Interfaces Between two Dissimilar Elastic Materials

In this paper the near tip solutions for interface corners written in terms of the stress intensity factors are presented in a unified expression. This single expression is applicable for any kinds of interface corners including corners and cracks in homogeneous materials as well as interface corners and interface cracks lying between two dissimilar materials, in which the materials can be any kinds of linear elastic anisotropic materials or piezoelectric materials. Through this unified expression of near tip solutions, the singular orders of stresses and their associated stress/electric intensity factors for different kinds of interface problems can be determined through the same formulae and solution techniques. This unified feature of solving interface problems is then implemented numerically through several different interface problems. Moreover, in order to improve the accuracy and efficiency of numerical computation, a special boundary element based upon the Green's function of bimaterials is introduced in this paper.     

Correspondence Relations for Fracture Parameters of Interface Corners in Anisotropic Viscoelastic Materials

The problems of the interface corners between two dissimilar anisotropic viscoelastic materials are studied in this paper. Through the use of the well-known correspondence principle between linear elasticity and linear viscoelasticity, fracture parameters in the Laplace domain can be obtained from the path-independent H-integral for the corresponding problems of anisotropic linear elastic materials. Further application of the correspondence relations for fracture parameters proposed in our recent study then leads us the solutions of fracture parameters in the time domain. To show the applicability and accuracy of the proposed method, several different kinds of numerical examples are presented such as a centered interface crack, free edges between two dissimilar materials, and the interface corners appeared within the electronic packages. The fracture parameters calculated in this study include the orders of stress singularity and the stress intensity factors of opening mode, shearing mode and tearing mode. The proposed method allows the orders of stress singularity be real or complex, repeated or distinct, and the fracture mode be pure mode or mixed mode.     

Analysis of an interface crack for a functionally graded strip sandwiched between two homogeneous layers of finite thickness

The interface crack problem for a composite layer that consists of a homogeneous substrate, coating and a nonhomogeneous functionally graded interphase was formulated for singular integral equations with Cauchy kernels, which were integrated using the Lobatto–Chebyshev collocation technique. Mixed-Mode Stress Intensity Factors (SIFs) and Strain Energy Release Rates were calculated. The SIFs were compared for accuracy with relevant results previously published. The parametric studies were conducted for the various thickness of each layer and for various nonhomogeneity ratios. Particular application to the Zirconia thermal barrier on steel substrate is demonstrated.     

Thermal stress intensities at an interface crack between two elastic layers

The thermal stress intensities (energy release rate and stress intensity factors) due to temperature changes are derived in closed-form for an interface crack between two elastic layers of dissimilar materials. The solutions are two-dimensional and tabulated over a wide range of material and layer thickness combinations. The tables serve as rapid evaluations of the thermal stress intensities for given temperature changes. A strain gauge technique is given for determining constraint coefficients which reflect the constraint conditions during the temperature changes. The solutions are compared with results from the literature. The stress intensities due to thermal and mechanical loads are generally superimposed. As an example of application, the solutions are utilized to obtain the complete thermal and mechanical stress intensities for a four-point bend specimen.     

On the dynamic crack propagation in an interphase with spatially varying elastic properties under inplane loading

This article provides a comprehensive theoretical investigation on a finite crack with constant length (Yoffe type crack) propagating in an interfacial layer with spatially varying elastic properties under inplane loading. The analytical formulations are developed using Fourier transforms and solving the resulting singular integral equations in terms of the opening and sliding displacements of the crack. The dynamic stress intensity factors and energy release rate are analyzed to study the dynamic fracture property of this inherent mixed mode crack problem. Numerical examples are provided to show the effects of the material properties, the thickness of the interfacial layer, the crack position and speed upon the dynamic fracture behaviour, and the singularity transition between the current crack and the corresponding interfacial crack for thin interphase.     

Singular Thermal Residual Stress Field near the Interface Corner of Bonded Dissimilar Materials

In this paper, a cooled composite interface corner consisting of two bonded dissimilar materials is considered as a plane problem. With the complex variable method, the thermal residual stress field is studied analytically. It is found that the regular stress term possesses the singularity either of lnr or ln²r. The exact expressions for the corresponding singular stress field are presented.     

