Numerical simulations of dynamic crack growth along an interface

Dynamic crack growth is analyzed numerically for a plane strain bimaterial block with an initial central crack. The material on each side of the bond line is characterized by an isotropic hyperelastic constitutive relation. A cohesive surface constitutive relation is also specified that relates the tractions and displacement jumps across the bond line and that allows for the creation of new free surface. The resistance to crack initiation and the crack speed history are predicted without invoking any ad hoc failure criterion. Full finite strain transient analyses are carried out, with two types of loading considered; tensile loading on one side of the specimen and crack face loading. The crack speed history and the evolution of the crack tip stress state are investigated for parameters characterizing a PMMA/Al bimaterial. Additionally, the separate effects of elastic modulus mismatch and elastic wave speed mismatch on interface crack growth are explored for various PMMA-artificial material combinations. The mode mixity of the near tip fields is found to increase with increasing crack speed and in some cases large scale contact occurs in the vicinity of the crack tip. Crack speeds that exceed the smaller of the two Rayleigh wave speeds are also found.     

Line inclusions at anisotropic bimaterial interface

A line inclusion at the interface of an anisotropic bimaterial is studied. The line inclusion is assumed to be inextensible but with negligible bending rigidity. Complete singular fields near tips of the line inclusion are derived. The near-tip stress field exhibits singularities of the types in general with r being the distance measured from the tips. The near-tip fields are similar to those for fully closed interface cracks. In analogy to the stress intensity factors defined for interface cracks, strain intensity factors are introduced to characterize the near-tip fields. It is shown that there are only two independent strain intensity factors and corresponding modes of deformation. Complete displacement and stress fields and the corresponding strain intensity factors as the line inclusion is under uniform remote loading are given. Strain intensity factors for a line inclusion very near some anisotropic bimaterial interface are also derived.     

Dynamic response of bimaterial and graded interface cracks under impact loading

The interfacial fracture in bimaterial and functionally graded material (FGM) under impact loading conditions is investigated using experimental and numerical techniques that are valid for both type of interfaces. Experiments are conducted on epoxy based specimens in three point bend configuration and the complex SIF is measured using an electrical strain gage mounted close to the crack-tip. A complementary two-dimensional finite element simulation is performed using tup force and support reactions as input tractions, and the SIF-time history is determined using a displacement extrapolation technique. The experimentally determined SIF-histories match closely with numerical simulation up to the time of fracture initiation. The test results show that the mode-mixity remains nearly constant through out the test in both the materials, and the mixity values correspond to their respective static counterparts. The general dynamic response of the bimaterial and FGM specimens in terms of impact load, support reaction and the magnitude of complex SIF are comparable, and the mode-mixity is the parameter that distinguishes the graded interface from the bimaterial case.     

具有理想与非理想界面的双材料四点弯曲试件的界面断裂韧性

本文作者用边界元法研究了具有理想与非理想界面的双材料四点弯曲试件的界面断裂韧性.分析了理想界面裂纹尖端的复应力强度因子以及非理想界面裂纹前沿的应变能密度与试件的几何尺寸、双材料的性质等的关系.计算结果表明,当裂纹的长度小于试件内支点的跨度时,上述两个物理量在很大范围内不随裂纹长度而变化.这种稳态的特性为两者的临界值的实验测定提供了方便.      

Weight functions for bimaterial interface cracks

An efficient approach using the analytically decoupled near-tip displacement solution for bimaterial interface cracks presented in this paper involves: (1) the calculation of the decoupled strain energy release rates G _I and G _II associated respectively with the decoupled stress intensity factors K _I and K _II and (2) the extension of Rice's displacement derivative representation of Bueckner's weight function vectors beyond the homogeneous media. It is shown that the stress intensity factors for a bimaterial interface crack predicted by the present approach agree very well with those solutions available in the literature. The computational efficiency is enhanced through the use of singular elements in the crack-tip neighborhood.As reported in the homogeneous case, the calculated weight function for a bimaterial interface crack is load-independent but depends strongly on geometry and constraint conditions. Due to the coupling nature of the stress intensity factors of a bimaterial interface crack, the invariant characteristics of the dimensionless weight function vectors are different from those of a crack in homogeneous material. In addition, the elastic constants of two constituents can significantly alter the weight function behavior for a cracked bimaterial medium.Due to the load-independent characteristic of the weight functions, the stress intensity factors for a bimaterial interface crack can be obtained accurately and inexpensively by performing the sum of worklike products between the applied loads and the weight functions for the cracked bimaterial body under any loading conditions once the weight functions are explicitly predetermined. The same calculation can also be applied for the identical cracked bimaterial medium with different constraint conditions by including the self-equilibrium forces that contain both the external loads and the reaction forces induced at the constraint locations. Moreover, the physical interpretation of the weight functions can provide a guidance for damage tolerant design application.     

Greens functions for boundary element analysis of anisotropic bimaterials

We present several Greens functions for anisotropic bimaterials for two-dimensional elasticity and steady-state heat transfer problems. The details of the various Greens functions for perfect, slipping, and cracked interfaces are given for mechanical loading conditions. Previously reported formulations for cubic materials are extended to materials with general anisotropy in which plane strain deformations can exist. We also give the steady-state Greens function for thermal loading of a bimaterial with a perfectly bonded interface. The Greens functions are incorporated in boundary integral formulations and method of fundamental solutions formulations for analysis of finite solids under general boundary conditions.     

