stresses is in the curvedportion of the overlaminate, as indicated in Table 4. It was argued earlier that some of the discrepancy in the static test results could have been due to fabrication variations.Furthermore, parallel work on tee joints [17] shows that it is the curved region that iscrucial to the crack propagation tendency. Hence the focus of the fracture studies isthe overlaminate region.

Two types of crack variations for each of the three load cases were studied} in#uence on crack depth and in #uence of crack length.

3.4.1. Crack depthFig. 7 shows the variation of G with crack depth. In Fig. 7a, pertaining to the

three-point bend, it can be noted that there is a peak value of G which corresponds toa crack depth of 4 mm. Cracks which are deeper than 4 mm give rise to lower values of G. It is anticipated that the reason why the value of G calculated for the crack at 2 mmdepth is lower than expected is due to the proximity of the crack to the surface. Cracksclose to the surface are more di $ cult to model than those deeper within the overlami-nate due to the limited area available to mesh with elements. This problem can beavoided to a degree, by re " ning the mesh close to the surface. All the values of G are,however, less than the critical value of 0.5 kJ/m [18]. This indicates that none of thesecracks under the three-point bend would propagate. The trend does, however, suggestthat under three-point bending, cracks which are deeper within the overlaminate areless likely to propagate than those nearer the surface. Similar trends can be observedfor the reverse bend and straight pull-o ! load cases as well, see Fig. 7b and 7c,respectively. The strain energy release rates are of similar orders of magnitude as in thethree-point bend case.

3.4.2. Crack lengthFig. 8 shows the variation of G with crack length. Each crack is at a depth of 6 mm

from the outer surface of the overlaminate. From Fig. 8a for the three-point bend case,it can be noted that the values of G increase at a steady rate as the crack lengthincreases. From the trends, it can be concluded that cracks greater than 38 mm inlength at a depth of 6 mm under these loading conditions are likely to propagate. Forthe reverse bend condition, whose e ! ect is shown in Fig. 8b, the G values are relativelylow indicating that this mode of loading is not as critical as the previous case. Themost severe condition in this respect is the straight pull-o ! ; the trends are indicated in



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Fig. 7. Variation of G with crack depth: (a) three-point bend; (b) reverse bend; (c) pull-o ! .



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Fig. 8. Variation of G with crack length: (a) three-point bend; (b) reverse bend; (c) pull-o ! .



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Fig. 8c. The nature of the curve is similar to that in the three-point bend condition.However, it can be seen that the fracture toughness value is exceeded at crack lengthsof about 30 mm.

4. Discussion

The results of the " nite element strength models are in good agreement with theexperimental results, particularly in the case of the three-point bending load. The resultshave shown that the damage prone areas are (i) in the curved region of the over-laminate and (ii) in the central region of the #ange plate. This is indicated by thepresence of high through-thickness stresses in the curved region of the overlaminate

and also the presence of high in-plane stresses in the #ange.The stress results have shown that the dominant failure modes of the top-hatsti ! eners under the three modes of loading include delamination in the overlaminate," llet-to- #ange interface cracking, " llet-to-overlaminate cracking, " llet cracking and#exural failure in the #ange. In the case of damage tolerance calculations, it is theinitial failure mode which must be predicted since it is at this point when thestructure 's load-bearing capabilities are gradually reducing. Thus, it is the initialfailure mode which is considered to be the most important in this case. In the case of the three-point bending, the initial failure mode was in the form of delaminations inthe overlaminate. Damage in the #ange plate was also visible in both the three-pointbending and reverse bending cases but this was a " nal failure mode and is, therefore,less signi " cant from a damage tolerance aspect. For these reasons, the delaminationswhich have been modelled in the energy-based assessment which followed are thosewithin the curved part of the overlaminate.

