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Composites: Part B 38 (2007) 193–200

Fracture toughness of transverse cracks in graphite/epoxy laminatesat cryogenic conditions

Sukjoo Choi 1, Bhavani V. Sankar *

Department of Mechanical and Aerospace Engineering, University of Florida, 231 MAE-A Building, PO Box 116250, Gainesville, FL 32611, USA

Received 12 December 2005; received in revised form 12 March 2006; accepted 29 June 2006Available online 14 September 2006

Abstract

Stress singularity of a transverse crack normal to ply-interface in a composite laminate is investigated using analytical and finite ele-ment methods. Four-point bending tests were performed on single-notch bend specimens of graphite/epoxy laminates containing a trans-verse crack perpendicular to the ply-interface. The experimentally determined fracture loads were applied to the finite element model toestimate the fracture toughness. The procedures were repeated for specimens under cryogenic conditions. Although the fracture loadsvaried with specimen thickness, the critical stress intensity factor was constant for all the specimens indicating that the measured fracturetoughness can be used to predict delamination initiation from transverse cracks. For a given crack length and laminate configuration, thefracture load at cryogenic temperature was significantly lower. The results indicate that fracture toughness does not change significantlyat cryogenic temperatures, but the thermal stresses play a major role in fracture and initiation of delaminations from transverse cracks.� 2006 Elsevier Ltd. All rights reserved.

Keywords: A. Polymer-matrix composites; B. Fracture toughness; C. Finite element analysis; D. Thermal analysis; Cryogenic temperature

1. Introduction

The next generation of space vehicles is supposed to pro-vide a ten-fold reduction in the launch cost, from $10,000to $1,000 per pound of payload. To reduce the launch cost,reducing the structural weight penalty of the space vehicleis necessary. Because of their high specific stiffness andstrength fiber reinforced composites such as graphite/epoxycomposites are candidate materials for cryogenic storagesystems used in space vehicles, e.g., the liquid hydrogen(LH2) tank.

A previous design of liquid hydrogen composite tankused composite sandwich structure made of graphite/epoxycomposites and a honeycomb core. Typically a cryogeniccomposite tank is subjected to extreme temperature varia-tion during and after re-entry into the atmosphere. During

1359-8368/$ - see front matter � 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.compositesb.2006.06.005

* Corresponding author. Tel.: +1 352 392 6749; fax: +1 352 392 7303.E-mail address: sankar@ufl.edu (B.V. Sankar).

1 Postdoctoral Associate.

the testing of a prototype composite tank microcracksdeveloped in the inner facesheet of the sandwich structureat cryogenic conditions. Then the microcracks, which usu-ally develop in the transverse plies, could become delamin-ations. This could have led to catastrophic failure of thesandwich structure [1]. The damage progression in lami-nated composites at cryogenic temperatures is illustratedin Fig. 1. At cryogenic temperatures, the microcracks initi-ate and propagate in laminated composites due to differ-ence in thermal contraction between the fiber and matrixphases [2]. These microcracks propagate and result intransverse cracks. When the transverse crack develops fur-ther, the crack deflects through the interface between layersand delamination initiates. The delaminations connect themicrocracks in adjacent layers and provide a leakage pathfor the cryogen. In the case of composite sandwich con-struction, debonding of the facesheet also develops. In aliquid hydrogen composite tank, this hydrogen leakagethrough the transverse cracks and delamination couldcause the failure of the composite sandwich structures [1].This failure motivates the present study on predicting the

Fig. 1. Damage progression at cryogenic conditions.

194 S. Choi, B.V. Sankar / Composites: Part B 38 (2007) 193–200

fracture toughness of a transverse crack in composite lam-inates at cryogenic temperatures.

When a microcrack propagates normal to a ply-interfaceor causes a delamination between composite layers, itsfracture toughness is governed by the stress singularity atthe crack tip. Normal stresses at a crack tip are governedby stress singularity k and stress intensity factor KI asshown in Fig. 2. Williams [3] found the normal stressesahead of a crack tip are proportional to r�k (0 < Re[k] < 1) where r is the distance from the crack tip. The stres-ses normal to the crack ahead of a crack tip can beexpressed as r = KIr

�k. The stress singularity of a trans-verse crack in laminated composites is governed by aniso-tropic material properties at the vicinity of a crack tip.

