Antiplane Crack Problem Research Articles

Yoffe–type moving crack in a functionally graded piezoelectric material

In this paper, the problem of a functionally graded piezoelectric material (FGPM) with a constantvelocity Yoffetype moving crack is considered. The strip is assumed to be under an antiplane mechani...

Higher order fields for damaged nonlinear antiplane shear notch, crack and inclusion problems

Damaged nonlinear antiplane shear problems with a variety of singularities are studied analytically. A deformation plasticity theory coupled with damage is employed in analysis. The effect of microscopic damage is considered in terms of continuum damage mechanics approach. An exact solution for the general damaged nonlinear singular antiplane shear problem is derived in the stress plane by means of a hodograph transformation, then corresponding higher order asymptotic solutions are obtained by reversing the stress plane solution to the physical plane. As example, traction free sharp notch and crack, rigid sharp wedge and flat inclusion, and mixed boundary sharp notch problems are investigated, respectively. Consequently, higher order fields are obtained, in which analytical expressions of the dominant and second order singularity exponents and angular distribution functions of the near tip fields are derived. Effects of the damage and hardening exponents of materials and the geometric angle of notch/wedge on the near tip quantities are discussed in detail. It is found that damage leads to a weaker dominant singularity of stress, but to little stronger singularities of the dominant and second order terms of strain compared to that for undamaged material. It is also seen that damage has important effect on the angular distribution functions of the near tip stress and strain fields. As special cases, higher order analytical solutions of the crack and rigid flat inclusion tip fields are obtained, respectively, by reducing the notch/wedge tip solutions. Effects of damage and hardening exponents on the dominant and second order terms in the solutions of the crack and inclusion tip fields are discussed.

A complex variable boundary element method for antiplane stress analysis around a crack in some nonhomogeneous bodies

A boundary element method based on the Cauchy integral formulae, i.e. a complex variable boundary element method (CVBEM), is proposed for the numerical solution of an antiplane crack problem involving an elastic body with shear modulus that varies continuously in space. The shear modulus assumes a certain form which is quite general to allow for multiparameter fitting of its variation. The method reduces the problem to a system of linear algebraic equations and can be readily implemented on the computer. For clarity, the CVBEM formulation is first carried out for a straight crack and then its extension to include an arbitrary curved crack is indicated.

A hypersingular boundary integral equation for antiplane crack problems for a class of inhomogeneous anisotropic elastic materials

An antiplane multiple crack problem is considered for a class of inhomogeneous anisotropic elastic materials. The problem is reduced to a boundary integral equation involving hypersingular integrals. The boundary integral equation may be solved numerically using standard procedures. Some crack problems for a particular inhomogeneous material is considered in detail and the stress intensity factors are obtained in order to assess the effect of the anisotropy and inhomogeneity on the stress field near the crack tips.

A hypersingular boundary integral equation for a class of antiplane multiple crack problems for inhomogeneous elastic materials

A hypersingular boundary integral equation for a class of antiplane multiple crack problems for inhomogeneous elastic materials

A hypersingular boundary integral equation for a class of antiplane multiple crack problems for inhomogeneous elastic materials

An antiplane multiple crack problem is considered for inhomogeneous isotropic elastic materials. The problem is reduced to a boundary integral equation involving hypersingular integrals. The boundary integral equation may be solved numerically using standard procedures. Some crack problems for a particular inhomogeneous material are considered in detail and the stress intensity factors are obtained in order to assess the effect of the inhomogeneity on the stress field near the crack tips. Copyright © 1999 John Wiley & Sons, Ltd.

On the fracture of paramagnets and soft ferromagnets

Expressions of the energy-release rates are established on the basis of the rotationally invariant (finite-strain) quasi-magnetostatic theory of elastic paramagnets and soft ferromagnets for which neither magnetic ordering nor spin effects need to be introduced. The corresponding path-independent integrals useful in fracture studies are constructed and this is shown to yield essentially the same results as the canonical field-theoretic approach using the notions of Eshelby srress and material forces. A simple application to the antiplane crack problem of a magnetostrictive body in an axial bias magnetic field illustrates the use of the obtained expressions. The same notions could be used to study the so-called magneto-plastic effect.

Interfacial fracture of a radially inhomogeneous elastic bimaterial

Anti-plane strain crack problems in radially inhomogeneous materials are considered; the model is used as a simple analogy with a non-linear power law material. Both an asymptotic and a rigorous analysis are used to determine the crack tip behaviour. A combined Mellin transform-difference equation method is used to solve the problem of a crack at an interface between a uniform elastic medium and a radially inhomogeneous material. These rigorous results are compared with asymptotic non-linear bimaterial results of Champion and Atkinson [Proc. R. Soc. Land.A429, 247–257 (1990)]. Some of the crack tip behaviour associated with the non-linear power law material is shown to be due to the apparent modulus tending to zero or infinity at the crack tip. Problems of cracks at an arbitrary angle to the interface can also be considered using this approach. We briefly consider such cases. To emphasize further similarities between the radially inhomogeneous and the non-linear material we derive some integral invariants.

