Bimaterial Systems Research Articles

A bimaterial thermal model for microlayer applications

An alternative method to describe the temperature profiles of bimaterial systems for resistive heating is proposed. The thermal model based on the solution of a second order harmonic oscillator equation, is interpreted as a function of the oscillating parameters. We highlighted the importance to select adequately the initial conditions to reproduce the experimental results more realistic, as well as the inclusion of the diffusion time constant as a key parameter for interpretation. We discussed the theoretical temperature profiles obtained and the experimental results obtained on film and substrate by means of K-type micro thermocouples for different bimaterial systems such as Au/glass, Au/Si, Al/glass and Al/Si. A better agreement was found with the bimaterial model proposed as compared with the reported before. We found that physical properties and geometrical data play an important role on the temperature profiles obtained. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Stress intensity factors for penny-shaped cracks perpendicular to graded interfacial zone of bonded bi-materials

This paper examines the stress intensity factors that are associated with a penny-shaped crack perpendicular to the interface of a bi-material bonded with a graded interfacial zone. Elastic modulus of the graded interfacial zone is assumed to be an exponential function of the depth. The stress intensity factors are calculated numerically using a so-called generalized Kelvin solution based boundary element method. Three cases of normal or shear tractions acting on the crack surfaces are examined. Values of the stress intensity factors are examined by taking into account the effects of the following four parameters: (a) the crack front position; (b) the non-homogeneity parameter of the graded interfacial zone; (c) the crack distance to the graded interfacial zone; and (d) the graded interfacial zone thickness. The numerical results are compared well with existing solutions under some degenerated conditions. These results are useful to furthering our knowledge on fracture behavior of bi-material systems with or without a graded interfacial zone.

Dynamic crack kinking from a PMMA/Homalite interface

The behavior of a pre-existing, dynamically loaded, interfacial crack kinking away from the interface separating two materials was experimentally investigated under dynamic loading conditions. Dynamic fracture experiments were performed on pre-cracked bimaterial panels of PMMA bonded with Homalite-100 impact loaded using a high-speed gas gun. By varying the location of impact, a large range of mixed mode loading at the crack tip was produced. Information about the stress state surrounding the crack tip was obtained through use of the lateral shearing interferometer of coherent gradient sensing in conjunction with high-speed photography. The high-speed interferogram corresponding, to the time of crack initiation was analyzed in each case to find the preinitiation mode mixity at the crack tip. Measurement of both the local initiation mode mixity and the crack kink angle allows for possible extension of existing quasi-static interface crack kinking criteria, such as maximum opening stress or maximum energy release rate, to the case of dynamic loading. It was found that for bimaterial systems with small material property mismatch, such as the PMMA/Homalite system, the maximum opening stress criterion accurately predicts the relation between crack tip mode mixity and resulting kink angle for small initial crack kinking speeds.

Fatigue corrosion crack extension across the interface of an elastic bi-material

In this work crack propagation in a bi-material composed of a thin elastic layer ideally bonded to a large elastic substrate is studied. A flaw is assumed existing on the surface of the layer. Cracks nucleate from the flaw and propagate through the bi-material. The cracks have realistic geometrical shapes, where the crack tip is an integral part of the crack surface. Thus the crack propagation is associated with a crack surface evolution. Material loss due to corrosion of the crack surface is the physical ground for the evolution. A controlling mechanism for the surface advancement is the rupture of a brittle corrosion-protective film, which is continually building-up along the corroding surface. The rate of surface evolution is a function of the degree of protective film damage, caused by the surface straining. This leads to a moving boundary formulation, for which a numerical solution is proposed. Fatigue loading is considered as a suitable way to maintain crack evolution at a constant peak load level. Under the assumed model, the cracks always pass the interface. The elastic mismatch is shown to influence the growth rate variation around the interface. Crack extensions are presented as functions of the elastic mismatch and as functions of the initial flaw size. It is shown how the results can be used in designing bi-material systems. A typical morphology evolution of a crack passing through an interface with a weak–stiff transition is presented. An example of fatigue corrosion fracture is offered, which shows that the crack morphology of the model resembles the one observed in reality. It is concluded that the realistic crack geometry is an effective concept and the moving boundary formulation could be a very successful tool for simulating realistic crack propagation.

