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Assessment of delamination failure of laminated
composite beam with geometrical discontinuity
Mark Gandelsman, Ori Ishai
Faculty of Mechanical Engineering, Technion - Israel Institute ofTechnology, Haifa 32000, Israel
Abstract
A laminated composite beam with geometrical discontinuity serves as ananalytical and experimental model, representing the mechanical behavior ofstiffened panels under flexural load.
Failure in this case initiates at the corners of the rectangular groove andpropagates along the interlaminar plane. Numerical analysis shows a singularityon both interlaminar tensile and shear stress distribution at the free edge close tothe sharp 90° corner. This singularity changes into a finite maximum in the caseof a rounded corner. The maximum stress close to the corner tends to vary as afunction of the depth of the groove and the radius of the curvature at the corner.
Results of the experimental investigation indicate a significant reduction ofmoment at delamination initiation with increasing depth of groove and higherdelamination moment in the case of rounded corners.
This finding was in agreement with the attribution of interlaminar failureinitiation mainly to average tensile stress at the critical zone. The materialparameters which control this failure mechanism are the interlaminar tensile andshear strength, where the tensile component seems to be the predominant one.
1 Introduction
High performance structural composites which have been used for aerospace andmarine applications are mainly produced as thin wall laminates. Such elementsare usually under plane stress and loading, except at small zones close to edgeswhich are taken care of to prevent out of plane failure. In structural elementswhich are designed to sustain flexural loading the thin plates are strengthened byribs and form a stiffened panel configuration [1-2]. Other design concepts forflexural loading are: sandwich panels and thick laminates [3-].
Thick laminated plates and beams are usually formed with thicknessvariations [4] following structural design aiming to accommodate loadingconditions, functional restraints and weight saving requirements. In this case, aswell as in stiffened panel concepts, an abrupt change in geometry induce out of
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shear and normal stresses close to the geometrical discontinuity. Theseinterlaminar stresses tend to approach a singularity in case of rigid and linearelastic material behavior.
In light of the significantly low interlaminar strength in laminated composites(as compared with other strength components) an interlaminar failure(delamination) may be the prevailing failure mode of such structural elements.
The premature delamination must be avoided in composite structure if theirhigh performance potential, based on the superior fiberous characteristics, has tobe utilized.
Many research works and publications were dedicated during the last decadeto the study of delamination mechanism and interlaminar fracture toughness (IFF)characteristics [5]. These investigations were successful in the assessment ofdelamination propagation and its dependence on the composite composition andproperties. The problem of delamination initiation and its relationship with thestress field and composite interlaminar strength, is treated to a lesser extentprobably due to complexity of the 3-D state of stresses and its highly nonuniformdistribution. Another shortcoming which does not allow the extension of 2-Davailable design and analysis towards the 3-D level, is the shortage of compositeinterlaminar basic properties such as: elastic moduli and interlaminar tensile andshear strength parameters. The non-availability of this essential data base ismainly due to the technical complexity in direct testing of a composite specimenin the third dimension (which is limited by its thickness) and conforming withbasic standard requirement of homogeneous and uniform stress distribution [6].
The present paper reports a part of a project titled: "Strengthening ofComposite in the Third Dimension". Its first part [7] was devoted to thedevelopment of testing methodology for interlaminar characterization and theestablishment of a data base of interlaminar properties which are relevant to 3-Danalysis and design.
The final objective of this project is to develop analytical and empirical toolsfor evaluation of the effectiveness of methods to improve the interlaminarperformance in two ways:
a. Reduction of interlaminar stresses by geometrical variations or localinterlaminar toughening [5,8].
b. Local strengthening of the critical region by 3-D reinforcing technologies[9].
The current research activity concerns the analytical and experimental studyof a structural model which may represent the initiation of delamination failuremechanism and its dependence on stress field in the case of geometricaldiscontinuity.
The objectives of the present report are thus three-fold as follows:a. Study of the interlaminar stress field in the region close to the
discontinuity as a function of its geometrical variations.b. Assess the effect of the state of interlaminar stresses in light of available
strength criteria and empirical interlaminar strength characteristics.c. Evaluate the effect of the discontinuity edge geometry on stresses and
failure prediction to provide design guides for delaying interlaminarfailure and improving structural performance.
