Elastic–plastic and elastic anti-plane shear of two parallel cracks (original) (raw)

A finite elastic body with a curved crack loaded in anti-plane shear

International journal of solids and …, 1993

Ahatraet-This paper presents a Boundary Integral Equation Method (BIEM) for an arbitrarily shaped, linearly elastic, homogeneous and isotropic body with a curved crack loaded in anti-plane shear. The crack must be modeled as an arc of a circle and wholly inside the solid-otherwise its position and orientation with respect to the boundary of the body is arbitrary.

Effect of Couple Stresses on the Stress Intensity Factors for Two Parallel Cracks in an Infinite Elastic Medium under Tension

Mathematical Problems in Engineering, 2012

Stresses around two parallel cracks of equal length in an infinite elastic medium are evaluated based on the linearized couple-stress theory under uniform tension normal to the cracks. Fourier transformations are used to reduce the boundary conditions with respect to the upper crack to dual integral equations. In order to solve these equations, the differences in the displacements and in the rotation at the upper crack are expanded through a series of functions that are zero valued outside the crack. The unknown coefficients in each series are solved in order to satisfy the boundary conditions inside the crack using the Schmidt method. The stresses are expressed in terms of infinite integrals, and the stress intensity factors can be determined using the characteristics of the integrands for an infinite value of the variable of integration. Numerical calculations are carried out for selected crack configurations, and the effect of the couple stresses on the stress intensity factors i...

Antiplanar shear problem for a crack between dissimilar nonhomogeneous isotropic elastic layers

Engineering Fracture Mechanics, 1992

This paper deals with the problem of determining the stress intensity factor when two dissimilar nonhomogeneous bonded elastic layers have a crack at the interface. It is assumed that the faces of the crack are subjected to prescribed antiplane shear stress. The mixed boundary value problem is reduced to a singular integral equation of the second kind which is further reduced by using Chebyshev polynomials, to a system of algebraic equations. Numerical results for the stress intensity factor are presented in the form of graphs.

Dynamic stresses around two cracks placed symmetrically to a large crack

International Journal of Fracture, 1996

Dynamic stresses around three cracks in an infinite elastic plate have been solved. Two cracks, which are small and equal, are situated ahead of a large crack so as to allow for geometrical symmetry. Time-harmonic normal traction acts on each surface of these cracks. To solve the problem, two solutions are combined. One of them is a solution for a crack in an infinite plate and another is that for two collinear cracks in an infinite plate. The Schmidt method is used to satisfy the boundary conditions on the cracks' surfaces with use of the combined solutions. Stress intensity factors are calculated numerically for some of these crack configurations.

Analytical solution for an interfacial crack subjected to dynamic anti-plane shear loading

Acta Mechanica, 2006

A closed form solution for an interfacial crack problem is obtained. The crack lies on the interface of two bonded dissimilar orthotropic strips. Its surfaces are subjected to a dynamic anti-plane shear traction. Separation of variables technique is employed, to reduce the problem to a singular system of triple series equations, then to a singular integral equation. That is solved exactly, such that the asymptotic stress field distribution and the stress intensity factor are obtained in closed form expressions. The validity of the solution is proved. Further, a parametric study is introduced to investigate the effects of elastic and geometric characteristics of the composition on the values of the dynamic stress intensity factor (DSIF).

The interaction of two parallel non-coplanar identical surface cracks under tension and bending

International Journal of Pressure Vessels and Piping, 1999

In this paper, the interaction between two identical, non-coplanar, semi-elliptical surface cracks is investigated. The interacting cracks are assumed to be in an infinite plate subjected to remote tension or to pure bending loads. The stress intensity factors (SIFs) for these cracks are calculated using three-dimensional linear finite element analysis. A parametric study involving the relative horizontal and vertical separation distance between the two surface cracks is carried out for a specific crack shape and crack depth to plate thickness ratios of 0.3 and 0.2, respectively. An empirical formula is derived that relates the effects of the relative positions of these cracks to their SIFs. ᭧

The stress field near the front of an arbitrarily shaped crack in a three-dimensional elastic body

The problem stated in the title is investigated with special emphasis on the first three terms of the stress expansion, proportional to r-i/2, to= 1 and r 1/2 respectively, where r denotes the distance to the crack front. The particular case of a plane crack with a straight front and of stresses independent of the distance along the latter is studied first. It is shown that the classical plane strain and antiplane solutions must be supplemented by a few additional particular solutions to obtain the full stress expansion. The general case is then considered. The stress expansion is studied by writing the field equations (equilibrium, strain compatibility and boundary conditions) in a system of suitable curvilinear coordinates. It is shown that the number of independent constants in the stress expansion is the same as in the particular case considered previously but that the curvatures of the crack and its front and the non-uniformity of the stresses along the latter induce the appear...

Mode Stresses for the Interaction between Straight and Curved Cracks Problem in Plane Elasticity

Journal of Applied Mathematics and Physics, 2014

In this paper, the complex variable function method is used to obtain the hypersingular integral equations for the interaction between straight and curved cracks problem in plane elasticity. The curved length coordinate method and suitable quadrature rule are used to solve the integrals for the unknown function, which are later used to evaluate the stress intensity factor, SIF. Three types of stress modes are presented for the numerical results.

Elastic plastic mode III crack under internal shear

International Journal of Fracture - INT J FRACTURE, 1998

A complete solution is presented for the problem of a mode III crack in an infinite elastic perfectly-plastic solid under internal shear stress. This problem is the anti-plane strain equivalent of a mode I crack with internal pressure. The problem is transformed into a boundary value problem for a potential function. The particular case when the applied stress σA is equal to the yield stress σ0 is solved analytically, and the distance to the elastic-plastic boundary is obtained in closed form. The general case when σA σ0 is solved numerically by using the Boundary Element Method for potential problems. Numerical results are given for the distance to the elastic-plastic boundary and the crack tip opening displacement. The extent of the plastic zone ahead of the crack tip is shown to vary linearly with the ratio σA/σ0) when 0.5 ≤ (σA/σ0) ≤ 1.