The boundary finite element method for predicting directions of cracks emerging from notches at bimaterial junctions

The analysis of a bimaterial medium with various notch opening angles has been carried out using boundary finite element method (BFEM) under arbitrary loading conditions. Introduced as novel method for stress concentration problems at geometrical discontinuities, cracks, bimaterial notches etc., the BFEM has been proved as numerically highly efficient. This has become more and more important because wedge type construction creates stress concentrations which may lead to crack initiation in many practical situations where multi-layered composite material is used, e.g. within aerospace, ship or automobile structures. So, the computational prediction of potential directions for crack initiation is essential for the knowledge of weak regions. All the analysis results are based on the hypothesis of Erdogan and Sih and have been verified by the well established finite element method. Results for potential crack initiation angles of both homogeneous and bimaterial media are presented with multiple examples of different wedge angles and different loading combinations.     

Determination of stress intensity factors for bimaterial interface stationary rigid line inclusions by boundary element method

The stress intensity factors for a rigid line inclusion lying along a bimaterial interface are calculated by the boundary element method with the multiregion and the discontinuous traction singular elements. The relationships between the stress intensity factors and the inclusion surface stresses are derived. The numerically computed stress intensity factors for the bimaterial interface rigid line inclusion in the infinite body are proved to be in good agreement within 3% when compared with the previous exact solutions. In the finite bimaterial models, the stress intensity factors for the center and edge rigid line inclusions at the interface are computed with the variation of the rigid line inclusion length and the shear modulus ratio under the uniaxial and biaxial loading conditions.     

Elastodynamics of a crack on the bimaterial interface

The paper is an application of boundary integral equations to the problem of a crack located on the bimaterial interface under time-harmonic loading. A system of linear algebraic equations is derived for solving the problem numerically. The distributions of the displacements and tractions at the bimaterial interface are obtained and analysed for the case of a penny-shaped crack under normal tension-compression wave. The dynamic stress intensity factors (normal and shear modes) are also computed. The results are compared with those obtained for the static case.     

Numerical simulations of dynamic interfacial crack growth allowing for crack growth away from the bond line

Dynamic crack growth is analyzed numerically for a plane strain bimaterial block with an initial central crack subject to impact tensile loading. The material on each side of the bond line is characterized by an isotropic hyperelastic constitutive relation. Potential surfaces of decohesion are interspersed in the material on either side of the bond line and along the bond line. The cohesive surface constitutive relation allows for the creation of new tree surface and dimensional considerations introduce a characteristic length into the formulation. Full transient analyses are carried out. The resistance to crack initiation, the crack speed history and the crack path are predicted without invoking any ad hoc failure criterion. Three calculations are carried out for a PMMA/Al bimaterial. The imposed loading and the properties of the adjacent materials are kept fixed, while the bond line strength is taken to be 1/4, 1/2, and 3/4 of the strength of PMMA. The nominal crack speed decreases with increasing bond line strength. When the bond line strength is 1/4 that of PMMA, the crack remains on the bond line although there is an attempt at branching off the bond line. For the intermediate case, a bond line strength 1/2 that of PMMA, repeated branching of the main crack off the bond line into the PMMA occurs, together with micro-crack nucleation on the bond line. The crack branches off the bond line into the PMMA when its strength is 3/4 that of PMMA, with the main direction of growth being parallel to the bond line, but with the crack progressively drifting further into the PMMA.     

Green's functions for dislocations in bonded strips and related crack problems

Green's functions are derived for the plane elastostatics problem of a dislocation in a bimaterial strip. Using these fundamental solutions as kernels, various problems involving cracks in a bimaterial strip are analyzed using singular integral equations. For each problem considered, stress intensity factors are calculated for several combinations of the parameters which describe loading, geometry and material mismatch.     

Kinking of an interface crack in an orthotropic bimaterial

We investigated the asymptotic problem of a kinked interface crack in an orthotropic bimaterial under in‐plane loading conditions. The stress intensity factors at the tip of the kinked interface crack are described in terms of the stress intensity factors of the interface crack prior to the kink combined with a dimensionless matrix function. Using a modified Stroh formalism and an orthotropy rescaling technique, the matrix function was obtained from the solutions of the corresponding problem in transformed bimaterial. The effects of orthotropic and bimaterial parameters on the matrix function were examined. A reduction in the number of dependent material parameters on the matrix function was made using the modified Stroh formalism. Moreover, the explicit dependence of one orthotropic parameter on the matrix function was determined using an orthotropic rescaling technique. The effects of the other material parameters on the matrix function were numerically examined. The energy release rate was obtained for a kinked interface crack in an orthotropic bimaterial.     

