Near crack line elastic-plastic analysis for a finite plate loaded by two pairs of antiplane point forces

Abstract

In this paper, the improved near crack line analysis method proposed in Refs. [I] and [2] I..IntroductionThe near crack line analysis method has been greatly improved by Yi tl' 21. In [1,2], the improved near crack line analysis method has been used to investigate a mode III crack in an elastic-perfectly plastic solid. And the small scale yielding conditions have been completely abandoned, and completely new and precise solutions of the elastic-plastic fields of a mode III stationary crack and a model III quasi-statically growing crack with remote antiplane shearing in an elastic-perfectly plastic material have been obtained, respectively. In [3] we analyzed the near crack line elastic-plastic stress and deformation fields for a center crack loaded by a pair of antiplane point forces in an infinite body in an elastic-perfectly plastic material. The solutions in [1--3] are suitable to the plastic zone no matter how large it is.The elastic-plastic analysis for a cracked plate with finite dimensions is one of the most difficult fields of Elastic-Plastic Mechanics. In this paper, we use the improved near crack line analysis method to analyze the near crack line elastic-plastic Stress and deformation fields for a center crack loaded by two pairs of antiplane point forces in a finite body in an elasticperfectly plastic material. This problem often exists in the practical engineering and is easily investigated with experiment, so the investigation of the problem is important both on the theory and in the applications. Similar to Ref. [1--3], the assumptions of small scale yielding theory have been given up and no other assumptions have been taken. So the results of this paper are sufficiently precise near the crack line region. However, we" found that the t Chongqing Jiaotong Institute,

General forms of elastic-plastic matching equations for mode-III cracks near crack line

“…Equations (7)-(9) are different in form from those given in rectangular coordinates x and y [1,6,[8][9] . The superscript (p) is neglected in Eqs.…”

“…Clearly, the partial differential equation system (1)-(3) has been changed to ordinary differential equation system (7)- (9). Equations (7)-(9) are different in form from those given in rectangular coordinates x and y [1,6,[8][9] .…”

“…To give the general matching equations and its solving procedure, Eqs. (4)- (6) have been given in polar coordinates r and θ, which are different in form from those given in rectangular coordinates x and y [1,6,[8][9] .…”

“…In the end, sufficiently accurate elastic-plastic field and plastic zone geometry near the crack line beyond the limitation of magnitude of the yielding scale are obtained. As an independent elastic-plastic crack analysis measure, the crack line analysis method solves some crack problems [8][9][10][11][12] and has gradually been introduced into geo-mechanics and concrete fracture analysis [13][14][15] , etc. It also applies well to linear elastic fracture mechanics and has been developed into an effective way of solving the stress intensity factors of cracks [16][17][18][19][20] .…”

“…Some sufficiently accurate elastic-plastic fields and elastic-plastic boundaries for some particular problems [1,6,[8][9] have been given. However, the solutions are aimed at special conditions individually, and the general form of the matching equation and the general formulation procedure are still ready to take shape.…”