2 The Structural Model
The following beam model was selected for the present investigation (see Fig. i)to represent the critical situation, common for stiffened panel and thick laminate
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with abrupt thickness variation.It has the following advantages:Delamination failure is the prevailing mode under pure moment loading.It is simple to use for both numerical study and experimental testing.Delamination occurs spontaneously, starting at a specified well defined pointand is easy to detect visually.Failure initiation is accompanied by non-linearity of the load-deflectionrelationship.The effects of geometrical parameters (such as depth of groove and curvatureat the corner) is easy to investigate due to the simple preparation procedure ofthe specimens.Same apply for the study of local strengthening effects.
3 Materials and Specimens
The composite laminates used for the experimental part of the research werecomposed of industrial NEMA/ASTM G-10, Eglass/epoxy. The layup is a"simple sequence" of plies with the same direction of warp fibers. Crimple anglesof warp and fill yarns are smaller than 10°. They were fabricated by a hotpressing process
Two types of laminates were used:a) For determination of material properties in the third dimension - a laminate
having 32 mm thickness (160 fabric plies).b) For testing the beam model - a laminate having 6.3 mm thickness (32
fabric plies).The specimens were cut from the laminate by using diamond coated disks
under water. Then they were machined carefully to the exact required dimensionsas shown in Fig. 1.
In the case of specimens used for interlaminar tensile strength, 3 pieces -thickness wise - were bonded together, tabbed and machined to the final shape asshown in Fig. 6 of Ref. 7. Similarly for deriving interlaminar moduli rectangularspecimen were used, without any thickness or width reduction.
4 Material Characteristics
The data base required for the numerical analysis consists of:Interlaminar tensile strength (ITS) (F ) and Interlaminar shear strength (ISS)(Fg), Interlaminar Young's Modulus (E ) and the respective Poisson ratio (v^ «v ), and the Interlaminar Shear Modulus (G^ — G ). These parameters are inaddition to the usual inplane properties which were determined by availablestandard methods (E%% = E^ ; v^ = v^, and G ).
The interlaminar parameters were derived by using new and availablemethods as follows:Dog bone specimen, similar to the one recommended by ASTM D638 standard,but with two dimensional-thickness and width reduction, were used to derive F^(see Fig. 6 of Ref. 7). Interlaminar shear strength and modulus were derived byusing a double notch specimen following ASTM D3846 standard. In these tests,slightly nonuniform stress distribution is expected at the failed cross-section andhence the significance of the derived strength based on the average stress concept[10] may be argued from the statistical size effect point of view [11]. However,using this concept throughout the present article, may be justified due to the
Transactions on Engineering Sciences vol 10, © 1996 WIT Press, www.witpress.com, ISSN 1743-3533
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confinement of interlaminar stresses in the structural model, to a very smallvolume.
The interlaminar elastic moduli E^ and v^ = v , were derived by tensiletesting of rectangular specimens (composed of 3 thickness wise pieces bondedtogether). In this case two couples of cross-plied strain gages were used forstrain measurements (see Fig. 14 of Ref. 7).
All the properties which were determined experimentally and were used asinput in the numerical analysis are given in Table 1.
Table 1. Data base of experimental parameters to be used as input in thenumerical solution
Property
Units
EZZ
MPa
9120
Exx=Evv
MPa
22,000
v =vxz vz
0.22
v =vXV VX
0.17
GZX
MPa
2910
Fzt
MPa
45.6
FZX
MPa
45.5
5 Experimental Procedure
Beam specimens as shown in Fig. 1, were loaded by pure moment in the Instronloading machine. Constant cross head speed of 1 mm/min was maintained duringloading up to the delamination initiation level (DIL). The loading procedure andthe DIL values were monitored in three ways:
a - Visual inspection of the specimens (coated by brittle white paint) duringloading (by video camera).
b - Cracking noises detected by a stethoscope attached to the specimens.c - Non-linearity in the load-deflection curve recorded through the test.A typical horizontal delamination pattern initiated at the corner of the
rectangular groove as detected by the video camera is shown in Fig. 2.24 specimens were tested for the study of the effect of geometrical parameters onDIL which consisted of different groove depths and the comparison of a straight90° corner with a curved one (r = 1.0 mm). 3 specimens were tested for eachvariable.
The variation in the groove depth affects directly the shear and tensile stresslevel at DIL, whereas the variation in the corner curvature demonstrate the effectof singularity vs. continuous patterns in stress distribution on the DIL.
6 Test Results
The effect of geometrical variation of the groove depth and corner curvature onthe moment at DIL is shown in Fig. 3.