A microscopic image of cracks in a graphite/epoxy lam-inate is shown in Fig. 3. The 0� layer is stiffer than the 90�

Fig. 2. Local stress field in the vicinity of a crack tip.

Fig. 3. SEM images of micro-crack propagation in composite laminatesafter thermo-mechanical cycles.

layer in the in-plane direction. When the transverse crackreaches a stiffer layer, it deflects into the ply-interfacebetween layers and the interfacial crack or delaminationcontinues to propagate. When the transverse crack reachesa softer layer, it penetrates into the next layer and contin-ues to propagate until it reaches a stiffer layer [4]. In thisstudy, conditions under which a transverse crack becomesa delamination are studied, and the fracture toughness ofthe transverse crack is quantified and measured.

Many researchers have studied the problem of stress sin-gularity in bi-material systems, but not much work hasbeen done on such crack propagation in fiber reinforcedcomposite laminates. Zak and Williams [5] estimated thesingularity for isotropic bi-material systems by solving aset of eigen functions developed by the continuity equa-tions of normal and tangential stresses and displacementsat the ply-interface. Ting and Chou [6] have developedmethods to predict singularity at the free-edge of a ply-interface of laminated composites. The general equationsof displacement and stresses are derived in terms of arbi-trary constants. Stress singularity is determined when theboundary condition at a crack plane and the continuityequations at the ply-interface are satisfied. Later, Tingand Hoang [7] used this method to predict singularity ofa transverse crack in laminated composites. Hutchinsonand Suo [8] formulated a characteristic solution to predictstress singularity for isotropic bi-material systems in termsof Dundur’s bi-material parameters a and b. Gupta et al.[4] formulated a characteristic solution to predict the singu-larity for anisotropic bi-materials in terms of bi-materialparameters and individual material parameters. However,the characteristic equation is difficult to solve.

The behavior of the transverse fracture and ply delami-nation of composite laminates has been investigated bymany researchers. Takeda and Ogihara [9] conductedexperimental investigation to determine Young’s modulusreduction and the mode II interlaminar fracture toughnessKII at room temperature and at 80 �C. Wang and Kariha-loo [10] investigated the transverse crack delamination ofcomposite laminates in two cases. First, when the trans-verse crack resides within a layer, model II fracture loadFII was determined using the analytical approach [11]. Withthe results, the layer orientation of a sample composite sys-tem was optimized to minimize interfacial stresses thatcause mode II fracture. Second, when the transverse crackreaches the interface of an adjacent layer, the mode II stresssingularities were determined for various composite materi-als with varying the ply orientation of the adjacent layer[11]. However, their study does not include the effects oftemperature on transverse fracture. Petrossian and Wis-nom [12] developed the finite element method using theinterface elements to predict the failure loads of mode IIdelamination applying the plasticity theory.

The purpose of the study is to investigate the effect ofcryogenic temperature on transverse crack propagation.The finite element model was developed to evaluatefracture toughness of the transverse crack in laminated

Fig. 4. Geometry of interfacial fracture specimens and a crack normal to laminate interface with different stacking sequence.

S. Choi, B.V. Sankar / Composites: Part B 38 (2007) 193–200 195

composites at room and cryogenic temperatures. Prior tothe FE analysis, fracture loads were measured by experi-mental investigation at room and cryogenic temperatures.Comparison of fracture toughness values at room andcryogenic temperatures provide an understanding of therole of thermal stresses on the behavior of transverse cracksin laminated composites. The results from this study will beuseful in understanding the effects of transverse cracks incomposite storage systems at cryogenic temperatures.

2. Crack tip stress singularities for a crack normal

to a ply-interface

The analytic approach is used to evaluate the singularityat the tip of a transverse crack in glass/epoxy and graphite/epoxy (IM7/977-2) composites with stacking sequence [03],[0/90/0] and [90/0/90] (see Fig. 4). In this study, stress sin-gularity of a transverse crack in laminated composites iscalculated using Ting’s methods [6,7], and finite elementanalysis is used to compute the crack tip stress fields in var-ious laminated composite models.

