Delamination damage analyses of adhesively bonded lap shear joints in laminated FRP composites

Three-dimensional non-linear finite ele- ment analyses have been carried out to evaluate the out-of-plane stresses in the adhesive layer existing between the lap and the strap adherends of the Lap Shear Joint (LSJ) in laminated FRP composites for varied delamination lengths. The delaminations are presumed to be pre-embedded in the thin resin rich layer existing between the first and second plies of the strap adherend. Sublaminate technique has been used to model the LSJ with the delamination. Contact finite element analyses have been performed in order to avoid interpenetration of delaminated surfaces. The effects of varied delamination lengths on the peel and interlaminar shear stresses and the individual modes of Energy Release Rate (ERR) in the delamination zones are highlighted in this paper. It is seen that three-dimensional effects exist near the free edges of the overlap end of the joint. The delamination propagation significantly affects the stress distributions in the adhesive layer existing between the lap and the strap adherends of the LSJ. The variations of interlaminar stresses and ERRs on both the delamination fronts are found to be significantly different and thus, indicate that the propagation of delamination does not occur at same rate at the two delamination fronts. This may throw some light to the evaluation of structural integrity of the LSJ in the presence of pre-embedded delaminations.     

Damage Analyses of Adhesively Bonded Single Lap Joints Due to Delaminated FRP Composite Adherends

Three-dimensional non-linear Finite Element Analyses (FEA) due to an in-plane loading have been performed to evaluate the out-of-plane normal and shear stresses over the overlap region of a Single Lap Joint (SLJ) on different surfaces. These surfaces have been considered as; (i) two interfacial surfaces between the adherends and the adhesive layer, (ii) the mid-surface of the adhesive layer and (iii) two surfaces beneath the surface ply of both the adherends adjacent to the adhesive layer. The critical locations of onset of adhesion, cohesion and delamination failures on the above mentioned surfaces of the SLJ have been determined using suitable damage criteria. A comparative study due to adhesion, cohesion and delamination failures in the SLJ with Fiber Reinforced Polymeric (FRP) composite adherends have been presented. The effects of simultaneous variations of the delamination positions on the out-of-plane peel and shear stress components have been studied by pre-embedding the delamination damages at the critical locations in both the adherends. It has been observed that the possibilities of onset of cohesion failures in the adhesive layer are higher compared to the adhesion and delamination failures. The detailed analyses showed that secondary peaks of out-of-plane stress components (σ _z , τ _yz and τ _xz ) on the mid surface of the adhesive layer appeared at the locations closer to the delamination fronts due to pre-embedded delamination damages. The highest stress magnitudes on the overlap edge of the SLJ have been reduced significantly when the centers of the delamination damages are exactly aligned with the overlap ends of the joint. No significant variations of stress magnitudes have been noticed either when the delaminations are pre-embedded outside the overlap regions or when the delamination damages are completely entrapped within the overlap region.     

Effect of damage levels and curing stresses on delamination growth behaviour emanating from circular holes in laminated FRP composites

This paper deals with the study of the effect of drilling induced delamination damage levels and residual thermal stresses (developed during manufacturing process of cooling the laminate form curing temperature to room temperature) on delamination growth behaviour emanating form circular holes in graphite/epoxy laminated FRP composites. Two sets of full three dimensional finite element analyses (one with the residual thermal stresses developed while curing the laminate and the other without residual thermal stresses i.e. with mechanical loading only) have been performed to calculate the displacements and interlaminar stresses along the delaminated interfaces responsible for the delamination onset and propagation. Modified crack closure integral (MCCI) techniques based on the concepts of linear elastic fracture mechanics (LEFM) have been used to calculate the distribution of individual modes of strain energy release rates (SERR) to investigate the interlaminar delamination initiation and propagation characteristics. Asymmetric variations of SERR obtained along the delamination front are caused by the overlapping stress fields due to the coupling effect of thermal and mechanical loadings. It is found that parameters such as ply orientation, drilling induced damage levels and material heterogeneity at the delaminated interface dictate the interlaminar fracture behaviour of laminated FRP composites.     