The results of the strength and fracture approaches give similar results. Forexample, the strength-based model of the three-point bending load shows that thehighest through-thickness stresses occur in the outer layers of the overlaminate. This

is shown in Fig. 5a. The energy-based approach shows that straight cracks which areclose to the outer surface of the overlaminate are more likely to propagate than thosewhich are deep. This is shown in Fig. 7a where greater values of G are obtained forshallow cracks (not including the value at a crack depth of 2 mm). Also, the graphshowing the e ! ect of crack length, shown in Fig. 8a shows that cracks which extendinto the curved part of the overlaminate are more likely to propagate than shortercracks which are contained within the #at portion of the overlaminate.

5. Conclusions

It has been shown that the delamination prone areas in top-hat sti ! eners arelocated in the curved region of the overlaminate close to the outer surface. Thedelaminations are likely to be due to excessive through-thickness stresses. The damagewhich occurs in the #ange is likely to be due to excessive in-plane stresses in the case of



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three-point bending loads and due to excessive through-thickness stresses in the caseof reverse bending loads.

Calculation of fracture parameters with regard to delaminations in the top-hatoverlaminates, have shown that curved delaminations are most likely to propagate

under a straight pull-o ! load. They are next likely to propagate under a three-pointbending load and are most stable under a reverse bending load. Also, delaminationsclose to the surface are more likely to propagate than deep delaminations in the caseof all three loading scenarios.

Results from the strength-based approach and the energy-based approach arecomparable and similar trends have been found.

Acknowledgements

The work presented in this paper was funded by the EPSRC/MoD. We are gratefulto Lt. Cdr. Mark Gray (MoD), Prof. John Sumpter, Richard Court, David Elliott,Philip Lay, Andrew Swift and Richard Trask (DRA) for their helpful discussionsduring the project.

Appendix A. Fracture mechanics criteria for damage modelling

A.1. Elastic stress xeld approach

Irwin [19] developed the stress intensity approach from linear elastic theory. In theregion of the crack tip, the stress intensity factor, K , determines the magnitude of theelastic stresses. The value of K , shown in Eq. (A.1) depends upon the magnitude of theapplied stress, , the length of the crack, 2 a , and a parameter which depends upon thecrack and specimen geometry, f (a / = ) where = is the specimen width:

K " a f a=

. (A.1)

Irwin proved that the achievement of a critical stress intensity factor, K , is exactlyequivalent to the Gri $ th }Irwin balance approach. This requires that the achievementof a stored elastic strain is equal to the critical strain energy release rate, G [20]. Fortensile loading, the relationship between K and G is given in Eq. (A.2) for planestress,

G "KE

plane stress. (A.2)

All stress systems in the vicinity of the crack may be derived from three modes of loading: (a) mode I which is the opening mode, (b) mode II which is the sliding modeand (c) mode III which is the tearing mode.



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A.2. Energy balance approach

The mode I strain energy release rate, G , can be written in terms of the modeI stress intensity factor, K , from Eq. (A.2) and with f (a / = ) in Eq. (A.1) being equal to

unity (i.e. an in " nitely long plate) as

G "KE

plane stress. (A.3)

The strain energy release rate, G, can be considered to be the amount of energy whichis available for crack extension and can be written in terms of the three stress intensityfactors for mixed-mode behaviour:

G"(K # K )( # 1)

8 #K2 , (A.4)

where K is the mode I stress intensity factor, K is the mode II stress intensity factor,K is the mode III stress intensity factor, is the material shear modulus, is theconversion factor between conditions of plane strain and plane stress, and is equal to(3! 4 ) for plane strain conditions and is the material Poisson 's ratio.

For the case where only modes I and II are applicable, mode III is assumed to givea negligible contribution to the strain energy release rate and hence the second term inEq. (A.4) can be neglected.

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[14] Bird J, Allan RC. The determination of the interlaminar strength of ship type laminates. in:Proceedings of the 7th International Conference Experimental Stress Analysis, Haifa, 1982:91 }104.

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