Composite Structures 94 (2012) 477–483

Contents lists available at SciVerse ScienceDirect

Composite Structures

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

Experimental determination of validated, critical interfacial modes I and IIenergy release rates in a composite sandwich panel q

Paul Davidson a, Anthony M. Waas b,⇑, Chandra S. Yerramalli c

a Dept. of Mechanical Engineering, University of Michigan, Ann Arbor, MI, USAb Dept. of Aerospace Engineering, University of Michigan, Ann Arbor, MI, USAc Composite Design and Analysis Lab, General Electric Global Research Center, Niskayuna, NY, USA

a r t i c l e i n f o

Article history:Available online 23 August 2011

Keywords:Sandwich compositeCohesive zoneEnd Notch FlexureFractureDelamination

0263-8223/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.compstruct.2011.08.007

q Based on a presentation at ICCS16, Porto, Portuga⇑ Corresponding author.

E-mail address: dcw@umich.edu (A.M. Waas).

a b s t r a c t

A validated experimental approach to obtaining critical mode I and mode II energy release rates for inter-facial failure in a sandwich composite panel is outlined in this paper. By modifying the geometry of thesandwich structure to align the face sheet-core interface to coincide with the neutral axis, it is possible toobtain critical mode I and mode II energy release rates by conducting Double Cantilever Beam (DCB) andEnd Notch Flexure (ENF) tests, respectively. The values so obtained were used to predict the crack growthhistories of modified DCB and ENF tests, and a Single Leg Bend (SLB) test, using a discrete cohesive zonemethod (DCZM). In addition, the influence of material and geometry were also analyzed.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Sandwich composite materials are finding increasing applica-tions in the aerospace and wind turbine industry due to high spe-cific (per unit mass) shear strength properties. A typical sandwichstructure is a two material system with a low stiffness core andhigh stiffness face sheets. The face sheets are bonded to the corematerial, which makes the interface the weakest section of thestructure. Most failure in sandwich composites is initiated at theinterface which is a transition region in a bi-material system. Con-siderable research has been devoted to understanding and charac-terizing bi-material interface fracture using analytical, numericaland experimental methods. Analytical approaches can be classifiedinto global (based on beam theory [1,2]) and local (based on cracktip region singular field [3]) formulations. These methods aredeveloped to extract energy release rate and/or stress intensity fac-tor and mode mixity ratios. Pioneering work by Suo and Hutchin-son [3], based on linear elastic fracture mechanics (LEFM), has beenextended to many different test configurations to extract mode Iand mode II energy release rates [4–6]. Improvements by account-ing for shear deformation [2] and root rotations [7] have also beenmade to classical formulations.

Available numerical methods used for analysis, generally followtwo approaches; they are either based on Irwin’s stress intensityfactor [9], or on energy release rates [8] attaining critical values,either as single mode problems or as mixed mode ones. For failure

ll rights reserved.

l, June 28–30, 2011.

prediction, particularly under mixed-mode conditions, cohesivezone based methods implemented using the finite element meth-od, for example [10], are more suitable because of its ease of imple-mentation and versatility in analyzing complicated geometries.Cohesive zone based methods require critical energy release ratesand cohesive strengths in pure mode I (GIc,rc) and mode II (GIIc,sc).Traditionally, DCB, ENF and lap-shear (and sometimes, button-peel) tests are employed to determine these critical quantities[11]. However, this is not as straight forward in the case of sand-wich structures, because the crack plane at the face-sheet/coreinterface, needed to determine critical interfacial parameters, isnot situated at a location that allows single mode (pure) tests tobe carried out.

There have been experimental methods reported to extract modeI and mode II energy release rates [12–14]. These methods are ingeneral a modification of two fundamental test configurations, Dou-ble Cantilever Beam (DCB) and End Notch Flexure (ENF) test. How-ever, due to the location of the crack plane, all configurations havesome element of mode mixity. Mixed mode tests, such as the un-symmetrical Double Cantilever Beam (UDCB) [4], UnsymmetricalEnd Notch Flexure (UENF) [6] and Single Leg Bend (SLB) [5,13] testhave found popularity among experimentalists due to their simplic-ity and available closed form solutions. Other more complicated testmethods like Uneven Bending Moment DCB (DCB-UBM) [7] havealso been used. All the methods mentioned above provide energy re-lease rate contributions to the total G obtained, however, when totalG is critical, the component values, GI and GII may not have attainedcriticality. Hence, extensive numerical iterations are required tomatch the load displacement curves of such coupon tests to subse-quently extract the component critical parameters.