Flexural studies on asymmetric hybrid Kevlar fabric/epoxy composites

For composites reinforced with Kevlar fabrics, the method of asymmetric hybridization is employed for the improvement of flexural properties such as maximum fibre yield stress and modulus of elasticity in bending. Calculations based on the elastic-plastic analysis are used to assess the shift in the neutral axis during bending, and the bimaterial beam model is invoked to estimate the arrangement and replacement of Kevlar fibres by carbon fibres in the compression face, for two relative fibre orientations. Flexural properties of the bimaterial are compared with those of unmodified Kevlar/epoxy composite for three different loading rates. Scanning electron microscopic examination of the fracture features is discussed.     

An interface integral equation method applied to a crack impinging upon a bimaterial,frictional interface

A crack impinging upon a frictional, bimaterial interface is studied theoretically. Specifically we consider the problem of an infinitely long, cracked, two-dimensional fiber, which is embedded in an infinite plane with distinct elastic properties. The composite is subjected to tensile loading parallel to the fiber. An interface integral equation method is developed to solve this problem. This method, involving to-be-determined distributions of line forces, reduces the specific problem considered here to four coupled integral equations which are solved numerically. The bimaterial effect appears to be significant with respect to the length of the slip zone along the interface and the interfacial shear stress. However, the blunting of the crack by the frictional interface is virtually independent of the bimaterial effect.     

Characterization of isochromatic fringe patterns for a dynamically propagating interface crack

The isochromatic fringes surrounding a crack propagating along a bimaterial interface have been developed and characterized. A parametric investigation has also been conducted to study the influence of various fracture parameters on this isochromatic fringe pattern. The relevant fracture parameters of interest were the crack-tip velocity, the mode mixity of loading and the non-singular stress field component. In all the cases the fringe pattern was compared with the more familiar patterns that are generated for the case of crack propagation in homogeneous media. It was found that both the crack tip velocity and the mode mixity of loading have a significant effect on the size and shape of the isochromatic fringe pattern surrounding a crack tip propagating along a bimaterial interface. However, the non-singular stress field component was found not to have a substantial effect on the fringe pattern. This is in contrast with the case of crack propagation in homogeneous media, where the non-singular stress field component determines the tilt of the fringe contours. The paper also presents an appropriate scheme to analyze experimental fringe contours to extract the various fracture parameters of interest. Finally, this scheme is employed to analyze actual experimental data from a typical bimaterial interface fracture experiment.     

The kinking behaviour of a bimaterial interface crack under indentation loading

The aims of this paper are twofold. The first is to evaluate the applicability of the formula for the crack kink angle—based on the maximum principle stress criterion—for predicting the interface kink angle in a bimaterial sample undergoing indentation loading. This formula was developed for cracks in homogenous materials but in this paper, it is used to predict the kink angle using the mode mixity at the tip of a crack lying on a bimaterial interface. The second aim is to examine the behaviour of the system, in terms of the crack kink angle and contact radius, for various coating thickness', crack lengths and combinations of properties of the coating and substrate. The system that is analysed consists of a planar bimaterial sample undergoing indentation with a tungsten-carbide spherical indenter. Two-dimensional, axisymmetric models are created to represent the system, with subdomains used for modelling the cracks. In order to determine the applicability of the kink angle formula, the angle predicted is compared to the angle that is directly calculated using boundary element method models that establish the angle of the kink which yields the maximum mechanical energy release rate. The second aim of the paper is achieved by varying the material property combinations and coating thickness of the bimaterial sample and observing the effect on the kink angle of the interface crack and the contact radius. The methodologies employed are initially verified on homogenous samples with known solutions.     

Deformation behavior of interpenetrating-phase composites

A simple, unit-cell model has been proposed to predict the deformation behavior of composites having two interpenetrating phases, continuous in three dimensions. By dividing the unit cell into several elements and using the isostress and isostrain bimaterial loading configurations, the composite deformation behavior has been constructed in terms of the behavior of its components. The formulation allows calculation of the deformation behavior of an interpenetrating-phase composite by a simplified numerical iteration. The estimates from this simplified model have been compared with experimental data on the stress/strain behavior of equi-volume Cd---Zn and Cu---Ag alloys and infiltrated Fe---Ag composites. A limited assessment of the present approach, in the light of the other methods of calculation such as finite-element and self-consistent methods, has been made.     

Analysis of the adhesion toughness of a CVD diamond coating

Diamond coating adhesion toughness has been analysed in this work. By means of a numerical simulation of an indentation test where the influences of both the geometry and material properties on adhesion were evaluated. In several test conditions the strain energy release rate of a crack at bimaterial interface was evaluated. This energy parameter was used to define bimaterial adhesion toughness.     

Crack deflection at an interface of alumina/metal joint: A numerical analysis

Deflection of a crack at the bimaterial interface is the initial mechanism required for obtaining enhanced toughness in bimaterial system. In this paper, a criterion is presented to predict the competition between crack deflection and penetration at the interface, using an energy release rate criterion. The finite element methods are used to calculate the strain energy release rates at the crack tip of alumina–metal bimaterial that either deflect or penetrate at the interface as a function of elastic mismatch and length of the deflected or penetrated crack. The effects of the elastic properties of two bonded materials were highlighted in order to evaluate the conditions for the crack deflection by the interface as well as the distance between the crack tip and the interface.