Crack growth analysis at adhesive–adherent interface in bonded joints under mixed mode I/II

The propagation of an interface crack subjected to mixed mode I/II was investigated for two 2024-T351 aluminum thin layers joined by means of DP760 epoxy adhesive produced by 3M^©. On the basis of beam theory, an analytical expression for computing the energy release rate is presented for the mixed-mode end loaded split (MMELS) test. The analytical strain energy release rate was compared by finite element (FE) analysis using the virtual crack closure technique (VCCT). Several fatigue crack growth tests were carried out in a plane bending machine to compare the experimental energy release rates to those of the analytical and FE solutions. Experimental results showed the relationship between the delamination modality and initial crack length rather than the applied load. The crack growth behavior showed stable crack growth followed by rapid propagation at the interface with the adhesive layer.     

Mixed-mode quasi-static failure criteria for adhesively-bonded pultruded GFRP joints

The strain energy release rates of adhesively-bonded pultruded GFRP joints were determined experimentally. The crack propagated in the adherend along paths outside the symmetry plane accompanied by fiber bridging. A new method, designated the “extended global method”, was introduced to facilitate mode partitioning in the mixed-mode experiments. Non-linear finite element models were developed in order to quantify the effect of the observed fiber bridging on crack propagation. An exponential traction-separation cohesive law was used to model the fiber bridging zone and calculate the energy release rate due to the fiber bridging, while the virtual crack closure technique was used for calculation of the fracture components at the crack tip. Experimental, analytical and numerical analyses were used to establish quasi-static mixed-mode failure criteria for crack initiation and propagation. The derived mixed-mode failure criteria can be used for simulating progressive crack propagation in other joint configurations comprising the same adhesive and adherends.     

Interfacial debonding behavior of composite beam/plates with PZT patch

This paper studies interfacial debonding behavior of composite beams which include piezoelectric materials, adhesive and host beam. The focus is put on crack initiation and growth of the piezoelectric adhesive interface. Closed-form solutions of interface stresses and energy release rates are obtained for adhesive layer in the piezoelectric composite beams. Finite element analyses have been carried out to study the initiation and growth of interfaces crack for piezoelectric beams with interface element by ANSYS, in which the interface element of FE model is based on the cohesive zone models to characterize the fracture behavior of the interfacial debonding. The results have been compared with analytical solution, and the influence of different geometry and material parameters on the interfacial behavior of piezoelectric composite beams have been discussed.     

Fatigue crack growth at the face sheet-core interface in a discontinuous ceramic-tile cored sandwich structure

The fatigue failure mechanism of a sandwich structure with discontinuous ceramic tile core is characterized. The sandwich structure in consideration comprises ceramic core tiles bonded to composite face sheet with a compliant adhesive layer. The discontinuous nature of the core results in a non-uniform stress field under in-plane loading of the sandwich. Static tensile tests performed on sandwich coupons revealed first damage as debonding at the gaps between adjacent tiles in the core. Tension–tension fatigue tests caused debonding at the gaps followed by initiation of cracks in the adhesive layer between the face sheet and core. Experimental data for crack length versus number of cycles is collected at various load levels. Crack growth rates (da/dN) are determined based on the experimental data acquired. The energy release rate available for crack propagation is computed using an analytical model and finite element analysis. Mode separation performed using the Virtual Crack Closure Technique (VCCT) revealed that crack propagation is completely dominated by shear (mode II). Fatigue crack growth behavior for the discontinuous sandwich structure is quantified by correlating the cyclic energy release rate with the rate of crack propagation. The loss of specimen stiffness with crack propagation is quantified using an analytical model.     

Effect of adhesive thickness on fatigue and fracture of toughened epoxy joints – Part II: Analysis and finite element modeling

The effect of bondline thickness on the fatigue and fracture of aluminum adhesive joints bonded using a rubber-toughened epoxy adhesive was studied using finite element analysis. The fatigue data of Part I examined the dependence of the fatigue threshold and cyclic crack growth rate on the adhesive thickness under both mode-I and mixed-mode loading. The fracture data of Part I illustrated the relation between the adhesive thickness and the quasi-static crack initiation and steady-state critical strain energy release rates. These experimental trends are explained in terms of the effects of the adhesive thickness and the applied strain energy release rate on the stress distribution in the bondline, the stress triaxiality at the crack tip, and the plastic zone size in the adhesive layer.     

