Moving Dugdale crack along the interface of two dissimilar magnetoelectroelastic materials

In this paper, the concept of Dugdale crack model and Yoffe model is extended to propose a moving Dugdale interfacial crack model, and the interfacial crack between dissimilar magnetoelectroelastic materials under anti-plane shear and in-plane electric and magnetic loadings is investigated considering the magneto-electro-mechanical nonlinearity. It is assumed that the constant moving crack is magneto-electrically permeable and the length of the crack keeps constant. Fourier transform is applied to reduce the mixed boundary value problem of the crack to dual integral equations, which are solved exactly. The explicit expression of the size of the yield zone is derived, and the crack sliding displacement (CSD) is explicitly expressed. The result shows that the stress, electric and magnetic fields in the cracked magnetoelectroelastic material are no longer singular and the CSD is dependent on the loading, material properties and crack moving velocity. The current model can be reduced to the static interfacial crack case when the crack moving velocity is zero.     

Prediction of arbitrary crack growth from the interface between two dissimilar elastic materials

Based on the universal laws of stress distribution around a crack edge, the general analysis of crack start from the interface is given. The solution for the original crack is assumed to be known. In order to classify different possible cases of crack growth beginning, both a slip-region ahead of the opening zone and a core region near the crack edge are introduced. The former provides non-overlapping of the crack surfaces and removes an undesirable oscillating stress field singularity which is produced mathematically at the assumption of a completely opening crack. The latter means that we consider the damage of an elementary volume (geometrical measure of the microstructure) as a discrete fracture operaton. Two asymptotical cases are studied: the slip-region is much smaller or much larger than the cross-section of the core region. Then the stress-strain state on the core region periphery qualitatively is the same as for a completely opening or shear interface crack, respectively. A characteristic crack opening appears instead of a characteristic length of the slip-region for a blunted crack. The angles of crack departure are predicted according to different known criteria of fracture. In passing, parametric, analysis of stresses and energy density angle distributions are given. Plane and penny-shaped cracks are examined as the illustration.     

Griffith crack moving along the interface of two dissimilar piezoelectric materials

The problem of an anti-plane Griffith crack moving along the interface of dissimilar piezoelectric materials is solved by using the integral transform technique. It is shown from the result that the intensity factors of anti-plane stress and electric displacement are dependent on the speed of the Griffith crack as well as the material coefficients. When the two piezoelectric materials are identical, the present result will reduce to the result for the problem of an anti-plane moving Griffith crack in homogeneous piezoelectric materials. This revised version was published online in August 2006 with corrections to the Cover Date.     

Mixed mode fracture criterion of interface crack between dissimilar materials

This study presents an application of fracture mechanics to the interface crack between dissimilar materials. In this study, a concept of the stress intensity factors of an interface crack is discussed, and various types of specimens are tested experimentally for investigating the mixed mode fracture toughness criterion of an interface crack. The fracture toughness based on the stress intensity factors of an interface crack is decided by the fracture test and the boundary element analysis using the contour integral method. The mixed mode fracture toughness criterion is successfully characterized by the stress intensity factors of an interface crack.     

Boundary element analysis for an interface crack between dissimilar elastoplastic materials

The boundary element method (BEM) is presented for elastoplastic analysis of cracks between two dissimilar materials. The boundary integral equations and integral representation of stress rates are written in such a form that all integrals can be evaluated by the regular Gaussian quadrature rule. An advanced multidomain BEM formulation is suggested for the solution of analysed problems where the substantial reduction of stiffness matrix is observed. The elastoplastic behaviour is modelled through the use of an approximation for the plastic component of the stresses. The boundary and the yielding zone are discretized by elements with quadratic approximations. In numerical examples the path independence of the J- and L-integrals for a straight interface crack and a circular arc-shaped interface crack are investigated, respectively. The influence of the different values of Young's modulus on the J-integral, shape and size of plastic zones is treated too.     

A moving Griffith crack at the interface of two dissimilar elastic layers

The anti-plane shear problem of a Griffith crack traveling with a constant velocity at the interface of two dissimilar isotropic elastic layers is considered. Integral transform method is used to reduce the problem to the solution of a singular integral equation which is further reduced, by using Chebyshev polynomials, to a system of algebraic equations. The results for the particular cases of a moving Griffith crack at the interface of a layer and a half-space and two half-spaces are derived. Numerical results for the stress intensity factor are displayed graphically.     

