Elastic-plastic analysis of the crack surface vicinity under a pair of anti-plane forces applied at an arbitrary point on the crack surface

Feng Huang,Qingguo Yang,Ya Li,Zhijian Yi,Yinhua Ma,Jianyi Gu,Chaohua Zhao,Xiaobing He

doi:10.1063/1.5023724

Abstract

An elastic-plastic analysis of the mode III crack surface vicinity was performed in an infinitely wide elastic-perfectly plastic plate, in which a pair of anti-plane forces applied at an arbitrary point on the crack surface. The crack line analysis method was used without the traditional small-scale yield condition. The plastic zone length, the plastic zone shape, and the elastic-plastic stress field in the vicinity of the crack surface were obtained analytically. Moreover, the plastic zone lengths in the vicinity of the crack surface and crack line were compared, and it was found that under a pair of anti-plane forces applied at an arbitrary point on the crack surface, the plastic zone length in the vicinity of the crack surface reached its maximum faster than that in the vicinity of the crack line under the same conditions, which indicates the stress state near the crack surface region is more detrimental than that near the crack line region. The variation of plastic zone length with the load position was also studied, and it was shown that when the point forces were closer to the crack tip, the plastic zone length was smaller and the stress state of the crack was more disadvantageous.

Highlights

Elastic-plastic analysis near the crack tip region has always been difficult and a significant research focus in fracture mechanics
In 1957, a stress-strain field closed-form solution near the crack tip region was obtained by Hult-McClintock,[1] but this solution was based on the small-scale yield condition
In 2010, Yi6 applied the crack line analysis method to study the Hult-McClintock closed-form solution, analyze the inappropriateness of the basic assumptions in the traditional small-scale yield conditions, and illustrate that the strain field obtained with the crack line analysis method does not possess singularity

Summary

INTRODUCTION

Elastic-plastic analysis near the crack tip region has always been difficult and a significant research focus in fracture mechanics. Expand equation (7) in the Taylor series and substitute it into equation (8), one can be obtain the precise solutions of the elastic stress field in the vicinity of the crack surface: τxz. During the solution of the problem, the small-scale yield condition is not introduced, the stress function satisfies the compatibility equation and the elastic stress components satisfy the boundary conditions, so the results are sufficiently accurate in the vicinity of crack surface. After these stresses are obtained, the strains and displacements can be solved, which is omitted here.

Matching elastic stress and plastic stress on the elastic-plastic boundary

Comparative analysis of the maximum plastic zone length

Influence of the loading position on the plastic zone length

CONCLUSION