Fracture behaviour of composite maritime T-joints

This paper outlines a study on the fracture behaviour of a glass fibre reinforced polymer T-joint commonly used in composite marine vessels. Finite element analysis was conducted using the virtual crack closure technique (VCCT) to investigate the fracture behaviour of the structure. The structure analysed contained initial disbond in various locations with various sizes under a straight pull-off load. The strain energy release rate (SERR) at the disbond tips were used to predict the failure loads and crack growth mechanism of the structure. The experimental results validated the VCCT as a tool for assessing the fracture behaviour and damage criticality of such structures. It was also discovered that skewed loading affected the SERR at the crack tips which altered the fracture behaviour of such structures, therefore sensitivity analysis is recommended to enhance the prediction accuracy.     

Calculation of transient strain energy release rates under impact loading based on the virtual crack closure technique

This paper describes an interface element to calculate the strain energy release rates based on the virtual crack closure technique (VCCT) in conjunction with finite element analysis (FEA). A very stiff spring is placed between the node pair at the crack tip to calculate the nodal forces. Dummy nodes are introduced to extract information for displacement openings behind the crack tip and the virtual crack jump ahead of the crack tip. This interface element leads to a direct calculation of the strain energy release rate (both components G_I and G_II) within a finite element analysis without extra post-processing. Several examples of stationary cracks under impact loading were examined. Dynamic stress intensity factors were converted from the calculated transient strain energy release rate for comparison with the available solutions by the others from numerical and experimental methods. The accuracy of the element is validated by the excellent agreement with these solutions. No convergence difficulty has been encountered for all the cases studied. Neither special singular elements nor the collapsed element technique is used at the crack tip. Therefore, the fracture interface element for VCCT is shown to be simple, efficient and robust in analyzing crack response to the dynamic loading. This element has been implemented into commercial FEA software ABAQUS^® with the user defined element (UEL) and should be very useful in performing fracture analysis at a structural level by engineers using ABAQUS^®.     

Bending strength of adhesive joints in microelectronic components: Comparison of edge-bonding and underfilling

The bending strength of underfilled and edge-bonded ball grid array (BGA) microelectronic packages assembled on printed circuit boards (PCBs) was compared using double cantilever beam (DCB) specimens. All specimens with fillets of the same size and shape failed at the same load, with cracks initiating and propagating within the PCB. This was consistent with measurements of the crack initiation strain energy release rate for PCB interfacial failure, which was significantly smaller than that of cohesive failure within the adhesives. Finite element analysis (FEA) indicated that the stress state in the PCB near the PCB-fillet interface in both underfilled and edge-bonded specimens was only a function of the adhesive fillet size and shape, and independent of the extent of the adhesive layer between the PCB and the BGA, and independent of the adhesive mechanical and thermal properties over the broad range of properties of the tested adhesives. This explained why decreasing the fillet curvature in edge-bonded specimens produced a significant increase in the joint strength. The crack path in the PCB of the edge-bonded specimens was found to change with the adhesive cure temperature; however, this had a negligible effect on the failure load.     

Adherend thickness influence on fatigue behavior and fatigue failure prediction of adhesively bonded joints

The effect of the adherend thickness, h, on mode-I fatigue behavior of a toughened epoxy adhesive system was examined in terms of the substrate global stiffness and curing residual stress. It was found that a change in adherend thickness from 1.6 mm to 12.7 mm caused a reduction in the fatigue performance; i.e. the threshold energy release rate decreased and the crack growth rate increased for a given applied energy release rate. Finite element modeling showed that the fatigue results could be explained in terms of an increase in the crack tip stresses and an enlarged plastic zone due to the greater global stiffness of thicker joints. No difference in fatigue behavior was observed for mixed-mode loading at relatively small phase angles; however, it is expected that at higher phase angles the adverse effect of h would be observed.     

An analytical analysis of energy release rate in bonded composite joints in a mode I condition

A complete analytical solution of mode I strain energy release rate, G_I, was derived for bonded composite joints based on an augmented double cantilever beam (DCB) model. Good agreement was obtained between current and existing comparable theoretical solutions for this joint with a long adhesive bond. For a short bond length joint, the current solution can greatly reduce the degree of the mathematical singularity encountered in analyses of thick, short beams and avoid it entirely for thin, long beams. A correlation between the current theoretical and associated ASTM solutions was established. A bonded DCB laminate test case was conducted, and good agreement was obtained between the experimental and current theoretical results. Commentary was included regarding the tested critical strain energy release rate and the deduced critical adhesive peel stress.     

Progressive delamination growth analysis using discontinuous layered element

In this paper, a fracture mechanic approach is used to analyze delamination propagation between layers of composite laminates. A finite element method based on layer-wise theory is extended for the analysis of delamination growth. In this approach, delamination is modeled by jump discontinuity conditions at the interfaces. The layer-wise finite element is developed to calculate the strain energy release rates based on the virtual crack closure technique (VCCT). A procedure is proposed to handle the progressive delamination of laminates. Finally, analyses of the edge delamination propagation for several composite laminates are performed and the corresponding failure stresses are calculated. The predicted results are compared with the available experimental and numerical results. It is shown that the predicted failure stresses using this method are comparable with those obtained using interface elements.     