Interaction between an interface crack and a parallel subinterface crack in dissimilar anisotropic composite materials

In this paper, the pseudo-traction method is combined with the edge-dislocation method (i.e. PTDM) to solve the interaction problem between an interface crack and a parallel subinterface crack in dissimilar anisotropic materials. After deriving the fundamental solutions for an interface crack loaded by normal or tangential tractions on both crack surfaces and the fundamental solutions for an edge dislocation beneath the interface in the lower anisotropic material, the interaction problem is reduced to a system of a singular integral equations by adopting the well-known superposition technique. The equations are then solved numerically with the aid of the Chebyshev numerical integration and the Chebyshev polynomial expansion technique. Several typical examples are calculated and numerical results are shown in figures and tables from which a series of valuable conclusions is obtained. Since the present results should be verified and since no previous results exist to compare them with a consistency check in introduced which starts from the conservation law of the J-integral in anisotropic cases. It is shown that the check provides a powerful tool to examine the results, although it really presents a necessary condition rather than a sufficient way to the crack-tip parameters of the interface crack and the subinterface crack in the dissimilar anisotropic materials.     

Anti-plane shear crack in a magnetoelectroelastic layer sandwiched between dissimilar half spaces

The crack problem of a magnetoelectroelastic layer bonded to dissimilar half spaces under anti-plane shear and in-plane electric and magnetic loads is considered. Fourier transforms are used to reduce the mixed boundary value problems of the crack, which is assumed to be permeable, to simultaneous dual integral equations, and then expressed in terms of Fredholm integral equations of the second kind. Numerical results show that the stress intensity factors are influenced by the magnetoelectric interactions and the geometry size ratio.     

Boundary element analysis of dissimilar materials and interface crack

The highly-accurate BEM elastostatic program, which is especially useful for the analysis of dissimilar materials and interface cracks, is introduced in brief. By using this program, we can deal with the elastostatic poblems of isotropic or orthotropic dissimilar materials and also the bonded residual stress due to the mismatch of material constants. This paper shows some applications of the BEM program to the analysis of dissimilar materials and interface cracks considering the residual stress quantitatively, and also shows the method to evaluate the strength of dissimilar materials based on the interfacial fracture mechanics. Some experimental results and the evaluation on the strength of dissimilar materials are also presented.     

Stress intensity factor analysis of a three-dimensional interface crack between dissimilar anisotropic materials

A new numerical method to calculate the stress intensity factors (SIFs) of a three-dimensional interface crack between dissimilar anisotropic materials was developed. In this study, the M-integral method was employed for mode separation of the SIFs. The moving least-square method was utilized to calculate the M-integral. Using the M-integral with the moving least-square method, SIFs can be automatically calculated with only the nodal displacements from the finite element method (FEM). Here, SIFs analyses of some typical three-dimensional problems are demonstrated. Excellent agreement was achieved between the numerical results obtained by the present method and the corresponding results proposed by other researchers. In addition, the SIFs of a single-edge crack, a through crack, and a semi-circular crack between two anisotropic solids in three-dimensional structures were analyzed.     

A permeable interface crack between dissimilar thermopiezoelectric media

Summary This paper presents an explicit treatment of the generalized 2D thermopiezoelectric problem of an interfacial crack between two dissimilar thermopiezoelectric media by means of the extend Stroh formalism. In comparison with the other relevant studies, the present work has two features: one is that the crack is assumed to be a permeable slit across which the normal electric displacement and the tangential electric field are continuous. The other is that the heat loading is applied at infinity, rather than on the crack faces. As a result, the field intensity factors and the electric field inside the crack are obtained in explicit closed-forms, respectively. As examples, the solutions of several particular cases, including that of an impermeable crack and that of a homogeneous material with a crack are also presented. It is shown that the electric field inside a crack may be singular and oscillatory for the case of an interfacial crack, while for the case of a crack in a homogeneous medium it is linearly variable. Moreover, it is also found that for a homogeneous medium with a crack the stress intensity factors based on the impermeable model and permeable model are same, but the intensity factor of the electric displacement is not.     

Elastic and plastic stress analysis of an interface crack between two dissimilar layers

In the present paper, the mixed-mode Dugdale model is applied to investigate the plastic zone size and the crack tip opening displacement of an interface crack between two dissimilar layers. In the analysis, both normal and shear stresses are assumed to exist in the plastic zones and satisfy the Von Mises yield criterion. The plastic zone sizes can be determined on condition that the stress intensity factors caused by the stresses in the plastic zones and applied loading are zero. Then, the crack tip opening displacement can be obtained by dislocation theories. In numerical examples, the plane stress condition is considered. The plastic zone size and the crack tip opening displacement of an interface crack between two dissimilar layers under a uniform load are examined. The effects of Dundurs’ parameters and the thickness of materials on the plastic zone size and the crack tip opening displacement are investigated in detail. Numerical results show that in the case of small thickness, the values of the normalized plastic zone size and the normalized crack tip opening displacement decrease with increasing Dundurs’ parameters, α and β, while, in the case of infinite thickness, the value of the normalized plastic zone size is independent of α, and the value is symmetric about the axis on which β = 0.     