The crack tip of the transverse crack is placed at theinterface between top and mid-layers. The temperaturedependent laminate properties used in this analysis areshown in Table 1 [2,13]. The singularities are compared

Table 1Temperature dependent properties of carbon/epoxy laminates

T = 293 K T = 77 K

E11 (GPa) 159 160E22, E33 (GPa) 8.60 106G12, G13 (GPa) 3.95 5.35G23 (GPa) 2.95 3.64m12, m13 0.256 0.254m23 0.446 0.448a11 (10�6/�C) �0.512 �0.621a22, a33 (10�6/�C) 16.3 14.1

Fig. 5. Deformed geometry in the vicinity of

with the finite element results. The commercial computerprogram MATLAB� is used to solve the analytical equa-tions. Finite element analysis is used not so much to verifythe results from the analytical model but to determine themesh refinement needed to obtain the proper singularityat the crack tip. In the finite element analysis the laminatedcomposite beam was modeled using eight-node solid ele-ments with 20 integration points. Glass/epoxy and graph-ite/epoxy (IM7/977-2) composites with stacking sequence[03], [0/90/0] and [90/0/90] are chosen to verify the stresssingularity of the transverse crack. The ply thickness wastaken as 2.2 mm. The length of the beam was 146 mmand the width 18.7 mm. An initial crack normal to a ply-interface is placed at the center of the beam subjected totensile or bending loads (see Fig. 5). The region surround-ing the crack tip was refined using 31,000 quadratic solidelements.

The composite beam model is subjected to four-pointbending and tensile loading conditions as shown inFig. 6. For the tensile case, uniform displacement in thein-plane direction is applied at the end of the bar. Forbending cases, the beam is simply supported at 63.7 mmaway from the crack. The top load is located at 19.5 mmaway from the crack. The normal stresses ahead of thetransverse crack tip are used to calculate the stresssingularity.

A logarithmic plot of the normal stresses as a functionof distance from the crack tip is used to determine the sin-gularity in the FE model. The crack tip stress field isassumed to be of the form r = KI Æ r�k, where 0 < k < 1.The stress singularity k is estimated by calculating the slopeof a logarithmic plot of normal stress as a function of dis-tance r ahead of a crack tip.

The stress singularities determined from the finite ele-ment analyses are compared with the analytical resultsfor various laminates in Tables 2 and 3. There seems tobe a good agreement between the two sets of results. The

a crack tip of the finite element model.

Table 2Singularity at the tip of a transverse crack in various E-glass/epoxylaminates

Layers Analytical(Ting’s)

FEM (ABAQUS)

Tensile Differencefromanalytical (%)

Bending Differencefromanalytical (%)

[03] 0.50 0.50 0.3 0.50 0.2[0/90/0] 0.38 0.38 1.1 0.39 2.3[903] 0.50 0.50 0.3 0.50 0.1[90/0/90] 0.63 0.63 1.1 0.61 3.1

Table 3Singularity at the tip of a transverse crack in various graphite/epoxylaminates

Layers Analytical (Ting’s) FEM (ABAQUS)

Tensile Error(%)

Bending Error(%)

[03] 0.50 0.50 0.5 0.50 0.0[0/90/0] 0.26 0.27 2.6 0.29 7.8[903] 0.50 0.50 0.5 0.50 0.1[90/0/90] 0.71 0.70 4.8 0.69 5.9

Fig. 7. Four-point bending test to determine the fracture load.

Table 4Dimensions of specimens with various mid-ply thicknesses

[0/90/0] Length(mm)

Width(mm)

Layer thickness

Top and bottom0� layer (mm)

Mid 90�layer (mm)

Specimen 1 145.4 18.6 2.4 1.8Specimen 2 146.2 18.7 2.4 2.4Specimen 3 145.7 18.8 2.4 3.0

Fig. 6. Contour plots of stress distribution in a [0/90/0] compositelaminate model at the crack tip under: (a) tensile load; (b) bending load.

196 S. Choi, B.V. Sankar / Composites: Part B 38 (2007) 193–200

maximum difference between the two values is 7.8%. Whenthe laminate orientation of the materials on both side ofply-interface are identical as in the case of unidirectionallaminates, ([03] and [903]), the singularity k = 0.5. Whenthe laminate ahead of the crack tip is stiffer, as in [0/90/0] laminates, the stress singularity k becomes less than0.5, and it is greater than 0.5 when the crack is in the 0�ply touching the 0/90 interface as in [90/0/90] laminates.The results provide confidence in the accuracy of the finiteelement models in capturing the singularity for transversecracks in a composite laminate. Then the FE model canbe used to analyze several composite systems used in frac-ture tests.