Internal failures in model elastomeric composites

Finite element methods have been used to calculate the rate of release of strain energy caused by growth of an internal crack in some model elastic composites under tension. A layer of a linearly elastic material was considered, bonded between two flat or two spherical rigid surfaces. The reduction in strain energy caused by a small circular crack at the interface was found to be only about one-half of that due to a similar crack in the centre of the layer, in accord with the conjecture of Andrews and King. Cracks in the centre of a thin layer bonded between flat surfaces caused about the same release of energy as a crack in the centre of a thick specimen under the same tensile stress. On the other hand, a crack in a thin layer bonded between two spherical surfaces caused a much larger rate of energy release, depending on the radius of the layer relative to its minimum thickness. Growth of an initial crack would thus occur at a small applied stress. For thin layers between both flat and spherical surfaces, the rate of release of energy decreased as the crack grew, indicating that the crack would stabilize at a finite size. These conclusions are in accord with some observations of cracks in thin elastic layers.     

Energy release rate and mode-mixity of adhesive joint specimens

Fracture behaviour of adhesive joints under mixed mode loading is analysed by using the beam/adhesive-layer (b/a) model, in which, the adherends are beamlike and the adhesive is constrained to a thin flexible layer between the adherends. The adhesive layer deforms in peel (mode I), in shear (mode II) or in a combination of peel and shear (mixed mode). Macroscopically, the ends of the bonded part of the joints can be considered as crack tips. The energy release rate of a single-layer adhesive joint is then formulated as a function of the crack tip deformation and the mode-mixity is defined by the shear portion of the total energy release rate. The effects of transversal forces and the flexibility of the adhesive layer are included in the b/a-model, which can be applied to joints with short crack length as well as short bonding length. The commonly used end-loaded unsymmetric semi-infinite joints are examined and closed-form solutions are given. In comparison to the singular-field model in the context of linear elastic fracture mechanics, the b/a-model replaces the singularity at the crack tip with a stress concentration zone. It is shown that the b/a-model and the singular-field model yield fundamentally different mode-mixities for unsymmetric systems. The presented closed-form b/a-model solutions facilitates parametric studies of the influence of unbalance in loading, unsymmetry of the adherends, as well as the flexibility of the adhesive layer, on the mode mixity of an adhesive joint.     

Energy-based delamination theory for biaxial loading in the presence of thermal stresses

This paper addresses the issue of using energy balance methods and crack closure concepts to predict the growth of delaminations associated with ply cracks during the progressive loading of cross-ply laminates subject to a combination of in-plane biaxial stresses and thermal residual stresses. When the effective applied stresses and the temperature are held fixed during delamination growth, and there is negligible interaction of the delamination tips with the ply cracks, very simple analytical formulae for the energy release rate can be derived for unconstrained and generalised plane strain conditions, which are exact when the ply crack separation tends to infinity.     

Interfacial crack propagation in a thin viscoelastic film bonded to an elastic substrate

Edge decohesion along the interface of a thin viscoelastic film bonded to an elastic substrate under tensile residual stresses is considered. The tensile residual stress in the film is replaced by a combination of edge loads, and an explicit relation of strain energy with respect to time is obtained through simple beam analysis. The strain energy function is discretized into time steps which are assumed to be very small so that the dissipation effects over the time steps can be neglected. The energy release rate is then calculated using a Griffith type energy balance. An analytical model is developed to predict the crack growth and its velocity. Extent of crack growth along the interface is prediced based on a fracture criteria. The analytical predictions are compared with results from a viscoelastic finite element analysis.     

Fatigue fracture in plates in tension and out-of-plane shear

Straight cracks near a stiffening element, or curved cracks, in a pressurized shell can be subjected to out-of-plane tearing stresses in addition to normal tensile stresses due to the membrane stresses in the shell. To predict the rate of fatigue crack growth in such situations a theory and a crack growth rate correlation are needed. Such loadings are modelled as a superposition of plane stress tensile fracture (mode I) and Kirchhoff plate theory shearing fracture (mode 2). Finite element analyses using shell elements are used to compute the energy release rate and stress intensity factors associated with the loading. Three fatigue crack growth rate experiments were carried out on sheets of 2024-T3 aluminium alloy loaded in tension and torsion. The first set of experiments is constant amplitude fatigue crack growth tests. The second consists of experiments where crack closure is artificially eliminated to determine the rate of crack growth in the absence of crack face contact. The third is a set of constant stress intensity factor amplitude tests. The results all show that as the crack grows extensive crack face contact occurs, retarding crack growth. In the absence of crack face contact, however, the addition of out-of-plane shear loading increases the crack growth rate substantially.     