Parallel crack near the interface of magnetoelectroelastic bimaterials

A parallel crack near the interface of magnetoelectroelastic bimaterials is considered. The crack is modelled by using the continuously distributed edge dislocations, which are described by the density functions defined on the crack line. With the aid of the fundamental solution for the edge dislocation, the present problem is reduced to a system of singular integral equations, which can be numerically solved by using the Chebyshev numerical integration technique. Then, the stress intensity factor (SIF), the magnetic induction intensity factor (MIIF) and the electric displacement intensity factor (EDIF) at the crack tips are evaluated. Using these fracture criteria, the cracking behaviour of magnetoelectroelastic bimaterials is investigated. Numerical examples demonstrate that the interface, mechanical load, magnetic load and material mismatch condition are all important factors affecting the fracture toughness of the magnetoelectroelastic bimaterials.     

Virtual crack closure technique for an interface crack between two transversely isotropic materials

The virtual crack closure technique makes use of the forces ahead of the crack tip and the displacement jumps on the crack faces directly behind the crack tip to obtain the energy release rates \({{\mathcal {G}}}_I\) and \({\mathcal {G}}_{II}\). The method was initially developed for cracks in linear elastic, homogeneous and isotropic material and for four noded elements. The method was extended to eight noded and quarter-point elements, as well as bimaterial cracks. For bimaterial cracks, it was shown that \({\mathcal {G}}_I\) and \({\mathcal {G}}_{II}\) depend upon the virtual crack extension \(\varDelta a\). Recently, equations were redeveloped for a crack along an interface between two dissimilar linear elastic, homogeneous and isotropic materials. The stress intensity factors were shown to be independent of \(\varDelta a\). For a better approximation of the Irwin crack closure integral, use of many small elements as part of the virtual crack extension was suggested. In this investigation, the equations for an interface crack between two dissimilar linear elastic, homogeneous and transversely isotropic materials are derived. Auxiliary parameters are used to prescribe an optimal number of elements to be included in the virtual crack extension. In addition, in previous papers, use of elements smaller than the interpenetration zone were rejected. In this study, it is shown that these elements may, indeed, be used.     

Dynamic SIF of interface crack between two dissimilar viscoelastic bodies under impact loading*

In this paper, the transient dynamic stress intensity factor (SIF) is determined for an interface crack between two dissimilar half-infinite isotropic viscoelastic bodies under impact loading. An anti-plane step loading is assumed to act suddenly on the surface of interface crack of finite length. The stress field incurred near the crack tip is analyzed. The integral transformation method and singular integral equation approach are used to get the solution. By virtue of the integral transformation method, the viscoelastic mixed boundary problem is reduced to a set of dual integral equations of crack open displacement function in the transformation domain. The dual integral equations can be further transformed into the first kind of Cauchy-type singular integral equation (SIE) by introduction of crack dislocation density function. A piecewise continuous function approach is adopted to get the numerical solution of SIE. Finally, numerical inverse integral transformation is performed and the dynamic SIF in transformation domain is recovered to that in time domain. The dynamic SIF during a small time-interval is evaluated, and the effects of the viscoelastic material parameters on dynamic SIF are analyzed.     

Stress intensity factor analysis for an interface crack between dissimilar isotropic materials under thermal stress

Thermal stresses, one of the main causes of interfacial failure between dissimilar materials, arise from different coefficients of linear thermal expansion. Two efficient numerical procedures in conjunction with the finite element method (FEM) for the stress intensity factor (SIF) analysis of interface cracks under thermal stresses are presented. The virtual crack extension method and the crack closure integral method are modified using the superposition method. The SIF analyses of some interface crack problems under mechanical and thermal loads are demonstrated. Very accurate mode separated SIFs are obtained using these methods.     

Elastic and plastic fracture analysis of a crack perpendicular to an interface between dissimilar materials

Elastic and plastic fracture analysis of a Mode I crack perpendicular to an interface between dissimilar materials is carried out. Continuously distributed dislocations are used to simulate the crack. The simulation will cause singular integral equations with Cauchy kernel. By solving the singular integral equations numerically, the effects of crack depth (distance from the interface to the crack middle point) and Dundurs’ parameters on the Mode I stress intensity factor are investigated systematically. Then, based on the Dugdale model, the plastic zone size, and the crack tip opening displacement of the crack under uniform loadings are investigated. The effects of uniform loadings, crack depth, and Dundurs’ parameters on the plastic zone size and the crack tip opening displacement are examined. Numerical results show that when the crack is embedded in a stiffer material, the values of both the normalized plastic zone size and the normalized crack tip opening displacement are larger than 1. On the contrary, if the crack is embedded in a softer material, the values of both the normalized plastic zone size and the crack tip opening displacement are less than 1.     

The stress field near a griffith crack at the interface of two bonded dissimilar elastic half-planes

The stress and displacement fields in the vicinity of a Griffith crack located at the interface of two bonded dissimilar elastic half-planes are determined. A systematic use of Fourier transforms reduces the problem to that of a solving a set of simultaneous dual integral equations and this in turn is shown to be equivalent to a Riemann boundary value problem with closed form solution. The particular case in which the crack is opened by constant pressure is discussed.