金属陶瓷功能梯度材料的颗粒界面断裂能量释放率的研究

研究了功能梯度材料富陶瓷区金属颗粒界面断裂能量释放率。采用双层嵌套模型给出了金属颗粒界面的热应力与金属体积浓度的关系,对于得到的第五梯度层中的颗粒界面热应力,分析了颗粒界面断裂的释放率,并研究了每一梯镀层中金属颗粒的临界尺寸变化规律。     

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.     

Analysis of the driving force for a generally oriented crack in a functionally graded strip sandwiched between two homogeneous half planes

The driving forces for a generally oriented crack problem embedded in a Functionally Graded strip sandwiched between two half plane are analyzed using singular integral equations with Cauchy kernels, and integrated using Lobatto-Chebyshev collocation. Mixed-mode Stress Intensity Factors (SIF) and Strain Energy Release Rates (SERR) are calculated. The Stress Intensity Factors are compared for accuracy with previously published results. Parametric studies are conducted for various non-homogeneity ratios, crack lengths, crack orientation and thickness of the strip. It is shown that the SERR is more complete and should be used for crack propagation analysis.     

Arbitrarily oriented microcracks near the tip of an interface macrocrack in bonded dissimilar anisotropic materials

It is well known that microcracking in brittle materials results in a reduction of the stress intensity factor (SIF) and energy release rate (ERR). The reduced SIF or ERR represents crack tip shielding which is of significant interest to micromechanics and material science researchers. However, the effect of microcracking on the SIF and ERR is a complicated subject even for isotropic homogeneous materials, and becomes much more formidable in case of interface cracks in bonded dissimilar solids. To unravel the micromechanics of interface crack tip shielding in bonded dissimilar anisotropic solids, an interface crack interacting with arbitrarily oriented subinterface microcracks in bonded dissimilar anisotropic materials is studied. After deducing the fundamental solutions for a subinterface crack under concentrated normal and tangential tractions, the present interaction problem is reduced to a system of integral equations which is then solved numerically. A J‐integral analysis is then performed with special attention focused on the J₂‐integral in a local coordinate system attached to the microcracks. Theoretical and numerical results reassert the conservation law of the J‐integral derived for isotropic materials 1 , 2 also to be valid for bonded dissimilar anisotropic materials. It is further concluded that there is a wastage when the remote J‐integral transmits across the microcracking zone from infinity to the interface macrocrack tip. In order to highlight the influence of microstructure on the interfacial crack tip stress field, the crack tip SIF and ERR in several typical cases are presented. It is interesting to note that the Mode I SIF at the interface crack tip is quite different from the ERR in bonded dissimilar anisotropic materials.     

Stress Intensity Factors for an Interface Kinked Crack in a Bi-Material Plate Loaded Normal to the Interface

Stress intensity factors for a kinked crack originating at interface of two bonded dissimilar materials subjected to normal tension are found by the finite element method.     

Anti-plane Shear Cracks Approaching a Bi-material Interface

A novel procedure is proposed for evaluation of stress intensity factors of planar Mode III shear cracks perpendicular to a nearby interface between two isotropic elastic solids. Shear cracks traversing a flat layer bonded to two different elastic solids are also analyzed. The method is based on superposition of singular near tip stress and displacement fields generated by both the main crack and certain image cracks. Both the main and the image cracks are loaded by self-equilibrating shear tractions of different magnitude, such that matching parts of the said fields are made to satisfy traction and displacement continuity conditions at the interface. Selected comparisons with results obtained by different methods show good agreement. Applications of the method to other crack problems are discussed.     

Crack-tip Caustics at a bi-Material Interface

The size and the shape of crack-tip caustics, at a bi-material interface, under static load, are studied. When the crack-tip, which is perpendicular to interface, is at the interface of the bi-material, the caustic depends on the properties of the two materials. Thus, the caustic is divided into two branches. The size of the two branches of the caustic mainly depends on the elastic modulus and Poisson's ratios of the two materials. This revised version was published online in July 2006 with corrections to the Cover Date.     

界面性能对陶瓷基复合材料拉伸强度的影响

基于陶瓷基复合材料拉伸试验现象引入了主裂纹损伤带的概念, 并将其宽度定义为界面脱粘长度. 由于界面性能对纤维应力集中有较大影响, 并且控制着材料的断裂模式, 分别给出了脆性断裂和韧性断裂的强度计算公式, 并引入了应力集中系数和界面脱粘能量释放率. 分析结果表明, 拉伸强度随着应力集中系数和界面脱粘能量释放率的增大而减小. 文中公式给出的预测值与试验值吻合较好, 表明断裂时纤维所承担的应力用脱粘段纤维平均应力来衡量是合适的.     