3. Fracture toughness at room temperature

Four-point bending experiments were performed todetermine the fracture loads of laminated beam specimensat room temperature as shown in Fig. 7. The four-point

bending test has the advantages that it would yield moreaccurate and repeatable results as the transverse crack isin a region under constant bending moment without anytransverse shear force. Even a small offset of the loadingpoint with respect to the crack location will not signifi-cantly affect the results.

The proposed specimen has three layers of graphite/epoxy laminate with stacking sequence [0/90/0]. The topand bottom layers for all specimens have the same thick-ness of 2.4 mm and the mid-layer has various thicknesses,1.8, 2.4 and 3.0 mm. The dimensions of specimens are listedin Table 4. An initial crack was created at the center of thespecimen below the top layer. The notch was cut using afine diamond saw, and then the razor blade was used tosharpen the crack tip. The initial crack tip is located inthe mid-layer and below the ply-interface of the top layer.The specimen is simply supported at 63.7 mm away fromthe initial crack. The top loads are applied at a distanceof 19.5 mm from the crack. The bending tests were con-ducted under displacement control in a material testingmachine at a loading rate of 1.0 mm/min.

The load-deflection results of various specimens areshown in Fig. 8. The load increases linearly until the cracktip reaches the ply-interface of the top layer. After theinterfacial fracture initiates, and as the crack propagatesas a delamination, the load remains almost constant andthe stiffness of the specimen reduces continuously. Whenthe crack approaches the beam support, the energy releaserate decreases and crack propagation stops. The load againincreases linearly with deflection. The fracture loads Fc aremeasured at the instant when interfacial fracture initiates.The fracture loads for the three different specimens arelisted in Table 5. One can note that the fracture loadincreases with the thickness of the middle 90� layer.

Displacement (m)

Load

(N

)

0 0.002 0.004 0.006 0.008

50

100

150

200

Specimen 1(Mid-layer thickness = 1.8 mm)

Displacement (m)

Load

(N

)

0 0.002 0.004 0.006 0.0080

50

100

150

200

250

Specimen 2(Mid-layer thickness = 2.4 mm)

Displacement (m)

Load

(N

)

0 0.002 0.004 0.006 0.0080

50

100

150

200

250

Specimen 3(Mid-layer thickness = 3.0 mm)

Fig. 8. Load–displacement curves of four-point bending tests at room temperature for various specimens with different mid-ply thicknesses.

Table 5Fracture load (Fc) and fracture toughness (KIc) at room and cryogenictemperatures

[0/90/0] Room temperature(T = 300 K)

Cryogenic temperature(T = 77 K)

Fc (N) KIc

(MPa-m0.29)Fc (N) KIc

(MPa-m0.29)

Specimen 1 122 58.1 88.1 55.6Specimen 2 127 57.9 81.5 58.1Specimen 3 133 58.0 74.7 58.8

Average 127 58.0 81.4 57.5

Standarddeviation (%)

4.3 0.2 8.2 2.9

Distance from a crack tip, r (m)

Fra

ctur

eto

ughn

ess

(Pa

-m

)

0 1E-05 2E-05 3E-050

1E+07

2E+07

3E+07

4E+07

5E+07

6E+07

7E+07

8E+07

Case 1Case 2Case 3

−λ

Fig. 10. Variation of K ¼ rrk with the distance from the crack tip at roomtemperature.

9.6

9.8

10

Case 1Case 2Case 3

S. Choi, B.V. Sankar / Composites: Part B 38 (2007) 193–200 197

Finite element analyses of the test specimens were per-formed to obtain the detailed stress field in the vicinity ofthe crack tip corresponding to the fracture loads. Due tosymmetry one-half of the specimen is modeled. The lami-nate properties of graphite/epoxy given in Table 1 are usedfor the FE model. The composite laminates are in stressfree condition at curing temperature (T = 455 K). Henceresidual stresses exist even at room temperature(T = 293 K). A contour plot of the stress distribution isshown in Fig. 9. The fracture toughness KIc can be calcu-lated in two ways. The first method is similar to the ‘‘stressmatching’’ [14] as described by the equation below (seeFig. 10):

KI ¼ limr!0

rðrÞrk ð1Þ

Fig. 9. Stress distribution for the four-point bending simulation at: (a)room temperature; (b) cryogenic temperature.

