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.     

DCB-specimen loaded with uneven bending moments

A double cantilever beam specimen loaded with uneven bending moments (DCB-UBM) is proposed for mixed mode fracture mechanics characterisation of adhesive joints, laminates and multilayers. A linear elastic fracture mechanics analysis gives the energy release rate and mode mixity analytically for both isotropic and orthotropic materials. By varying the ratio between the two applied moments, the crack tip stress state can be varied from pure mode I to pure mode II for the same specimen geometry. The specimen allows stable crack growth. A special test fixture is developed to create uneven bending moments. As a preliminary example, the DCB-UBM specimen was used for characterising fracture of adhesive joints between two laminates of thermoset glass fibre reinforced plastic.     

A novel fixture for mixed mode I/II/III fracture testing of brittle materials

A novel test‐loading device was suggested in order to study the fracture behavior of brittle materials under mixed mode I/II/III loading conditions. A version of the compact tension shear specimen was used as the test configuration. Using a three‐dimensional finite element analysis, the influence of mode mixity on the stress intensity factors, the T‐stress, and 3‐D plastic zone around the crack tip was investigated. In addition, an experimental study was performed on an epoxy polymer using the proposed setup. Finally, the fracture toughness of pure epoxy was measured under several loading conditions. The numerical and experimental results manifested that the proposed setup is able to determine a full range of mixed mode I/II/III fracture properties. At the end, the fracture envelope obtained using the practical study was compared with various three‐dimensional fracture criteria. A negligible discrepancy was concluded between the practical data and the theoretical data estimated by the maximum mean principle stress criterion.     

The influence of mode mixity and adhesive system on the fatigue life of adhesive joints

In real applications, adhesive joints are commonly subjected to fatigue and mixed mode loading conditions. The aim of the current work is to experimentally analyse the influence of mode mixity on the fatigue strength of joints with an epoxy‐based adhesive. Different adhesive systems (acrylic and epoxies) were considered for pure mode I fatigue loading conditions. To achieve this, Arcan joints with an epoxy adhesive were manufactured and tested at different mode mixities. Based on stiffness degradation, monitored during the tests, damage evolution was calculated for different loading conditions and for all the tested adhesives. Finally, fatigue envelopes were constructed for different fatigue life regimes. Results show that a shear loading component reduces both the static strength and fatigue life of the joints. A small reduction rate of the stiffness was found throughout the most part of the life until a sudden drop was observed, indicating a smooth damage evolution.     

Development of a simple mixed-mode fracture test and the resulting fracture energy envelope for an adhesive bond

Characterizing the fracture energy of bonded adhesive joints over a range of mode mixities often requires special fixtures or a variety of test configurations. By pairing a tapered and a constant thickness adherend, a hybrid double cantilever beam (DCB) specimen is proposed. This asymmetric tapered DCB configuration can be used to determine the fracture energy as a function of mode mixity. As the debond propagates, the relative stiffness of the adherends varies in a systematic manner, resulting in a range of mode mixities from 0° to approximately 20°. Strain energy release rates were obtained using corrected beam theory and a finite element fracture analysis. Single-leg bending tests were used to determine the fracture energy at mode mixity up to 56°. Constant thickness and tapered DCB tests were used to determine the mode I fracture energy. The resulting fracture envelope was constructed in order to show the dependence of the fracture energy on mode mixity for a two part acrylic adhesive.     

On the determination of constitutive properties of adhesive layers loaded in shear – an inverse solution

A method to determine constitutive properties of thin adhesive layers loaded in shear is presented. The test specimen consists of two adherends joined by the adhesive layer. By loading the specimen antisymmetrically with respect to the adhesive layer a state of pure shear is ensured. To avoid instability the test specimen is designed to give a non-uniform stress distribution in the adhesive layer. This is achieved by using a long specimen loaded at one side. The method is based on an exact inverse solution which is derived utilizing the balance of the energetic forces of the applied loads and of the adhesive at the start of the adhesive layer. The method is intended for determination of both hardening and softening behaviour of adhesives but is confined to monotonic loading.     