In spite of some scatter in test results the general trend is clear, namely:Decrease moment at DIL with increase in groove depth and higher moment at DILof specimen with curved corners as compared with their sharp cornercounterparts. It is noteworthy that even in the case of sharp corner, curvature of avery small radius practically still exists (r > 0), and the stress pattern is not totallysingular, as will be assumed for the analytical solution.
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1 Analytical Background
In engineering practice, the estimation of the strength of composite materials isoften based on phenomenological criteria of failure. However, the availablecriteria are not sufficiently universal, especially when applied to compositestructures having stress concentrators, like circular holes, corners or cracks. Insuch cases, the choice of the criterion may depend on the prevailing mode offailure, the type of composite material, its lay-up and chosen geometry ofspecimens. A comprehensive review of the available criteria of failure includinganalysis of their applicability to notched composite plates, possessing eithercircular holes or straight cracks, is given in [12]. Less attention was paid in theliterature to the development of the failure criteria for composite structures withcorners. Most of the studies concerning sharp corners use linear fracturemechanics and evaluate the singularity of the stress distribution in the vicinity ofthe corner point, assuming that the material is homogeneous and brittle. Whenapplied to composite structures, this approach does not take into account that thecatastrophic failure is anticipated by accumulation of damage in the zones of highstress concentration. It causes redistribution of stresses in the damaged zone.Thus, the criteria of failure, based on maximum point stress or a stresssingularity, do not match the fracture mechanism observed in compositestructures. Moreover, the stress analysis based on the assumption of linearelasticity can provide, in this case, only effective stresses within the damagedarea.
In the course of the present research, it has been found that the onset ofdelamination in the model specimens with grooves (Fig. 1) can be characterized bycritical values of averaged interlaminar normal and shear stresses, evaluatedwithin the corner zones of the grooves. The failure criterion, using averagedstresses was proposed in [10] in application to notched composite plates. In thiscriterion, the stresses are averaged over an interval with a characteristic length a^,chosen within the region of maximum stress concentration. The characteristiclength ac is considered as an adjusted parameter, which should be determinedexperimentally for each type of composite material. In general, a^ is interpreted asa characteristic size of the damaged zone of material at the onset of failure. Sincethe stress gradients arising in the beam specimens with grooves subjected tobending are essentially higher than the stress gradients achieved in the vicinity ofcircular holes, one can expect that the parameter a^ for the present modelspecimens should be much lesser than that determined in [10]. In this work, theparameter a^ is chosen based on the analysis of stress distribution in the cornerzones, as will be discussed in Section 9.
8 Numerical Analysis Procedure
Finite element models (FEM) are widely used for evaluation of stressesdistribution in the vicinity of corner points, in composite structures [13]. In suchmodels, the composite material is usually considered as a homogeneousorthotropic material with effective properties. This approximation was admitted inthe present work also. The initial (coarse) models aimed at the evaluation of thespecimen as a whole, as well as the submodels of corner zones were generatedusing the ANSYS_5 code. As an example, a fragment of the mesh, used in thecoarse model of the specimen with the 3 mm depth groove is shown in Fig. 4a.Similar models were generated for the specimens with the depth of grooves: 1, 2,
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3, 4 mm, for both cases: sharp and round corners. Due to the symmetry of theproblem only half of specimen was modelled.
In the case of round corners, it was found that a single submodel can providesufficiently accurate stresses distribution in the vicinity of the grooves' corners. Afan-shaped mesh combined of quadrilateral elements with the size of order 100(im was used in submodelling. The specimens with sharp corners were analysedby the finite element iteration method (FEIM), based on generation of a sequenceof submodels with gradually increasing resolution [14]. It was found that thesingular stress distribution predicted by the analytical theory is achieved only atdistances from the corner point of the order of 10-20 |im. At such distances, thereplacing of the composite material by a homogeneous material with effectiveproperties becomes meaningless. Therefore, the iteration procedure was truncatedat the third submodel, related to the area with the characteristic size of the order ofthe ply thickness (= 0.2 mm). This approximation enables to accurately calculatethe average stresses, despite the quasi singular stress distribution in the vicinity ofthe corner point.
9 Results of Numerical Analysis
The choice of the intervals, used for determination of average interlaminarstresses, is demonstrated in Fig.4b for the model specimens with round corners.An analogous approach was applied in the case of sharp corners. For each depth aof the groove, several intervals with respective heights: a, a-5, a-28, a-38, a-48,a-55 (where 5=0.2 is the ply's thickness) were tried. The average stresses weredetermined for each interval by numerical integration. As a lower limit of such anintegration, a point was chosen where the normal stress 0%% = 0 (points A, B,...in Fig.4b). The right limit of the integration was determined by the corner's edgepoint (points A*, B*,... in Fig.4b). The maximum of the average stressesobtained for the tried intervals was taken as a representative averaged stress. Inthe case of sharp corners, both the average tensile and shear stress componentsreach the maximum at z= a. Contrary to that, in the case of round corners, themaximum average stresses are reached at z=a-5.