An Atomistic Approach to the Transverse Shearing of Single Alnminum and Aluminum-Nickel Bimaterial Systems

An Atomistic Approach to the Transverse Shearing of Single Alnminum and Aluminum-Nickel Bimaterial Systems

A maximum allowable flaw size for debond-resistant bimaterial layers

Free-edge debonding and subsequent interface crack extension are common modes of failure in a variety of engineering applications in which bonded layers of dissimilar materials are subject to differential expansion stresses. In this study, the susceptibility to debonding of short interface edge cracks is investigated for the global plane elasticity problem of a bimaterial strip with a uniform edge load applied to the top layer (a general model of differential expansion). The goal of this study is to determine the maximum crack length L for which interface crack extension is inhibited, or more specifically, for which the singular interface normal stresses are compressive. This is equivalent to a maximum allowable flaw size, which is of interest to both designers and inspectors of bimaterial systems. The critical crack length L has been extracted from parametric finite element analyses over a wide range of bimaterial configurations using the commercial software package ABAQUS. Results indicate that the critical crack length L increases with both the relative stiffness and thickness of the contracting layer, and may represent a significant inspectable flaw size for a variety of practical bimaterial configurations.

Determination of the interface strength between two polymer materials by a new curved interface tensile test: Preliminary experimental results

Recently, the authors have proposed a new experimental method for the determination of adhesion strength between two different materials. A curved interface and special arrangement of materials is used for the tensile test of bimaterial specimens to avoid singular stress fields around corners and edges. The main advantage of the test consists in the fact that the strength is determined under conditions of a uniform tensile stress field normal to the interface in the region where debonding starts. The present paper presents experimental results for two bimaterial systems - PMMA/TPE and PC/TPE (two stiff standard polymers with a thermoplastic elastomer). The expected failure behaviour was observed during the experiments, thus enabling the estimation of adhesion strength by using calculated stress concentration factors. The influence of the radius of curvature is discussed in detail.

A new variable‐order singular boundary element for two‐dimensional stress analysis

AbstractA new variable‐order singular boundary element for two‐dimensional stress analysis is developed. This element is an extension of the basic three‐node quadratic boundary element with the shape functions enriched with variable‐order singular displacement and traction fields which are obtained from an asymptotic singularity analysis. Both the variable order of the singularity and the polar profile of the singular fields are incorporated into the singular element to enhance its accuracy. The enriched shape functions are also formulated such that the stress intensity factors appear as nodal unknowns at the singular node thereby enabling direct calculation instead of through indirect extrapolation or contour‐integral methods. Numerical examples involving crack, notch and corner problems in homogeneous materials and bimaterial systems show the singular element's great versatility and accuracy in solving a wide range of problems with various orders of singularities. The stress intensity factors which are obtained agree very well with those reported in the literature. Copyright © 2002 John Wiley & Sons, Ltd.

Residual stress effects on fracture energies of cement–bone and cement–implant interfaces

The effects of residual stresses, which are caused by the temperature difference arising after polymerisation of bone cement, on the fracture energies of cement–bone and cement–implant interfaces have been examined by using both experimental and numerical works. Only fracture loads of the test specimen having interfacial cracks have been measured in the experimental stage. The values of fracture loads and temperature difference after polymerisation have been applied to finite element models of the test specimens to calculate critical J-integral values of these both interfaces in the numerical stage. In addition, fracture energies of bone and cement, have been obtained by experimentally, using three-point bending test method The results have shown that residual stresses can produce changes in the fracture energies of these bimaterial systems, especially in cement-implant interface and J IC values of interfaces are considerably smaller than the experimentally determined J IC values of cement and bone.

Numerical analysis of directionally unstable crack propagation in adhesively bonded joints

This paper investigates the directional stability of crack propagation in adhesively bonded joints. First, an analytical model analyzing the energy balance during the crack propagation in double cantilever beam specimens is presented, and the directional stability of cracks is predicted. The results are consistent with the predictions made by Fleck, Hutchinson, and Suo (Int. J. Solids Struct. 27 (13) (1991) 1683) using a stress analysis approach, and also are consistent with experimental observations. Similar to the situation in homogeneous solids, cracks in adhesively bonded joints also tend to be directionally unstable when the T-stress is positive (tensile) whereas tend to be directionally stable when the T-stress is negative (compressive). Both interface mechanics and the finite element method are then employed to analyze the stress state at the crack tip and to predict crack trajectories. Through extending the criteria for direction of crack propagation to bi-material systems, the trajectory for directionally unstable cracks is simulated. The simulation result accurately reflects the alternating nature of directionally unstable cracks in adhesive bonds such as the characteristic length and the overall shape.