Fracture toughness analysis of inclined crack in cylindrical shell repaired with bonded composite patch

Adhesively bonded composite patch repair has been widely used to restore or extend the service life of cracked structural components due to its efficiency and cost-effectiveness compared to mechanical repair technique. Current available knowledge on patch repair mainly focus on flat damaged structures and the corresponding analysis methods and empirical databases are computationally efficient. In contrast, only limited work has contributed to studying patch repair to curved damaged structures. Authors have developed an adhesive element in conjunction with a shell element to investigate the effect of curvature on the adhesive stresses and mode I fracture toughness of the cracked host shell in the curved repairs. In this paper, this technology is again employed to model an adhesively bonded composite patch repair to a cylindrical shell embedded with an inclined through-thickness crack. The total strain energy release rate (SERR), calculated by the modified virtual crack closure technique (VCCT), is used to evaluate the mix-mode fracture toughness of the damaged structure and further to estimate the efficiency of patch repair. An automatic mesh generation scheme is proposed to conduct a quick parametric analysis, which can also be used to structural optimization design of composite patch repair. The numerical results are presented to show the effect of curvature and inclined angle of the through-thickness crack on fracture toughness of the repaired structure subject to different loads.     

Separation of crack extension modes in orthotropic delamination models

In modeling a crack along a distinct interface between dissimilar elastic materials, the ratio of mode I to mode II stress intensity factors or energy release rates is typically not unique, due to oscillatory behavior of near-tip stresses and displacements. Although methods have been developed for comparing mode mixes for isotropic interfacial fracture problems, this behavior currently limits the applicability of interfacial fracture mechanics in predicting delamination in layered materials without isotropic symmetry. The virtual crack closure technique (VCCT) is a method used to extract mode I and mode II energy release rate components from numerical fracture solutions. Energy release rate components extracted from an oscillatory solution using the VCCT are not unique due to their dependence on the virtual crack extension length, . In this work, a method is presented for using the VCCT to extract -independent energy release rate quantities for the case of an interface crack between two in-plane orthotropic materials. The method does not involve altering the analysis to eliminate its oscillatory behavior and it is similar to existing methods for extracting a mode mix from isotropic interfacial fracture models. Knowledge of near-tip fields is used to determine the explicit dependence of energy release rate parameters. Energy release rates are then defined that are separated from the oscillatory dependence on . A modified VCCT using these energy release rate definitions is applied to results from finite element analyses, showing that -independent energy release rate quantities result. The modified technique has potential as a consistent method for extracting a mode mix from numerical solutions. The -independent energy release rate quantities extracted using this technique can also aid numerical modelers, serving as guides for testing the convergence of finite element models. Direct applications of this work include the analysis of planar composite delamination problems, where plies or debonded laminates are modeled as in-plane orthotropic materials.     

Obtaining mode mixity for a bimaterial interface crack using the virtual crack closure technique

We review, unify and extend work pertaining to evaluating mode mixity of interfacial fracture utilizing the virtual crack closure technique (VCCT). From the VCCT, components of the strain energy release rate (SERR) are obtained using the forces and displacements near the crack tip corresponding to the opening and sliding contributions. Unfortunately, these components depend on the crack extension size, Δ, used in the VCCT. It follows that a mode mixity based upon these components also will depend on the crack extension size. However, the components of the strain energy release rate can be used for determining the complex stress intensity factors (SIFs) and the associated mode mixity. In this study, we show that several—seemingly different—suggested methods presented in the literature used to obtain mode mixity based on the stress intensity factors are indeed identical. We also present an alternative, simpler quadratic equation to this end. Moreover, a Δ-independent strain energy release based mode mixity can be defined by introducing a “normalizing length parameter.” We show that when the reference length (used for the SIF-based mode mixity) and the normalizing length (used for Δ-independent SERR-based mode mixity) are equal, the two mode mixities are only shifted by a phase angle, depending on the bimaterial parameter ε.     

含面\芯开裂损伤复合材料夹层板考虑几何非线性的能量释放率数值分析

基于一阶剪切变形理论,zig-zag变形假定和von Karman大挠度理论,提出了含不同形状面\芯开裂损伤复合材料夹层板在受压缩载荷作用下的开裂前缘能量释放率研究的有限元分析方法,研究了在轴向应变作用下,具有面\芯开裂损伤复合材料夹层板的分层断裂力学行为,并讨论了在大变形下几何非线性对能量释放率分布规律的影响。通过典型算例分析表明:具有面\芯开裂损伤复合材料夹层板的分层前缘能量释放率的大小和分布规律与开裂面积、开裂形状和受载方向有关。