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

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.