Energy-release rates and path-independent integrals in electroelastic crack propagation

Two energy-release rates due to quasistatic crack propagation in electroelastic materials are obtained by using a Griffith-type energy approach. Their difference represents the free electric field contribution to the propagation of the crack. Appropriate conditions for mechanical and electrical fields allow us to express the energy-release as path independent integrals, already obtained by Pak and Herrmann, and by Maugin and Epstein. The assumptions are verified on the solution of an antiplane crack problem and the integrals are evaluated in terms of electrical and mechanical stress intensity factors.

A spectral overlay method for quasi-static viscoplasticity: Applications to anti-plane crack and comparison with closed-form solutions

The modified spectral overlay finite element method is described for a two-dimensional antiplane viscoplastic problem under quasi-static, isothermal conditions. The essential feature of the spectral overlay method is that high resolution of localized steep gradients can be achieved by overlaying a spectral interpolant on a standard finite element mesh. In order to evaluate this method and compare it with the conventional finite element method, a closed-form solution of a shear localization problem in one dimension has been devised. The results show that this method is very powerful in capturing the shape of the gradient field and its peak value in the localization zone. Solutions for an antiplane crack problem are then given to illustrate the effectiveness of this method.

Coplanar cracks in a finite rectangular anisotropic elastic slab under antiplane shear stresses: A hypersingular integral formulation

An antiplane crack problem concerning an arbitrary number of pairs of coplanar cracks in a finite rectangular anisotropic elastic slab is considered. Using Fourier integral transforms and Fourier series, the problem is reduced to a system of Hadamard finite-part singular (hypersingular) integral equations which can be solved numerically by using a collocation technique. Once these integral equations are solved, the relevant crack energy and stress intensity factors can be readily computed. Numerical results for a specific case of the problem are given.

COPLANAR CRACKS IN A FINITE TRANSVERSELY ISOTROPIC ELASTIC SLAB UNDER ANTIPLANE SHEAR STRESSES

An antiplane crack problem concerning a pair of coplanar cracks in a finite transversely isotropic elastic slab is considered. Using Fourier integral transform together with singular integral equation which can be solve numerically by suing a collocation technique. Once the integral equation is solved, the relevant crack energy and stress intensity factors of the problem are given. The analysis present can be easily extended to include cases where there are two or more pairs of coplanar cracks in the slab.

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.

The elastic-perfectly plastic solution for antiplane problem of crack in the anisotropic plane with elliptic yield surface

In this paper, the elastic-perfectly plastic antiplane problem of crack in the anisotropic plane with elliptic yield surface is studied. Using the methods of Rice and Lekhnitskii, a similarity between the isotropic case and the case studied here has been found and an exact solution is obtained.

Numerical studies of loss of ellipticity near singularities in an elastic material

Numerical solutions of anti-plane shear crack problems and screw dislocation problems are presented for materials in which the equilibrium equation varies in type locally from elliptic to hyperbolic as a result of deformation. These results show the emergence of surfaces of discontinuity in the displacement field in some materials. In other materials they show a chaotic mixture of elliptic phases at intermediate distances from the singularity. A statistical analysis applied to the numerical solutions demonstrates the role of elastic stability in the mechanics of these deformations.

An antiplane crack problem for some kinds of regions

An antiplane crack problem for some kinds of regions is duscussed, while the regions consist of several rectangular subregions (Figs. 3, 5). When solving the Neumann problems of the Laplace equation, we divide the original considered region into several rectangular subregions. In addition, using a theorem of continuation of harmonic function, the solution on original region can be found. The procedure used here has a different form in place of that mentioned in our previous papers[1,2]. Using the energy release method, the K 3 values can be obtained. All numerical results are shown in Figs. 4, 6 and Tables 1 and 2 respectively. A format for deriving all basic relations is presented, which is of great importance to get all results cited below.

Antiplane crack problems for an inhomogeneous elastic material

This paper examines some antiplane crack problems in an elastic material with variable shear modulus. An expression for the energy release rate is obtained for each of the cracks considered and a comparison made with the energy release rate for the corresponding crack in a homogeneous material.

Finite-deformation crack in an infinite body under anti-plane simple shear

The anti-plane shear crack problem in an infinite body is studied within the context of finite-deformation elastostatics. The governing equations are found to be identical to those of certain previously studied small strain plastic problems under anti-plane shear. For a particular strain energy function, an exact solution of the problem is obtained through use of results in the literature.