Typical distributions of normal and shear stresses in the vicinity of sharp androunded corners are shown in Figs. 5 and 6, respectively. In the case of sharpcorners, the stress rapidly grows, when approaching toward the angular point, inaccordance with the analytical theory. The stress distribution at z=a. in the vicinityof round corners has a maximum displaced toward the narrow part of the beam(x>0). The stress distribution at z=a-8 shown in Figs 5,6 (dotted line)corresponds to maximum average stresses in the case of round corners.
10 Discussion of the Results
In Figs. 7a,b the ratios of the average tensile as well as shear stresses to thecorresponding (either tensile, or shear) strength are plotted vs. the depth ofgroove. The average stresses were calculated based on the results of FEM andFEIM for the cases of sharp (Fig. 7a) and round (Fig. 7b) corners, respectively,using the approach described in Section 9.
Obviously, the average tensile stress at the onset of delamination is almostindependent on the geometry of the specimen. The critical values of the averagetensile stress are close to the experimental interlaminar tensile strength ofcomposite (see Table 1), the corresponding ratio is close to unity for both the
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specimens with sharp and round corners. At the same time, the average shearstress essentially varies with the depth of the grooves, and, therefore, it cannotserve a criterion of the onset of delamination. An analogous conclusion can alsobe drown with respect to a interactive criterion based on the superposition of thesquares of the averaged tensile and shear stresses (see, Figs. 7).
Note, that the averaged shear stress can exceed the shear strength of thecomposite well before the initiation of failure. This observation matches the well-known fact, that the interlaminar shear (Mode II) fracture toughness of laminatedcomposites can be 3-4 times higher than their Mode I respective fracturetoughness [5]. Apparantly, this difference stems from the fact, that the non-uniform shear deformation is confined, while the tensile deformation may developfreely.
Thus, the results of the experimental and theoretical analysis allow us toconclude that the delamination at the corner points of the composite initiatesmainly due to the tensile stress component. The normal, stress averaged over thecharacteristic interval of its variation, in the vicinity of sharp as well as roundcorners, can serve as a criterion of delamination initiation near to the corner edges.
11 Conclusions
A beam with a rectangular central groove was found to be a successful model forempirical representation and analytical prediction of initial delamination instructural composite elements with geometrical discontinuity. The followingconclusions can be drawn from this investigation:• The predominant failure mode was found to be a delamination initiated at thecorner and propagated horizontally.
• The moment at delamination initiation was increasing with the decreasing ofdepth of groove.
• The moment of delamination initiation was significantly higher in the case ofspecimens with round corners as compared with their counterparts with sharpcorners.
• In the case of specimens with sharp corners, interlaminar shear and tensilestrength approach singularities close to groove edges as compared withcontinuous and lower stress levels in the case of their counterparts with roundcorners.
• Interlaminar stress levels increased with groove depth.• Interlaminar tensile stress component seems to be the predominant factoraffecting delamination onset in composite beam model with geometricaldiscontinuity.
• Average interlaminar tensile stress at delamination onset - a^ was found to beindependent of geometrical variables of groove corner and almost equal tointerlaminar tensile strength of the composite (F ). Hence, it may beconsidered as a material constant which controls the initiation of delaminationfailure process.
Acknowledgement
This research was partly supported by the fund for promotion of research at theTechnion - Israel Institute of Technology.
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References
1. Smith, C.S. Design of marine structures in composite material, Paragraph4.3.4, Compressive Buckling of Transversely Stiffened Panels, pp 204-246, Elsevier Applied Science, London and New York, 1990.
2. Paul, P.C., Saff, C.R., Sanger, K.B., Mahler, M.A., Kan, H.P. &Kautz, E.F. Analysis and test techniques for composite structures subjectedto out-of-plane loads, Composite Materials Testing and Design, ed.G.C. Grimes, Vol. 10, ASTM STP1120, pp 238-252, 1992.
3. Hall, J.C., Leon, G.F. & Nuismer, R.J. The application of the modifiedHashin's failure criterion and 2D solid finite element analysis to thickcomposite structures, pp. 430-437, Proceedings of the Ninth Interna-tional Conference on Composite Materials (ICCM/9), Madrid, 1993.