478 P. Davidson et al. / Composite Structures 94 (2012) 477–483

In this study, a simpler approach is employed to obtain GIc andGIIc experimentally. These values are validated using the resultsfrom an independent mixed mode test in conjunction with a pre-diction using the DCZM and a finite element model.

2. Sandwich specimen designs

Obtaining critical mode I and mode II strain energy release ratesand corresponding cohesive strengths, for an interface between theface-sheet and core of sandwich panel is difficult because thisinterface is shifted away from the neutral axis of the sandwich pa-nel, causing both shear and peel to exist even for traditionally puremode I and mode II tests that use DCB and ENF configurations. For-mulations for unsymmetrical DCB and ENF have been developed;however, these methods only provide the contribution of individ-ual failure modes and not the critical energy release rates fromeach mode. To obtain pure mode I and mode II energy release rates,the approach used here was to simply modify the geometry of thesandwich structure such that the intended plane of fracture coin-cides with the neutral axis. This is achieved by using a sandwichspecimen that has approximately similar bending stiffnesses aboveand below the cracking plane. The resulting coupon geometry is anunsymmetrical sandwich with respect to the geometrical midplane but is symmetrical with respect to the interface betweenthe top face sheet and core, which is the plane of interest.

The approach, though simple, can be difficult to achieve withactual composite material, because thickness of the face sheetsare multiples of individual lamina (ply) thickness, which providesdiscrete fixed values of thickness. Hence, an optimization formula-tion should be used to obtain geometries with fracture plane sym-metry by minimizing the difference between the bending stiffnessof laminates above and below the interface.

min e ¼ jDT � DBj ð1Þ

with constraints on the thickness

Fig. 1. Bi-material system under general loads.

−10 −5 0 5 10

Exx1

Exy1

νxy1

νyx1

Exx2

νxy2

(a) DCB

0.92

0.94

0.96

0.98

1

1.02

1.04

1.06

1.08

Variation in properties [%]

Gi /

Gi0

Fig. 2. Change in energy release rate due to variation in

h1 þ h2 þ h3 � H ¼ 0; h2 > 0 ð2Þ

here, subscripts ‘T’ and ‘B’ refer to the top and bottom laminate ofthe bi-material sandwich interface, H is the total sandwich thick-ness, which is a fixed value and h1, h2 and h3 are the top face sheet,core and bottom face sheet thicknesses respectively. Di denotes thebending stiffness which is a function of material properties andthickness.

DT ¼ f ðE1jk; m

1jk;G

1jk;h1Þ; DB ¼ f ðE2;3

jk ; m2;3jk ;G

2;3jk ; h2;h3Þ ð3Þ

where, superscripts ‘1’, ‘2’, ‘3’ refer to the top face sheet, core andbottom face sheet respectively. Ejk, Gjk, mjk are the elastic modulus,shear modulus and Poison’s ratio, respectively, for orthotropicmaterial. The sub-laminate bending stiffnesses are calculated basedon classical lamination theory [15].

2.1. Influence of material and geometric parameters

The optimization procedure described above will provide theideal geometry required for pure mode I and pure mode II testing.However, in practice this might not be the case due to variations inmaterial and geometry. Hence, it is important to ensure that thereis no significant change in test results due to material and geomet-ric variation. To study the influence of material and geometry var-iation on pure DCB and ENF result, an analytical method wasemployed.

The basic analytical formulations used here follows the sheardeformable bi-layer beam theory proposed by Wang and Qiao[2], as shown in Fig. 1. The formulation is based on split beam the-ory and the energy release rate in mode I and mode II are obtainedusing a global approach. The expressions for mode I and mode IIenergy release rates are given as:

GI ¼12

1BTþ 1

BB

� �V þ k M þ hT N

2

� �� �2

ð4Þ

GII ¼1

hTnþ 2gðnM � gNÞ2 ð5Þ

here, M, N, V are the effective moment, normal and shear forces onthe bi-material interface crack tip. Calculations of M, N and V for theDCB and ENF, and other related parameters, are provided in Appen-dix A.