Vapor Pressure and Residual Stress Effects on Mixed Mode Toughness of an Adhesive Film

Temperature- and moisture- induced delamination leading to popcorn package cracking is a major package reliability issue for surface-mount plastic encapsulated microcircuits (PEM). Crack propagation along one of the interfaces of a ductile adhesive joining two elastic substrates is modeled to study interface delamination and toughness of PEMs. The polymeric adhesive is stressed by remote loading and residual stress. Along the crack front, the film-substrate interface is modeled by a strip of cells that incorporates vapor pressure effects on void growth and coalescence through a Gurson porous material relation. Results show that under high levels of vapor pressure, increasing film thickness will produce smaller enhancement on the steady-state fracture resistance of the interface, also referred to as the joint toughness. Across all mode mixity levels, vapor pressure effects dominate over residual stress. The adverse effects of vapor pressure are greatest in highly porous adhesives subjected to a strong mode II component. The latter is representative of the likely state of loading in IC packages since residual stress, resulting from the film-substrate thermal mismatch, induces a predominantly mode II component.     

Debonding strength of bundled glass fibers subjected to stress pulse loading

This paper reports experimental results of the debonding propagation of bundled-fibers specimens subjected to a tensile stress wave. In addition, the paper also presents a dynamic debonding model for the problem on the basis of the cohesive zone model, and verifies the model by comparing the predicted debonding to the experimental data. The established numerical model is used to study the propagation mode of the debonding, and the result suggests that in this particular specimen design and loading condition, the debonding initiated in a mixed mode condition. However, the mode II quickly increased and dominated the mode I during an early debonding propagation up to certain extend where the mode mixity became constant.     

Optimization of the adhesive joint Iosipescu specimen for pure shear test

This paper reviews some of the difficulties encountered in achieving a uniform stress distribution within the adhesive layer of bonded Iosipescu shear test specimens. The asymptotic singular stress field at the terminus of a skewed bimaterial interface, intersecting the straight free surface of the wedge, has been studied macroscopically and microscopically using the finite element method (FEM) and the finite element iterative method (FEIM). Different mechanical properties of the adhesives and adherends, and various skewed interface angles have been considered in this study. A critical skewed interface angle, _c=126°, has been found beyond which the interfacial stress singularity vanishes. This critical angle is independent of the elastic properties of the adhesives and adherends. Based on the results obtained in the present investigation, in conjunction with recently reported research on sharp notches [7, 21–23], an optimized adhesive joint Iosipescu specimen geometry is proposed. This specimen should be capable of generating a uniform shear stress state within its adhesive layer under pure shear loading conditions.     

On the analysis of a mixed mode bending sandwich specimen for debond fracture characterization

The mixed mode bending specimen originally developed for mixed mode delamination fracture characterization of unidirectional composites has been extended to the study of debond propagation in foam cored sandwich specimens. The compliance and strain energy release rate expressions for the mixed mode bending sandwich specimen are derived based on a superposition analysis of solutions for the double cantilever beam and cracked sandwich beam specimens by applying a proper kinematic relationship for the specimen deformation combined with the loading provided by the test rig. This analysis provides also expressions for the global mode mixities. An extensive parametric analysis to improve the understanding of the influence of loading conditions, specimen geometry and mechanical properties of the face and core materials has been performed using the derived expressions and finite element analysis. The mixed mode bending compliance and energy release rate predictions were in good agreement with finite element results. Furthermore, the numerical crack surface displacement extrapolation method implemented in finite element analysis was applied to determine the local mode mixity at the tip of the debond.     

J-Dominance in Mixed Mode Ductile Fracture Specimens

The asymptotic mixed mode crack tip fields in elastic-plastic solids are scaled by the J-integral and parameterized by a near-tip mixity parameter, M _{_p} . In this paper, the validity and range of dominance of these fields are investigated. To this end, small strain elastic-plastic finite element analyses of mixed mode fracture are first performed using a modified boundary layer formulation. Here, a two term expansion of the elastic crack tip field involving the stress intensity factor |K| the elastic mixity parameter M _{_e} as well as the T-stress is prescribed as remote boundary conditions. The analyses are conducted for different values of M _{_e} and the T-stress. Next, several commonly used mixed mode fracture specimens such as Compact Tension Shear (CTS), Four Point Bend (4PB), and modified Compact Tension specimen are considered. Here, the complete range of loading from contained yielding to large scale yielding is analyzed. Further, different crack to width ratios and strain hardening exponents are considered. The results obtained establish that the mixed mode asymptotic fields dominate over physically relevant length scales in the above geometries, except for predominantly mode I loading and under large scale yielding conditions. This revised version was published online in August 2006 with corrections to the Cover Date.     