The influence of ply sequence and thermoelastic stress field on asymmetric delamination crack growth behavior of embedded elliptical delaminations in laminated FRP composites

The influence of ply lay up and the interaction of residual thermal stresses and mechanical loading on the interlaminar asymmetric embedded delamination crack growth behavior have been investigated. Two sets of full three-dimensional thermo-elastic finite element analyses have been performed for the interlaminar elliptical delaminations, which may be due to manufacturing defects or other reasons and are located symmetrically with respect to the midplane in a quasi-isotropic FRP composite laminate lay up. Depending upon the through-the-thickness location of the embedded elliptical delaminations, four different laminate configurations have been considered. Strain energy release rate (SERR) procedures have been employed to assess the delamination crack growth characteristics at the interfaces. It is found that the individual fracture modes exhibit asymmetric and non self-similar crack growth behavior along the delamination front depending upon the location of the interfacial delaminations; ply sequence and orientation and thermo-elastic anisotropy of the laminae.     

A study on the strength of adhesively bonded joints with different adherends

In this study, mechanical properties of adhesively bonded single-lap joint (SLJ) geometry with different configurations of lower and upper adherends under tensile loading were investigated experimentally and numerically. The adherends were AA2024-T3 aluminum and carbon/epoxy composite with 16 laminates while, the adhesive was a two-part liquid, structural adhesive DP 460. In experimental studies, four different types of single-lap joints were produced and used namely; composite–composite (Type-I) with lower and upper adherends of the same thicknesses and four different stacking sequences, composite–aluminum (Type-II) with lower and upper adherends of the same thicknesses and four different stacking sequences, composite–aluminum (Type-III) with lower adherend (composite) of the same thickness but upper adherend of three different thicknesses, aluminum–aluminum (Type-IV) with lower adherend of the same thickness but upper adherend of three different thicknesses, composite–composite (Type-V) with [0]₁₆ stacking sequences and three different overlap length, aluminum–aluminum (Type-VI) with three different overlap length. In the numerical analysis, the composite adherends were assumed to behave as linearly elastic materials while the adhesive layer and aluminum adherend were assumed to be nonlinear. The results obtained from experimental and numerical analyses showed that composite adherends with different fiber orientation sequence, different adherend thicknesses and overlap length affected the failure load of the joint and stress distributions in the SLJ.     

Mesh design in finite element analysis of post-buckled delamination in composite laminates

The role of mesh design in the post-buckling analysis of delamination in composite laminates is addressed in this paper. The determination of the strain energy release rate (SERR) along the crack front is central to the analysis. Frequently, theoretical analysis is limited to treatment of the problem in two dimensions, since considerable complexity is encountered in extending the analysis to three dimensions. However, many practical problems of embedded delamination in composite laminates are inherently three-dimensional in nature. Although in such cases, the finite element (FE) method can be employed, there are some issues that must be examined more closely to ensure physically realistic models. One of these issues is the effect of mesh design on the determination of the local SERR along the delamination front. There are few studies that deal with this aspect systematically. In this paper, the effect of mesh design in the calculation of SERR in two-dimensional (2D) and three-dimensional (3D) FE analyses of the post-buckling behavior of embedded delaminations is studied and some guidelines on mesh design are suggested. Two methods of calculation of the SERR are considered: the virtual crack closure technique (VCCT) and crack closure technique (CCT). The 2D analyses confirm that if the near-tip mesh is symmetric and consists of square elements, then the evaluation of the SERR is not sensitive to mesh refinement, and a reasonably coarse mesh is adequate. Despite agreement in the global post-buckling response of the delaminated part, the SERR calculated using different unsymmetrical near-tip meshes could be different. Therefore, unsymmetrical near-tip meshes should be avoided, as convergence of the SERR with mesh refinement could not be assured. While the results using VCCT and CCT for 2D analyses agree well with each other, these techniques yield different quantitative results when applied to 3D analyses. The reason may be due to the way in which the delamination growth is modeled. The CCT allows simultaneous delamination advance over finite circumferential lengths, but it is very difficult to implement and the results exhibit mesh dependency. Qualitatively, however, the two sets of results show similar distributions of Mode I and Mode II components of the SERR. This is fortunate, since the VCCT is relatively easy to implement.     