Using the formulation above, a perturbation analysis was con-ducted, where independent material parameters were varied with-in ±10% of nominal, and thicknesses of the top and bottom facesheet were varied ±3 plies of nominal. Fig. 2 shows the effect of

0.94

0.96

0.98

1

1.02

1.04

1.06

1.08

1.1Exx

1

Eyy1

νxy1

νyx1

Exx2

νxy2

(b) ENF

0G

ii / G

ii

−10 −5 0 5 10Variation in properties [%]

material properties in, (a) DCB test and (b) ENF test.

−3 −2 −1 0 1 2 3

h1

h3

(a) DCB

−3 −2 −1 0 1 2 3

h1

h3

(b) ENF

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3G

i / G

i0

Variation in number of plies [−] Variation in number of plies [−]

0.8

1

1.2

1.4

1.6

1.8

2

Gii/G

ii0

Fig. 3. Change in energy release rate due to variation in face sheet thickness in, (a) DCB test and (b) ENF test.

Table 1Nominal specimen dimensions for DCB and ENF tests.

Type L (mm) b (mm) h1 (mm) h2 (mm) h3 (mm) a0 (mm)

DCB 120 25.4 4.83 3.5 2.76 53ENF 70 25.4 4.83 3.5 2.76 15

Fig. 4. Double Cantilever Beam (DCB) and End Notch Flexure (ENF) test coupongeometry.

Table 2Nominal specimen material properties.

Type E11 (GPa) E22 (GPa) l12 (–) l21 (–) G12 (GPa)

Composite 11.5 8.0 0.3 0.25 3.0Core 3.0 3.0 0.3 0.3 1.2

P. Davidson et al. / Composite Structures 94 (2012) 477–483 479

material variation on GI and GII with respect to nominal values G0I

and G0II. Overall, with 10% variation in material properties only

about ±6% variation in DCB GI values and �4% to 8% variation inENF GII is seen, indicating material variations have small impacton values of GI/II. As expected, the thickness variation due to chang-ing the number of plies in the bottom face sheet laminate has ahigher impact on the values obtained for both DCB and ENF energyrelease rates. Reduction in thickness has greater influence on GI/II

with maximum change of about 25% in case of DCB and about dou-ble that in the case of ENF as shown in Fig. 3. The variation is par-ticularly severe in case ofthe ENF test. Clearly, the analysisindicates criticality of the bottom face sheet thickness when mod-ifying geometries for pure mode I and pure mode II experiments.Overall, if the material thickness is maintained at a given value,then the variation in GI/II are within ±10%, which is reasonable.

3. Experiment

Using the optimization formulation described above, coupondimensions corresponding to DCB and ENF testing was deter-mined. The manufactured specimen thicknesses are listed inTable 1.

3.1. Modified coupon DCB and ENF test

Displacement controlled DCB and ENF experiments were con-ducted with the modified sandwich panels. The geometry of thesample is shown in Fig. 4 and Table 1 lists the dimensions. The ini-tial crack was introduced between the top face sheet and the adhe-sive core using a Teflon� film, inserted during manufacturing of thesandwich coupons. For DCB tests, steel blocks with a transversethrough hole at its center were bonded to the free end of the lam-inates for pin joint load transfer. The pin joint was lubricated usingTeflon lubricant to reduce frictional loss. A three point bend fixturewas employed for the ENF test. Clear markings on the specimenside surfaces were used to track crack growth. Material propertiesof the bi-axial face sheet and adhesive core are given in Table 2

The tests were conducted on an MTS universal test machinewith a crosshead displacement rate of 1 mm/min. Load was mea-sured continuously using a high accuracy tension/compressionload cell linked up to a data acquisition system. A high resolutionSLR camera, time synchronized with loading, was used to capturecrack zone images with a framing rate of 1 frame per second.The images were then analyzed manually, using a linear pixel mea-suring software calibrated against a reference grid pattern markedon a typical specimen. This method gives crack length in the time

domain which can be then converted to plot crack length againstload and load point displacement.

In the DCB specimen, though the failure was mainly through theinterface (Fig. 5a), beyond crack growth of about 15 mm, an oscil-

(a)

(b)

Fig. 5. Double Cantilever Beam (DCB) – modified sandwich coupon.