In the second method a logarithmic plot of r vs. r is usedto determine the best value of K by fitting (see Fig. 11):

rðrÞ ¼ KIr�k ð2Þ

log r

log

σ 11

-7 -6.8 -6.6 -6.4 -6.2 -6 -5.8 -5.6 -5.4 -5.2 -59

9.2

9.4

Fig. 11. Logarithmic plot of the stresses as a function of distance from thecrack tip.

198 S. Choi, B.V. Sankar / Composites: Part B 38 (2007) 193–200

In both methods the singularity k derived from the ana-lytical method was used. The results for K from both meth-ods were very close, and in this paper results from the stressmatching method Eq. (1) are used.

From the results shown in Table 5, one can note that theincrease in fracture load Fc is about 8% with 67% increaseof mid-ply thickness. However the variation in the fracturetoughness KIc is less than 1/2%. The results show that thefracture toughness is independent of the mid-ply thickness.Fracture toughness is only dependent on local materialproperties at the crack tip, but not on the global propertiesof the laminate system.

4. Fracture toughness at cryogenic temperatures

The effect of cryogenic temperature on fracture tough-ness is investigated by performing the fracture tests atliquid nitrogen temperature. Liquid nitrogen (LN2) is usedas the cryogenic refrigerant for several reasons. It is chem-ically inactive and non-toxic. Unlike hydrogen, nitrogen issafe to use in the laboratory. Liquid nitrogen is a colorlessfluid like water.

The beam specimens were submerged initially in liquidnitrogen for about 5 min to reduce thermal gradients inthe specimens (Fig. 12). The boiling temperature of LN2

is 77 K. The specimen is placed in the cryogenic containerwith the liquid nitrogen. When the temperature of speci-men reaches the boiling temperature, LN2 boiling disap-pears. During this process, some specimens experienceddelamination on the edge of mid-ply as shown in Fig. 13.

Finite element analysis was performed to investigate theedge delamination in the laminated specimens. The quarterregion of the actual specimen was modeled using eight-

Fig. 12. Cryogenic experimental setu

Fig. 13. Crack propagation in the 90� layer of a gra

node 3-D solid elements. A contour plot of stresses intwo-direction is shown in Fig. 14 when the FE model issubjected to cryogenic temperature (T = 77 K). The stres-ses in two-direction stay constant in 80% of the widthand increases sharply near the edge as shown in Fig. 14.The sudden temperature decrease can be a reason for theedge delamination. Since graphite/epoxy composite hasnegative longitudinal CTE in the one-direction (see Table1), the mid-layer expands and the top and bottom layershrinks at cryogenic temperature. Therefore, Mode I frac-ture behavior can be expected at the edge. The result indi-cates that the edge delamination is not too deep to affectthe experimental results for the fracture toughness of trans-verse cracks.

The four-point bending test fixture is placed in an insu-lated container and liquid nitrogen (LN2) is filled upslowly. The LN2 boiling disappears when the temperatureof the test fixture becomes stable. During experiment,LN2 is continuously added into the container so that spec-imen is completely submerged since LN2 vaporizes due tothe heat entering from the atmosphere. The four-pointbending test is performed following the same proceduresused for room temperature tests.

The load–displacement results are shown in Fig. 15. It isfound that the fracture load decreases as the mid-ply thick-ness increases. Fracture load decreases by 15% with 67%increase in the mid-ply thickness as shown in Table 5. Asshown will be later fracture load decrease may be due tothermal stresses in the vicinity of the crack tip at cryogenictemperature. Fracture toughness at cryogenic temperatureis predicted using the finite element analysis. The tempera-ture dependent laminate properties are used for the FEanalysis at cryogenic temperature as shown in Table 1.

p of the four-point bending test.

phite/epoxy laminate at cryogenic temperature.

Distance from a center to an edge (m)

Str

ess

(Pa)

0 0.002 0.004 0.006 0.0080

5E+06

1E+07

1.5E+07

2E+07

2.5E+07

3E+07

3.5E+07

4E+07

4.5E+07

5E+07

Fig. 14. Contour plot of stresses normal to ply direction near the free-edgein a graphite/epoxy laminate at cryogenic temperature.

Distance from a crack tip, r (m)

Fra

ctur

eto

ughn

ess

(Pa

-m

)

0 1E-05 2E-05 3E-050

1E+07

2E+07

3E+07

4E+07

5E+07

6E+07

7E+07

8E+07

Case 1Case 2Case 3

−λ

Fig. 16. Variation of K ¼ rrk with the distance from the crack tip atcryogenic temperature.