Delamination Damage Analyses of FRP Composite Spar Wingskin Joints with Modified Elliptical Adhesive Load Coupler Profile

Three-dimensional non-linear finite element analyses (FEA) for delamination damage onset and its growth in Graphite Fiber Reinforced Plastic (GFRP) composite Spar Wingskin Joints (SWJ) with modified elliptical adhesive load coupler profile for varied ratios of base width to height of the spar have been presented in this paper. Both in-plane and out-of-plane normal and shear stress variations on the interfacial surface of the wingskin between the spar and the wingskin have been evaluated. Coupled stress failure criterion has been used to predict the locations of initiation of failures due to delamination induced damages. Based on the stress and delamination damage analyses, suitable geometry of the modified elliptical adhesive load coupler profile of the SWJ has been recommended. The delamination damage has been observed to be initiated from the toe-end of the interfacial surface of the spar and the wingskin of the SWJ. Subsequently, the delamination propagations have also been studied by calculating the individual and the total Mode of Strain Energy Release Rate (SERR) along the delamination front using Modified Crack Closure Integral (MCCI) technique based on Linear Elastic Fracture Mechanics (LEFM) approach. It is seen that SERR variations along the delamination front i.e. across the width of the SWJ are not uniform. Therefore, a straight delamination front may grow into a curved delamination front as the delamination propagates. Also, it is found that Mode I SERR (G _I) governs the delamination propagation predominantly for the SWJ. Accordingly, suitable delamination arresting mechanism has been suggested.     

Delamination tolerance studies in laminated composite panels

Determination of levels of tolerance in delaminated composite panels is an important issue in composite structures technology. The primary intention is to analyse delaminated composite panels and estimate Strain Energy Release Rate (SERR) parameters at the delamination front to feed into acceptability criteria. Large deformation analysis is necessary to cater for excessive rotational deformations in the delaminated sublaminate. Modified Virtual Crack Closure Integral (MVCCI) is used to estimate all the three SERR components at the delamination front from the finite element output containing displacements, strains and stresses. The applied loading conditions are particularly critical and compressive loading on the panel could lead to buckling of the delaminated sublaminate and consequent growth of delamination. Numerical results are presented for circular delamination of various sizes and delamination at various interfaces (varying depth-wise location) between the base- and the sub-laminates. Numerical data are also presented on the effect of bi-axial loading and in particular on compressive loading in both directions. The results can be used to estimate delamination tolerance at various depths (or at various interfaces) in the laminate.     

Vibrations of multiple delaminated beams

The free vibrations of beams with two enveloping delaminations have been solved analytically without resorting to numerical approximation. The multiple delaminated beam is analyzed as several interconnected Euler–Bernoulli beams. The differential stretching and the bending–extension coupling are considered in the formulation. The influence of the sizes and locations of the delaminations on the primary and secondary frequencies and mode shapes of a beam are investigated. For clamped–clamped beams, the primary frequency shows a high sensitivity for the long delamination but a low sensitivity for the second short delamination, while for the secondary frequency, the sensitivity is high for both delaminations. For cantilever beams, the primary and secondary frequencies show a high sensitivity for the long delamination but low sensitivity for the second short delamination. Results are compared with the analytical and experimental data reported in the literature to verify the validity of the present model.     

A Study on Skin Delaminations Growth in Stiffened Composite Panels by a Novel Numerical Approach

In this paper, a study on skin delamination growth in stiffened composite panels made of carbon fibres reinforced polymers and subjected to compressive load is presented. A robust (mesh and time step independent) numerical finite elements procedure, based on the Virtual Crack Closure Technique (VCCT) and on the fail release approach, is used here to investigate the influence of skin delamination size and position on the damage tolerance of stiffened composite panels. Four stiffened panels configurations with skin delaminations differently sized and positioned are introduced. Bay delaminations and delaminations under the stringer foot are considered. The novel numerical procedure has been used to simulate the delamination growth for all the investigated panel configurations and to evaluate the influence of the delaminations’ geometrical parameters on the growth development. As a confirmation of the applicability and effectiveness of the adopted numerical tool, the numerical results, obtained for all the analysed configurations, in terms of grown delaminated area, displacements and strains measured in various panel locations, have been compared with experimental data available in literature.     

Dynamics of cracked composite material structures

As the result of this work models of the finite cracked beam element, delaminated beam element, and also delaminated plate element have been developed. These models have been used for the analysis of the influence of the fatigue cracks and delaminations on the dynamic characteristics of the constructions made of unidirectional composite materials. The method of modelling cracks and delaminations presented in this work enables its easy modification according to specific cases of damage (i.e. oblique crack, two-side crack, inside crack, multiple delaminations etc.). The results obtained from numerical calculations of the presented models are in good agreement with the known influence of damage parameters like: the position and the depth of the crack or the length and the position of the delamination on the natural frequencies. Simultaneously, a strong influence of the material parameters on these changes has been observed, which does not exist in the case of isotropic materials.     