Mode-I,mode-II and mixed-mode I+II fracture behavior of composite bonded joints: Experimental characterization and numerical simulation

The fracture behavior of composite bonded joints subjected to mode-I, mode-II and mixed-mode I + II loading conditions was characterized by mechanical testing and numerical simulation. The composite adherents were bonded using two different epoxy adhesives; namely, the EA 9695 film adhesive and the mixed EA 9395-EA 9396 paste adhesive. The fracture toughness of the joints was evaluated in terms of the critical energy release rate. Mode-I tests were conducted using the double-cantilever beam specimen, mode-II tests using the end-notch flexure specimen and mixed-mode tests (three mixity ratios) using a combination of the two aforementioned specimens. The fracture behavior of the bonded joints was also simulated using the cohesive zone modeling method aiming to evaluate the method and point out its strengths and weaknesses. The simulations were performed using the explicit FE code LS-DYNA. The experimental results show a considerable scatter which is common for fracture toughness tests. The joints attained with the film adhesive have much larger fracture toughness (by 30–60%) than the joints with the paste adhesive, which exhibited a rather brittle behavior. The simulation results revealed that the cohesive zone modeling method performs well for mode-I load-cases while for mode-II and mixed-mode load-cases, modifications of the input parameters and the traction-separation law are needed in order for the method to effectively simulate the fracture behavior of the joints.     

Face/core interface fracture characterization of mixed mode bending sandwich specimens

Debonding of the core from the face sheets is a critical failure mode in sandwich structures. This paper presents an experimental study on face/core debond fracture of foam core sandwich specimens under a wide range of mixed mode loading conditions. Sandwich beams with E‐glass fibre face sheets and PVC H45, H100 and H250 foam core materials were evaluated. A methodology to perform precracking on fracture specimens in order to achieve a sharp and representative crack front is outlined. The mixed mode loading was controlled in the mixed mode bending (MMB) test rig by changing the loading application point (lever arm distance). Finite element analysis was performed to determine the mode‐mixity at the crack tip. The results showed that the face/core interface fracture toughness increased with increased mode II loading. Post failure analysis of the fractured specimens revealed that the crack path depends on the mode‐mixity at the crack tip, face sheet properties and core density.     

Three‐dimensional mixed‐mode (I and II) crack‐front fields in ductile thin plates — effects of T‐stress

It has been well‐established that the non‐singular T‐stress provides a first‐order estimate of geometry and loading mode (e.g. tension versus bending) effects on elastic–plastic crack‐front field under mode I loading conditions. The objective of this paper is to exam the T‐stress effect on three‐dimensional (3D) crack‐front fields under mixed‐mode (modes I and II) loading. To this end, detailed 3D small strain, elastic–plastic simulations are carried out using a 3D boundary layer (small‐scale yielding) formulation. Characteristics of near crack‐front fields are investigated for a wide range of T‐stresses (T/σ₀ = ?0.8, ?0.4, 0.0, 0.4, 0.8). The plastic zones and thickness and angular and radial variations of the stresses are studied, corresponding to two values of the remote elastic mixity parameters M_e = 0.3 and 0.7, under both low and high levels of applied loads. It is found that different T‐stresses have a significant effect on the plastic zones size and shapes, regardless of the mode mixity and load level. The thickness, angular and radial distributions of stresses are also affected markedly by T‐stress. It is important to include these effects when investigating the mixed‐mode ductile fracture failure process in thin‐walled structural components.     

Experimental study on CFRP-to-steel bonded interfaces

This paper presents an experimental study on the behaviour of CFRP-to-steel bonded interfaces through the testing of a series of single-lap bonded joints. The parameters examined include the material properties and the thickness of the adhesive layer and the axial rigidity of the CFRP plate. The test results demonstrate that the bond strength of such bonded joints depends strongly on the interfacial fracture energy among other factors. Nonlinear adhesives with a lower elastic modulus but a larger strain capacity are shown to possess a much higher interfacial fracture energy than linear adhesives with a similar or even a higher tensile strength. The variation of the interfacial shear stress distribution in a bonded joint as the applied load increases clearly illustrates the existence of an effective bond length. The bond–slip curve is shown to have an approximately triangular shape for a linear adhesive but to have an approximately trapezoidal shape for a nonlinear adhesive, indicating the necessity of developing different forms of bond–slip models for different adhesives.     