S. Choi, B.V. Sankar / Composites: Part B 38 (2007) 193–200 199

The composite beam experiences temperature decreasefrom curing temperature (T = 455 K) to cryogenic temper-ature (T = 77 K). The contour plot of the stress distribu-tion is shown in the Fig. 9. Fracture toughness iscalculated following the same procedure as described inthe previous section for room temperature tests. The vari-ation of normal stresses with the distance from the cracktip is shown in Fig. 16. Although the fracture loadsdecreases by 15% with 67% increase in mid-ply thickness,fracture toughness increases by only 5%. The variation offracture toughness between the three specimens tested atcryogenic temperature is insignificant. The result indicatesthat fracture toughness is not significantly affected by the

Displacement (m)

Load

(N)

0 0.001 0.002 0.003 0.004 0.0050

20

40

60

80

100

120

140

160

180

200

Specimen 1(Mid-layer thickness = 1.8 mm)

Displacem

Load

(N

)

0 0.002 0.0040

20

40

60

80

100

120

140

160

Specimen 2(Mid-layer thic

Fig. 15. Load–displacement curves from four-point bending tests at cryogen

cryogenic conditions. But, the fracture load significantlydecreases due to thermal stresses present in the vicinity ofthe crack tip. At both room and cryogenic temperaturesfracture toughness is estimated as 58 MPa. The result indi-cates fracture toughness is a characteristic property of thematerial system not governed by temperature changes.

It should be noted that the specimen dimensions andgeometry are nominally the same for room temperatureand cryogenic temperature tests. But, the fracture load issignificantly lower at cryogenic temperature. However thefracture toughness, the critical stress intensity factor, seemsto be the same. This is because there are significant thermalstresses at cryogenic temperature, which increases thisstress intensity factor to a higher value. The same inferencecan also be made from the standard deviation of resultsshown in Table 5. The standard deviation for fractureloads is much higher than that for the fracture toughnessat both room temperature and cryogenic temperature.Another observation is that the standard deviation of frac-ture toughness at cryogenic temperature is higher thanthat for room temperature tests indicating that it is diffi-cult to obtain repeatable measurements under cryogenic

ent (m)0.006 0.008

kness = 2.4 mm)

Displacement (m)

Load

(N

)

0 0.002 0.004 0.006 0.0080

20

40

60

80

100

120

140

160

Specimen 3(Mid-layer thickness = 3.0 mm)

ic temperature for various specimens with different mid-ply thicknesses.

200 S. Choi, B.V. Sankar / Composites: Part B 38 (2007) 193–200

conditions, and the test methods for cryogenic measure-ments need to be improved.

5. Conclusions

The stress singularity at the tip of a transverse cracktouching a ply-interface in graphite/epoxy laminates wasdetermined suing an analytical procedure. The results werealso verified by performing a finite element analysis of four-point bending and uniaxial tensile specimens containing atransverse crack. The results also provided confidence inthe accuracy of the finite element models in capturing thesingularity accurately. Fracture tests were performed usingsingle edge notch bend specimens under four-point bend-ing. The fracture load, the load at which delamination ini-tiated from the transverse crack, was input in the FE modelto determine the stress intensity factor and hence the frac-ture toughness. The temperature dependent properties wereused for the analysis at room and cryogenic temperatures.The specimen is assumed to be in stress free condition atcuring temperature. The experiments were repeated forvarious crack lengths and it was found that the fracturetoughness was same for all specimens. The fracture testswere performed under cryogenic conditions by immersingthe specimens in liquid nitrogen. The specimens failed ata much lower load compared to the room temperaturetests. However, the results from the FE analysis showedthat the fracture toughness was same as that at room tem-perature. The thermal stresses in the vicinity of the cracktip contributed to the increase in stress intensity factorcausing the specimens to fracture at a lower load comparedto room temperature tests. The results from this study willbe useful in the design of composite storage systems forcryogenic applications.

Acknowledgements

The authors gratefully acknowledge the technical andfinancial support of NASA Glenn Research Center(NAG3-2750) and NASA Kennedy Space Center under

the Hydrogen Research and Education program. Partialsupport was provided by the CUIP (URETI) Programsponsored by NASA under NCC3-994, managed by NASAGlenn Research Center.

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