4. Tong, W. & Knaus, W.G. Stress analysis and damage detection in astepped composite, pp. 157-164, Proceedings of the Tenth InternationalConference on Composite Materials (ICCM/10), Whistler, Canada,1995.
5. Sela, N. & Ishai, O. Interlaminar fracture toughness and toughening oflaminated composite materials - a review, Composite Journal, 1989, 20,423-435.
6. Daniel, I.M. & Ishai, O. Engineering Mechanics of CompositeMaterials, Paragraph 8.7, pp 331-335, Oxford University Press, NewYork, Oxford, 1994.
7. Ishai, O. Strengthening of composite materials in the third dimension,Annual Report for the First Research Year, Material Mechanics Laboratory,Faculty of Mechanical Engineering, Technion, Haifa, Israel, 73 p., 1995.
8. Sun, T.C. & Norman, T.L. Design of a laminated composite withcontrolled-damage concept", Composite Science and Technology, 1990,39, 327-340.
9. Funk, J.G., Dexter, H.B. & Lubowinski, S.J. Experimental evaluation ofstitched graphite/epoxy composites, 3-D Composite Materials, NASAConference Publication No. 2420, pp 185-205, 1985.
10. Whitney, J.M. & Nuismer, R.J. Stress fracture criteria for laminatedcomposites containing stress concentration, J. Composite Materials,1974, 8, 253-265.
11. O'Brien, T.K. & Salper, S.A. Scale effects on the transverse tensilestrength of graphite/epoxy composites, Composite Materials Testing andDesign, Vol. 8, ASTM STP 1206, pp 23-52, 1993.
12. Awerbuch, J., Madhukar, M.,S., "Notched strength of composite laminate:Predictions and experiments - a review", Journal of Reinforced Plasticsand Composites, 1985, 4, p. 3-159
13. Carpenter, W.C., "A collocation procedure for determining fracturemechanics parameters at a corner", Int. J. Fracture, 1984, 24, 255-266
14. Sukumar, N., Kumosa, M., "Application of the finite elements iterativemethod to cracks and sharp notches in orthotropic", Int. J. Fracture, 1992,58, 177-192
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100mm
767
h=6.2 mm
80mm
Fig 1. Configuration of structural model.
Fig 2. Typical delamination failure in GFRP specimen under flexure.
e 2
E
— 1.5
I
.1 0.5
c0)o
Round cortiesr
).5 4.5I 1.5 2 2.5 3 3.5 4Groove depth ( a ) [mm]
Fig 3. The effect of groove depth on moment at delamination initiation.
Transactions on Engineering Sciences vol 10, © 1996 WIT Press, www.witpress.com, ISSN 1743-3533
762 Composite Material Technology V
A£B B*
w
\
^^- a
\
Fig 4. Mesh for numercal analysis of structural model (a) andgeneral scheme of loading (b)
30003a,
o
: 1. r = 0 mm, z = 3.0 mm! 2. r = 1 mm, z = 2.8 mm: 3. r = 1 mm, z = 3.0 mm
-1800 -900 0x [Jim]
900
Fig 5. Interlaminar tensile stress distribution close to the corner for a=3 mm
25003Cu
03<L>J=C/5
1 1. r = 0 mm, z = 3.0 mm2. r = 1 mm, z = 2.8 mm
: 3. r = 1 mm, z = 3.0 mm
-1800 900
Fig 6. Interlaminar shear stress distriution close to the corner for a=3 mm
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o
1 [
f 2t/5C/3C/52£to |
Equivalen
D
I 1 1 1 ! I 1 1 1 1 I I 1 1 1 1 I T "" "T 1 1 1 1 1 1 1 1
3 j ! :
L o i j; 6 6 :
: \ 0 E
' • •
: ! ! :
2 3Groove depth (a) [mm]
Eqvivalent stress-strength
ratio
D
—
K>
0A
/-N
r-i
3 ' ! :5 Q ; :
!_ f f j
: : : (
!_ f • J
2 3Groove depth (a) [mm]
Fig 7. Equivalent average stress-strength ratio as a function of the groove depthfor different failure criteria in the case of a sharp corner (a) and round corner (b)according to:
# - Interlaminar average tensile stress criterion —^~
O - Interlaminar average shear stress criterion ~^-
D - Interactive average stress criterion
1/2
Transactions on Engineering Sciences vol 10, © 1996 WIT Press, www.witpress.com, ISSN 1743-3533