Subinterfacial cracks in bimaterial systems subjected to mechanical and thermal loading

The effect of temperature on the propagation paths of subinterfacial cracks is studied. An aluminum/polymethylmethacrylate bimaterial specimen with large mechanical and thermal mismatches is used to investigate the effect of combined thermal and mechanical loads. The stress intensity factor (SIF) generated by mechanical loading in the presence of a temperature gradient is obtained by means of experiment and analyzed using the finite element method. A full-field optical shearing interferometry technique was used to measure the crack tip stress state. The results show that thermal effects can alter the SIFs sufficiently large enough to change the fracture behavior of subinterfacial cracks.

Interactions of fatigue cracks with elastic obstacles

To quantify the growth behaviour of fatigue cracks growing towards microstructural barriers or elastic obstacles, parametric solutions are obtained for crack-tip opening displacement and plasticity-induced crack closure of a mode I fatigue crack growing towards elastic obstacles. Three common bi-material systems are analysed using the finite element method, in which both constituent materials have identical elastic properties but only the phase that contains the crack can deform plastically. It has been found that under monotonic loading the crack-tip opening displacement decreases as the crack-tip approaches the interface boundary, but reaching a non-zero value when the crack-tip terminates at the boundary. For a fatigue crack growing under constant amplitude loading, the crack-closure stress has been found to increase as the crack grows towards the barrier. Based on these results a mechanistic model is proposed to quantify the influence of stress level on the fatigue threshold of microstructurally small fatigue cracks, with predictions being in close agreement with experimental data.

Crack deflection at an interface between dissimilar piezoelectric materials

The problem of crack deflection in bimaterial systems is considered in this paper. The material combinations may be of piezoelectric-piezoelectric, or one is piezoelectric and the other is not. Based on the Stroh formulation for anisotropic material, Green's functions for various bimaterial combinations are presented within the framework of two-dimensional electroelasticity, allowing the crack problem to be expressed in terms of coupled singular integral equations. A crack impinging on an interface joining two dissimilar materials may arrest or may advance be either penetrating the interface or deflecting into the interface. The competition between deflection and penetration is investigated using the maximum energy release rate criterion. Numerical results are presented to study the role of remote electroelastic loads on the path selection of crack extension.

Bimaterial Interfacial Crack Growth With Strain Gradient Theory

The purpose of this paper is to investigate the effect of material heterogeneity on damage evolution and subsequent crack propagation in bimaterial systems. Strain gradient theory analysis reveals that a higher stress triaxiality always occurs on the softer material side due to the material mismatch in yield capacity and the corresponding strain gradient along the interface. High stress triaxiality is a major condition which promotes ductile damage and facilitates crack growth. To investigate this link, numerical simulations of ductile interface crack growth are performed using a damage based constitutive model. Both the numerical and experimental results show that a crack may grow along the interface or deviate into the softer material, but never turn into the harder material. The theoretical and numerical analysis reveal three factors which strongly affect the direction of crack growth and the resistance capacity of the bimaterial system against fracture. These are the boundary conditions which determine the global kinematically admissible displacement field, the stress/strain gradient near the interface due to the material mismatch, and the distance from the crack tip to the interface.

Thermal Shock Behaviour of Thin Bi-Material Ceramic Systems

AbstractThis work describes a methodology developed to predict the thermal shock behaviour of thin bi-material ceramic systems. An experimental procedure based on controlled air cooling has been devised to simulate the flow of a gas stream over the surface of a thin two-layer ceramic system. Results of microstructural and fractographic investigations conducted on tested samples, including representative fracture patterns and crack initiation sites, are presented. A probabilistic-deterministic approach to predict the thermal shock behaviour of bi-material ceramic systems is proposed. Failure diagrams are constructed from a combination of the experimental and analytical studies. Critical thermal transient conditions typical of start-up and shut-down operation in solid oxide fuel cell are determined.