Interaction between matrix cracking and edge delamination in composite laminates

Matrix cracking and edge delamination are two main damage modes in continuous-fibre composite laminates. They are often investigated separately, and so the interaction between two damage modes has not yet been revealed. In this paper, a simple parallel-spring model is introduced to model the longitudinal stiffness reduction due to matrix cracking and edge delamination together. The energy release rate of edge delamination eliminating the matrix crack effect and the energy release rate of matrix cracking in the presence of edge delamination are then obtained. Experimental materials include carbon- and glass-fibre-reinforced bismaleimide composite laminates under static tension. The growth of matrix cracks and edge delaminations was recorded by means of NDT techniques. Results show that matrix cracks may initiate before or after edge lamination. This depends on the laminate layup, and especially on the thickness of the 90° plies. Edge delamination may also induce matrix cracking. Matrix cracking has a significant effect on the stiffness reduction in GRP laminates. The present model can predict the stiffness reduction in a laminate containing both matrix cracks and edge delaminations. The mixed-mode delamination fracture toughness obtained from the present model shows up to 50% differences compared with O'Brien's model for GRP laminates. However, matrix cracking has a small effect on the mixed-mode interlaminar fracture toughness of the CFRP laminates.     

Delamination modeling in doubly curved laminated shells for free vibration analysis using zigzag theory-based facet shell element and hybrid continuity method

We present a finite element (FE) formulation for the free vibration analysis of doubly curved laminated composite and sandwich shells having multiple delaminations, employing a facet shell element based on the efficient third-order zigzag theory and the region approach of modeling delaminations. The methodology, hitherto not attempted, is general for delaminations occurring at multiple interfacial and spatial locations. A recently developed hybrid method is used for satisfying the continuity of the nonlinear layerwise displacement field at the delamination fronts. The formulation is shown to yield very accurate results with reference to full-field three-dimensional FE solutions, for the natural frequencies and mode shapes of delaminated shallow and deep, composite and highly inhomogeneous soft-core sandwich shells of different geometries and boundary conditions, with a significant computational advantage. The accuracy is sensitive to the continuity method used at the delamination fronts, the usual point continuity method yielding rather poor accuracy, and the proposed hybrid method giving the best accuracy. Such efficient modeling of laminated shells with delamination damage will be of immense use for model-based techniques for structural health monitoring of laminated shell-type structures.     

Analytical Solution of Buckling of Beams with Two Delaminations

A stability problem of composite beams with multiple delamination was tackled. A closed-form solution was found and buckling loads of composite beams with two delaminations were determined in order to obtain their compressive load-carrying capacity. Crack-opening mode was assumed for each detached delaminated region. Seven different regions having different transverse deformations resulted from assumed positions of delaminations. Developing the derived continuity condition equations reduced the number of algebraic equations required to solve the problem analytically. The results of the work were validated by comparing them to those reported in the literature. The effects of length, location, and distribution of multiple delaminations were considered in the comparison, and the results showed very good agreement. Buckling load decreases as delamination size increases. Buckling load for a beam with two delaminations is lower than that for the same beam with a single delamination.     

含分层复合材料层板的压缩性能

使用商用有限元软件建立了含分层复合材料层板的有限元模型,采用Hashin失效准则对层板内单元进行损伤判断,并编写程序对失效单元进行刚度折减,使用cohesive单元模拟层间区域,并对缺陷区域进行弱化处理,利用应力失效判据和能量释放准则判断层板内起始分层与分层的扩展。对完好以及含分层缺陷复合材料单向层板试验件进行压缩实验研究,实验结果给出了分层位置和尺寸及对材料压缩性能的影响。研究表明,有限元模拟结果与实验结果具有良好的一致性。     

Effect of the structural reinforcement of composite adherends on the mechanical strength of adhesive joints

This study proposes a novel method to strengthen fiber reinforced plastic (FRP) adherends in a single lap joint (SLJ) by using Kevlar threads. The adherend reinforcement procedure consists of applying a zigzag thread in the fiber glass layers that comprise the adherend in order to subsequently manufacture the adherends using the vacuum infusion method. For this study, three single lap joint configurations were used: Adherends without Kevlar reinforcement (SLJ₁), adherends with Kevlar reinforcement with a medium step zigzag (SLJ₂) and adherends with Kevlar reinforcement with a small step zigzag (SLJ₃). Mechanical tensile tests were carried out to determine the ultimate strength and displacement of the single lap joint configurations studied. Adherends reinforced by Kevlar threads increase the strength and displacement of the single lap joint. However, the influence of the step size of zigzag threads on the adherend does not significantly influence the strength, but significantly affects the maximum displacement of the single lap joint.     