An experimental analysis of the fracture behavior of composite bonded joints in terms of cohesive laws

Modeling adhesive joints by means of cohesive models relies on the definition of cohesive laws. Although cohesive laws are known to be dependent on the loading mode, there is a lack of experimental evidences to describe this dependence. At the same time, the adherend and adhesive thicknesses are known to affect the fracture toughness of the bond, but their effect on the cohesive law has not been clarified. In this work, an experimental characterization of an epoxy adhesive is presented. The effect that the mode mixity has on the bond toughness and its cohesive law is compared against the effect of the adhesive and adherend thicknesses. The impact of these two latest parameters is shown to be minor if compared to the influence of the mode mixity, which mainly defines the cohesive law shape. Finally, the implications of these experimental findings on the numerical simulation of adhesive joints are discussed.     

Characterization of crack tip stress fields in test specimens using mode mixity parameters

The aim of this study is to represent the combined effect of mode mixity, specimen geometry and relative crack length on the $T$ -stress, elastic–plastic stress fields, integration constant $I_{n}$ , angle of initial crack extension, and the plastic stress intensity factor. The analytical and numerical results are obtained for the complete range of mixed modes of loading between mode I and mode II. For comparison purposes, the reference fields for plane mixed-mode problems governing the asymptotic behavior of the stresses and strains at the crack tip are developed in a power law elastic–plastic material. For the common experimental fracture mechanics specimen geometries considered, the numerical constant of the plastic stress field $I_{n}$ and the $T$ -stress distributions are obtained as a function of the dimensionless crack length and mode mixity. A method is also suggested for calculating the plastic stress intensity factor for any mixed-mode I/II loading based on the $T$ -stress and power law solutions. It is further demonstrated that in both plane stress and the plane strain, the plastic stress intensity factor can be used to characterize the crack tip stress fields for a variety of specimen geometries and different mixed-mode loading. The applicability of the plastic stress intensity factor to analysis of the in-plane and out-of-plane constraint effect is also discussed.     

Effects of constitutive parameters on the accuracy of measured fracture energy using the DCB-specimen

Several methods exist to estimate the fracture energy for adhesive joints using the double cantilever beam specimen and linear elastic fracture mechanics. Since the mechanical properties of all adhesives are non-linear, errors are generated. By use of an exact solution experiments are simulated. These are evaluated with eight different methods. The influence of the constitutive parameters is systematically studied. This influence is small for most methods. The error due to the choice of evaluation method is considerably larger. One of the commonly used methods gives accurate results; the error is less than 3%. However, most methods yield substantial errors.     

Experimental and numerical investigations of mixed mode crack growth resistance of a ductile adhesive joint

Polymeric adhesive joints are extensively employed in various industrial and technological applications. It has been observed that in ductile adhesive joints, interface fracture is a common mode of failure which may involve stable crack propagation followed by catastrophic growth. The objectives of this paper are to investigate the effects of bondline thickness and mode mixity on the steady state energy release rate J_ss of such a joint. To this end, a combined experimental and numerical investigation of interfacial crack growth is carried out using a modified compact tension shear specimen involving two aluminium plates bonded by a thin ductile adhesive layer. A cohesive zone model along with a simple traction versus separation law is employed in the finite element simulations of crack growth. It is observed that J_ss increases strongly as mode II loading is approached. Also, it enhances with bondline thickness in the above limit. These trends are rationalized by examining the plastic zones obtained from the numerical simulations. The numerically generated J_ss values are found to agree well with the corresponding experimental results.     

Interface crack initiation at V-notches along adhesive bonding in weakly bonded polymers subjected to mixed-mode loading

In this paper, interface crack initiation at V-notches along adhesive in bonded Polycarbonate (PC) and Poly Methyl Methacrylate (PMMA) subjected to mixed-mode loading conditions was investigated based on a combined experimental, finite element and matched asymptotic analysis. The V-notch specimens with an adhesive interface starting from its tip made at different notch angles were tested under three-point bending conditions. The experimental observations show that the specimens mainly fail by cracks along the interface. Also, the load at the crack initiation increases when the notch angle increases. The computational results are then used to explain and to correlate with the experimental data. A two-fold criterion developed by Leguillon (Eur J Mech A/Solids 21:61?C72 2002) that requires a simultaneous satisfaction of both Griffith energy and stress conditions for the crack initiation at a notch in the specimen made of a homogeneous brittle material is first extended for V-notch specimens under mixed-mode loading conditions and then used to estimate the crack initiation load. The estimated loads appear to agree well with the experimental data. Finally, an inverse method is proposed to estimate the values of fracture toughness at different mode mixity ratios.