Intersonic crack propagation in bimaterial systems

This paper describes experimental observations of various phenomena characteristic of dynamic intersonic decohesion of bimaterial interfaces. Two separate but complementary optical methods are used in conjunction with high-speed photography to explore the nature of the large-scale contact and mach wave formation at the vicinity of running cracks in two different bimaterial systems. Theoretical predictions of crack tip speed regimes, where large-scale contact is implied, are confirmed. Also, the theoretically predicted mach wave emanating from the intersonically propagating crack tip is observed. Direct visual evidence is also obtained for another traveling mach wave emanating from the end of the intersonically moving contact zone. Subsequently, a physical model for intersonic crack propagation along bimaterial interfaces is presented and ratified in view of recent experimental observations and theoretical developments. Finally, the paper presents very recent experimental evidence that shows crack tip speeds exceeding the intersonic regime and becoming clearly supersonic.

A micromechanical model for interface crack extension in metal/ceramic bimaterial systems

A micromechanical model is proposed to explain a phenomenon observed in interface cracking in metal/ceramic bimaterial systems; that a crack along the interface may propagate in some cases by the growth of interfacial voids or microcracks ahead of the main crack and coalescence with the main crack. The model shows the importance of the local loading phase angle in the crack tip response. Depending on the local crystallographic orientation of the deformable component of the bimaterial, the model predicts that a brittle backwards growth of the microcrack may occur while the main crack tip remains inert. The predictions are consistent with experimental observations.

Dynamic Fracture Criteria for Crack Growth Along Bimaterial Interfaces

Dynamic fracture criteria based on experimental observations are proposed for subsonic crack growth along bimaterial interfaces. These criteria are based on the premise that the crack-face displacements at a point behind the crack tip increase exponentially with the instantaneous crack-tip velocity. This assumption establishes a generalized relationship between the dynamic energy release rate and the instanta-neous crack-tip velocity. Experiments are performed on PSM-1/aluminum bimaterial systems for both shear dominated and opening-mode dominated crack growth to verify the proposed criteria. Two different bimaterial specimen geometries are employed to obtain the complete range of crack-tip speeds in the subsonic regime. The dynamic loading is achieved either by detonating two explosive charges on the specimen or by impacting the specimen in one-point bend configuration. Dynamic photoelasticity in conjunction with high-speed photography is used to analyze the fracture event. Explosive loading of the interface crack results in crack propagation speeds on the order of 65 percent of the shear wave speed of PSM-1 and the crack growth is observed to be stable and opening-mode dominated. In contrast, the impact loading results in very high crack propagation speeds on the order of shear wave speed of PSM-1 and the crack growth is observed to be shear dominated.

Investigation of the mechanics of intersonic crack propagation along a bimaterial interface using coherent gradient sensing and photoelasticity

This paper describes the first experimental observations of various phenomena characteristic of dynamic intersonic decohesion of bimaterial interfaces. Two separate but complementary optical methods are used in conjunction with high speed photography to explore the nature of the large scale contact and mach wave formation at the vicinity of running cracks in two different bimaterial systems. Theoretical predictions of crack‐tip speed regimes where large scale contact is implied are confirmed. Also, the theoretically predicted mach wave emanating from the intersonically propagating crack‐tip is observed. Direct visual evidence is also obtained for another travelling mach wave emanating from the end of the intersonically moving contact zone.

Evaluation of fracture mechanics parameters in bimaterial systems using strain gages

An experimental study has been conducted in which strain fields were used to investigate and characterize the behavior of interfacial cracks in bimaterial systems under quasi-static load conditions. Strain field equations were derived from the available stress field equations. A parametric study was followed by experimentation, in which strain gage techniques were used to obtain values of the complex stress intensity factor, K, in the region of the crack tip. These values were then compared with the theoretical predictions. Furthermore, proven photoelastic techniques were also used to provide additional confirmation of the strain gage results. Experiments were conducted using a PSM-1/aluminum bimaterial system to determine K and mixity ψ. The results showed that values of K 1 obtained using strain gages averaged approximately 11% deviation from theory, while K 2 compared much better with an average of about 4% deviation from theory.