480 P. Davidson et al. / Composite Structures 94 (2012) 477–483

latory pattern is observed indicating the crack turning in and out ofthe adhesive. This is confirmed by examining the completely bro-ken samples of the tested coupons (Fig. 5b). A small amount of ri-gid body rotation is also observed. These inconsistencies can beattributed to manufacturing constraints arising from difficulty inmaintaining required dimensions, especially dealing with layeredmaterials. However, the fact that the crack tends to turn back tothe interface indicates that this test configuration can be used forpure mode I testing. Load displacement curves for the DCB testsare shown in Fig. 6. A through thickness fracture was observed in

0 5 10 15 20

DCB−S1DCB−S2DCB−S3

0

50

100

150

200

250

300

Crosshead Displacement [mm]

Load

[N]

Fig. 6. Force–displacement plots for the DCB tests. (For interpretation of thereferences to color in this figure legend, the reader is referred to the web version ofthis article.)

45 50 55 60 65 70

mean

min

max

G [N

/mm

]

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Crack length [mm]

Fig. 7. G v/s crack length variation for DCB tests.

one of the sample after the crack had propagated by 12 mm. Over-all, the load displacement response showed reasonable consistencyin peak load and post-peak response. Energy release rates from theDCB test results were calculated using Modified Beam Theory [16].Fig. 7 provides the G versus crack length curve, which showsslightly larger values at the beginning but the spread diminishesas the crack length increases, suggesting a fairly constant value.The average and standard deviation of GI is provided in Table 3,these are the values used as critical energy release rates, later inconjunction with the SLB test.

Fig. 8 shows a side view of a ENF test specimen with the crackpropagating entirely through the interface. There were two sam-ples that showed de-lamination occurring in the face sheets andparallel to the interfacial crack propagation, but near the loadinghead. The majority of ENF tests showed consistency in peak load,Fig. 9, however, the difference in stiffness indicates variabilitydue to manufacturing. The energy release rate for the ENF speci-men was calculated based on the compliance method. The averageand standard deviation of GII are also given in Table 3.

3.2. SLB validation test

To validate the critical GI and GII obtained using the modifiedDCB and ENF tests, an independent test is required. Hence, a dis-placement controlled Single Leg Bend (SLB) test was conductedthat drives an interfacial crack under mixed-mode conditions.The SLB geometry and configuration used are shown in Fig. 10and listed in Table 4. The single leg bend test is essentially a threepoint bend test with the lower half of the bi-material interface freeof loading. Even though the SLB is a mixed mode test, it is mode I

Table 3Energy release rates obtained from DCB and ENF tests.

Type Avg GI (N/mm) Std (N/mm) Avg GII (N/mm) Std (N/mm)

DCB 2.08 0.419 – –ENF – – 20.9 1.55

Fig. 8. End Notch Flexure (ENF) – modified coupon.

0 1 2 3 4 5 6

ENF−S1ENF−S2ENF−S3

Load

[N]

0

1000

2000

3000

4000

5000

6000

7000

8000

Crosshead displacement [mm]

Fig. 9. Force–displacement plots for ENF tests. (For interpretation of the referencesto colour in this figure legend, the reader is referred to the web version of thisarticle.)

Fig. 10. Validation using the Single Leg Bend (SLB) test.

Table 4Nominal specimen dimensions for SLB tests.

Type Lss

(mm)Lsc

(mm)Lsa

(mm)h1

(mm)h2

(mm)h3

(mm)a0

(mm)

SLB 120 60 20 4.83 10 4.83 10

SLB−S1SLB−S3SLB−S2

Interface de−bond

Interfacede−bond+ Facesheetde−lamination

Load

[N]

0

100

200

300

400

500

600

700

800

0 2 4 6 8 10

Crosshead displacement [mm]

Fig. 12. Interface debond and face sheet delamination observed during SLB test.(For interpretation of the references to colour in this figure legend, the reader isreferred to the web version of this article.)

30 32 34 36 38 400

0.5

1

1.5

2

2.5

3

3.5

4

Crack length [mm]

G [N

/mm

]

Fig. 13. Typical G vs. crack length curve for a SLB test.

P. Davidson et al. / Composite Structures 94 (2012) 477–483 481

dominated, in the sense that majority of energy is released due tocrack opening than crack sliding.

The SLB test specimens showed de-lamination in the top facesheet after about 10 mm of interface de-bonding as shown inFig. 11. This phenomenon confirms the basic notion that the SLB

Fig. 11. Interface debond and face sheet delamination observed during the SLB test.

test starts from a mode I dominated contribution and gradually in-creases the mode II contribution. De-lamination in the face sheetmay be caused because the mode II critical energy release rate ofthe composite face sheet is lower than the corresponding valueat the interface.