Numerical and experimental investigation of free vibration of multilayer delaminated composite beams and plates

The use of vibration-monitoring techniques as non-destructive methods for detection of delaminations in layered composite beam and plate structures is a current field of interest for many researchers. However, an extensive search of published literature shows that information on numerical and especially experimental investigations into the dynamic behaviour of delaminated layered composite beams and plates is limited. For this reason the present authors have developed theoretical models and carried out an extensive experimental investigation to establish changes in the first three bending natural frequencies due to delaminations. The subsequent results of these numerical calculations are consistent with the results of the corresponding experimental investigations. As the result of this work models of a finite delaminated beam element and delaminated plate element have been developed. The method of modelling delaminations presented in this work enables its easy modification according to specific cases of damage (i.e. multiple delaminations). Received 12 December 99     

XFEM simulation of delamination in composite laminates

In this paper, the extended finite element method (XFEM) is extended to simulate delamination problems in composite laminates. A crack-leading model is proposed and implemented in the ABAQUS® to discriminate different delamination morphologies, i.e., the 0°/0° interface in unidirectional laminates and the 0°/90° interface in multidirectional laminates, which accounts for both interlaminar and intralaminar crack propagation. Three typical delamination problems were simulated and verified. The results of single delamination in unidirectional laminates under pure mode I, mode II, and mixed mode I/II correspond well with the analytical solutions. The results of multiple delaminations in unidirectional laminates are in good agreement with experimental data. Finally, using a recently proposed test that characterizes the interaction of delamination and matrix cracks in cross-ply laminates, the present numerical results of the delamination migration caused by the coupled failure mechanisms are consistent with experimental observations.     

Straight-sided, buckling-driven delamination of thin films at high stress levels

The fracture mechanics of a straight-sided, thin film delamination at stress levels, which are high compared to the stress required to initiate the delamination is investigated. Buckling at a bifurcation point of the delaminated region, resulting from incompletely relieved stresses in this region, is analysed by a semi- analytical approach for delaminations of infinite extent. The results are compared to numerical predictions based on finite element calculations for finite sized delaminations. The finite element calculations are carried out in the post-buckling regime showing that parts of the crack front will close as a result of bifurcation buckling, while other parts will experience enhanced energy release rate and mode I stress intensity factor. The mode III stress intensity factor is shown to be negligible at the stress levels analysed.     

Growth behavior of internal delaminations in composite beam/plates under compression: effect of the end conditions

The effect of the end conditions, i.e. clamped-clamped vs. simply-supported ends on the initial postbuckling and growth behavior of delaminations in plates in studied. The study does not impose any restrictive assumptions regarding the delamination thickness and plate length. First, a closed form solution for the mode mixity, energy release rate and deformation quantities is derived for the case of a clamped-clamped delaminated plate, which complements the already existing solution for a delaminated simply-supported plate. A perturbation procedure is followed, which is based on an asymptotic expansion of the load and deformation quantities in terms of the distortion parameter of the delaminated layer, the latter being considered a compressive elastica. The additional complication in the clamped-clamped case arises because now the amplitude at the clamped end needs to be expanded in terms of the distortion parameter of the delaminated part, in addition to the amplitude at the common section and the distortion parameter of the base plate. The effects of the end conditions on the growth behavior are found to depend on the relative location of the delamination through the thickness. For the same plate length and thickness and the same delamination length and applied strain, delaminations located closer to the surface exhibit nearly the same energy release rate and mode mixity either in a clamped-clamped or a simply supported configuration. However, in delaminations located further away from the surface, for the same applied strain, the energy release rate is larger and there is also a higher mode II component in the simply-supported case. Moreover, the mid-point transverse displacement of the delaminated layer as well as that of the substrate part, is larger in the simply supported case. The same major trend that has been observed in the simply supported case, i.e. the increased growth resistance of the delaminations located near the surface relative to the ones located further inside the plate, is also observed in the clamped-clamped case.