Non-Axisymmetric Matrix Cracking and Interface Debonding with Friction in Ceramic Composites

A three-dimensional analytical model based on the principle of minimum potential energy is developed and applied to determine the stress state in a discrete fiber/matrix composite cylinder subjected to axial tensile loading in the fiber direction and containing a non-axisymmetric transverse matrix crack and an interface debond. The friction over the debonded interface is incorporated into the analysis. The strain energy release rates associated with the matrix crack and the interface debonding under the combination of the applied load and the interface frictional force are computed. The strain energy release rate criterion has been employed to evaluate the critical applied loads for the two fracture modes and to assess the competition between propagation of a matrix crack and growth of interface debonding. A parametric study has been carried out. The computed results show that the interface friction plays an important role in the failure of brittle matrix composites.     

A Method to Extract Interface Stress Intensity Factors for Bimaterial Problems using Interlayers

A numerical method is presented here to determine stress intensity factors for interface cracks in plane, isotropic, elastic bimaterial fracture problems. The method relies on considering a companion problem wherein a very thin elastic interlayer with a crack, is artificially inserted between the two material regions of the original bimaterial problem. Modes I and II stress intensity factors are obtained for the companion problem using the modified virtual crack closure method. These stress intensity factors for the companion problem are then converted to the stress intensity factors for the original interface crack problem with the help of a universal relation. This universal relation between the stress intensity factors of the two problems is established by considering an asymptotic problem where the thickness of the interlayer is small compared with all other length scales. Two benchmark problems are considered to demonstrate the effectiveness of the interlayer approach for determining interface stress intensity factors.     

Analytical-Numerical Solution of Elliptical Interface Crack Problem

The problem of elliptical interface crack, located between two bonded dissimilar elastic half spaces, is considered. To obtain a solution of the problem, the traction boundary pseudodifferential equations are used. An analytical-numerical method for solving these equations is proposed. Strain energy release rates along the crack contours are calculated for some examples. This revised version was published online in July 2006 with corrections to the Cover Date.     

The Mixed Mode Crack Problem in an Inhomogeneous Orthotropic Medium

The mixed mode crack problem in plane elasticity for a graded and oriented material is considered. The material property grading is intentional, whereas the property orientation or orthotropy is usually the consequence of material processing. It is assumed that the crack is located in a plane perpendicular to the direction of property grading and the principal axes of orthotropy are parallel and perpendicular to the crack. The four independent engineering constants E₁₁, E₂₂, G₁₂, and ν₁₂ are replaced by a stiffness parameter, E = √E₁₁ E₂₂, a stiffness ratio, δ = (E₁₁/E₂₂)^1/4, a Poisson's ratio, ν = √ν₁₂ ν₂₁, and a shear parameter κ₀ = (E/2G₁₂) - ν. The corresponding mixed boundary value problem is reduced to a system of integral equations which is solved for various loading conditions and material parameters. The results presented consist of the strain energy release rate, the stress intensity factors and the crack opening displacements. It is found that generally the stress intensity factors increase with increasing material inhomogeneity parameter and shear parameter and with decreasing stiffness ratio. This revised version was published online in July 2006 with corrections to the Cover Date.     

Effect of Biaxial Load on Crack Deflection/Penetration at Bi-material Ceramic Interface

The paper investigates the effect of the biaxial loading on crack deflection/penetration at a bi-material ceramic interface. A biaxially loaded geometry was numerically investigated using Finite Element Analysis in order to determine the energy release rate. The obtained results could be used in conjunction with a fracture criteria at interface for estimating the path of the crack after the interface was reached.     

Modeling of Bonding at an Interface Crack

A mechanical and mathematical model is suggested for an interface crack with bonding in its end zones. Normal and shear bond tractions occurring under the action of the external loads are searched for by solving a system of two singular integrodifferential equations. The stress intensity factors at the crack tip are calculated taking the compensating action of the bonds into account. Energetic characteristics of the interface crack (the deformation energy release rate and the rate of the energy absorption by the bonds) are analyzed. A sensitivity analysis is performed of the force and energetic characteristics of the interface crack to the end zone size, bond compliance and limit stretching. This revised version was published online in July 2006 with corrections to the Cover Date.