The force displacement curve for the SLB test is shown inFig. 12. Good test repeatability is seen between samples. A steadyincrease in the load is seen until start of composite de-lamination.The strain energy release rate for the SLB test, for the length ofinterface de-bonding, was calculated using the compliance methodand is shown in Fig. 13. An increase in G also indicated the increas-ing mode II contribution.

4. Numerical simulation

The numerical simulations of the DCB, and ENF tests, and theprediction of the SLB test, were conducted using the finite elementmethod in conjunction with the DCZM. An explicit DCZM code isimplemented through a user defined interface element (UEL) sub-routine in Abaqus� [11]. A triangular traction law was used in thesimulation, where for mode I GIc = 2.08 N/mm, rc = 10 MPa and formode II GIc = 20.9 N/mm, sc = 30 MPa values were used. UELs areplaced at the interface between the two arms of the DCB and

0 2 4 6 8 10

Simulationovershootingexperiment at point of de−lamination start

Crack initationin simulation

Crosshead displacement [mm]

Load

[N]

0

100

200

300

400

500

600

700

800

Fig. 14. The predicted force–displacement response compared against experimentfor the SLB tests.

482 P. Davidson et al. / Composite Structures 94 (2012) 477–483

ENF which is the crack path. The cohesive strengths, (rc and sc formodes I and II respectively) corresponding to the mean GIcr, GIIcr

(given in Table 3) was found in case of DCB and ENF geometriesby matching the simulation’s first crack initiation point with theexperimental crack initiation point.

The DCZM parameters were validated by simulating the SLBexperiment and comparing the load–displacement responseagainst the experimental results. In the SLB experiments, compos-ite face sheet de-lamination was observed, however, since the aimhere is to validate interfacial DCZM parameters, we restricted thepredictions to crack growth values of about 10 mm, such that inthis range there is no face sheet delamination. Fig. 14 shows thecomparison between the FE prediction and the experimental re-sults. Good agreement is observed with both initiation and subse-quent propagation. It is also interesting to note that the predictedforce–displacement response over-shoots the experimental resultapproximately at the same displacement point as where de-lami-nation of the face-sheet composite is observed. Further work,which can capture the interaction between the face sheet delami-nation and interfacial cracking is the subject of a future paper. It isobserved that the critical fracture parameters obtained using themodified sandwich specimens made with the same material sys-tems, are able to successfully replicate the SLB test results, the lat-ter being an independent validation.

5. Discussion and conclusion

Experiments, simulations and predictions reported here dem-onstrate that the critical traction separation parameters to be usedin a combined FE-DCZM model of a composite sandwich panel canbe obtained by conducting DCB and ENF tests on suitably designed,geometrically modified sandwich test coupons. By equalizing thebending stiffnesses of the two arms on either sides of the intendedcrack plane (such that crack plane and neutral axis coincide), it ispossible to obtain pure mode I and pure mode II energy releaserates experimentally. Though this is shown to be true for a thickcomposite and a stiff adhesive core sandwich system, this mightnot be the case for a soft core sandwich systems (soft foam coresfor example) where extensive crack tip rotation, and through-the-thickness shear and damage, needs to be accounted for. Per-haps the major constraint for geometrical modifications of the testcoupons for pure mode I and pure mode II, is in manufacturing ofthe composite sandwich panels to specified (and optimized)dimensions. As the perturbation study shows, DCB and ENF testsare relatively insensitive to the variation in material properties,

however, they are highly sensitive to the bottom face sheet ply var-iation. The analysis also indicates that small ply-to-ply thicknessdeviations from ideal coupon thickness values used in specimendesign would not significantly impact the test GI and GII values.Overall, the simple approach employed in this study can be aneffective replacement to more complex experimental and numeri-cal methods, as long as there is freedom to modify the coupongeometry. Other means of stiffening can also be employed if thebasic sandwich structure cannot be modified. Bonding stiffenerson the outer surface of sandwich will also achieve the same effect.

Appendix A

Basic decomposed energy release rate formulation is given inEqs. (4 and 5) and corresponding parameters are [2],

M ¼ M1 �gn

AM �1n

hB

2DB

� �Mt þ

gn

AN �1n

1CB

� �Nt ð6Þ

N ¼ N1 � AMMt þ ANNt ð7Þ

V ¼ V1 �gnþ hT

2

� �AM �

1n

hB

2DB

� �Vt ð8Þ

n ¼ hT

2DT� hB

2DB; g ¼ 1

CTþ 1

CBþ ðhT þ hBÞhB

4DBð9Þ

AM ¼ðDT þ DBÞhB þ nDT DB

2DBðDT þ DBÞgþ nDT DBðhT þ hBÞð10Þ

AN ¼2ðDT þ DBÞ

2CB½2ðDT þ DBÞgþ nDTðhT þ hBÞ�ð11Þ

k ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiBT BB½2ðDT þ DBÞgþ DTðhT þ hBÞn�

DT DBðBT þ BBÞð2gþ hTnÞ

sð12Þ

For DCB [2,17],

M1 ¼ Pa; N1 ¼ V1 ¼ 0; Mt ¼ Nt ¼ Vt ¼ 0 ð13Þ

For ENF [6],

M1 ¼ PT a; N1 ¼ 0; V1 ¼ PT ; Mt ¼ Pa=2;Nt ¼ 0; Vt ¼ P=2 ð14Þ

where P is the applied load, a is the crack length. PT is the load car-ried by the material above the interface in the ENF test and, theexpression for PT is provided by Sundararaman and Davidson [6].

References

[1] Williams JG. On the calculation of energy release rates for cracked laminates.Int J Fract 1988;36:101–19. doi:10.1007/BF00017790.

[2] Wang Jialai, Qiao Pizhong. Fracture analysis of shear deformable bi-materialinterface. J Eng Mech 2006;132(3):306–16.

[3] Suo Zhigang, Hutchinson John W. Interface crack between two elastic layers.Int J Fract 1990;43:1–18. doi:10.1007/BF00018123.

[4] Davidson BD, Sundararaman V. An unsymmetric double cantilever beam testfor interfacial fracture toughness determination. Int J Solids Struct1997;34(7):799–817. cited By (since 1996) 19.

[5] Davidson BD, Sundararaman V. A single leg bending test for interfacial fracturetoughness determination. Int J Fract 1996;78:193–210. doi:10.1007/BF00034525.

[6] Sundararaman V, Davidson BD. An unsymmetric end-notched flexure test forinterfacial fracture toughness determination. Eng Fract Mech1998;60(3):361–77.

[7] Lundsgaard-Larsen Christian, Sorensen Bent F, Berggreen Christian, OstergaardRasmus C. A modified dcb sandwich specimen for measuring mixed-modecohesive laws. Eng Fract Mech 2008;75(8):2514–30.

[8] Irwin G. Analysis of stresses and strains near the end of a crack traversing aplate. J Appl Mech 1957;24:361–4.

[9] Bazant Zdenek P, Planas Jaime. Fracture and size effect in concrete and otherquasibrittle materials. CRC.

[10] Xie De, Waas Anthony M. Discrete cohesive zone model for mixed-modefracture using finite element analysis. Eng Fract Mech 2006;73(13):1783–96.

[11] Gustafson Peter A, Waas Anthony M. The influence of adhesive constitutiveparameters in cohesive zone finite element models of adhesively bondedjoints. Int J Solids Struct 2009;46(10):2201–15. Special Issue in Honor ofProfessor Liviu Librescu.

P. Davidson et al. / Composite Structures 94 (2012) 477–483 483

[12] Berggreen C, Simonsen BC, Borum KK. Experimental and numerical study ofinterface crack propagation in foam-cored sandwich beams. J Compos Mater2007;41(4):493–520.

[13] Cantwell WJ, Scudamore R, Ratcliffe J, Davies P. Interfacial fracture in sandwichlaminates. Compos Sci Technol 1999;59(14):2079–85.

[14] Li Xiaoming, Carlsson Leif A. The tilted sandwich debond (tsd) specimen forface/core interface fracture characterization. J Sandwich Struct Mater1999;1(1):60–75.

[15] Hyer Michael. Stress analysis of fiber-reinforced composite materials. WCBMcGraw-Hill; 1997.

[16] ASTMD5528. Standard test method for mode i interlaminar fracture toughnessof unidirectional fiber-reinforced polymer matrix composites. ASTMInternational; 2007. doi:10.1520/D5528-01R07E03.

[17] Davidson BD. An analytical investigation of delamination front curvature indouble cantilever beam specimens. J Compos Mater 1998;24(11):1124–37.1990 Press.