UNIFIED SOLUTIONS TO MIXED MODE

CRACK TIP UNDER SMALL SCALE YIELDING

ZHANG Ya QIANG Hongfu YANG Yuecheng

(No.201 Faculty, Xi’an Hi-Tech Institute, Xi’an 710025 )

Abstract: Based on Yu Maohang’s unified strength theory, the unified analytical solutions to the shapes and sizes of Ⅰ,Ⅱ mixed mode crack tip plastic zone under small scale yielding are derived. Then a set of loci for crack tip plastic zone under different material parameters: The ratio of tensile strength to compressive strength  a, poisson’s ratio v and material constant b are obtained. Furthermore the influences of the material pa-rameters to the shapes and sizes of crack tip plastic zone are discussed essentially. Amongst them the  a parameter effects much more than other parameters, it causes discontinuity in crack’s up and down surface as  a¹1, meanwhile upper bound and lower bound of the loci for the plastic zone are corre-sponded to parameters using b=0 and b=1. The new solutions are compared with the former solutions to the problem by using Tresca criterion and Von Mises criterion, the former solutions are only the special cases or linear proximity to this problem. The new solutions have unification in the strength theory and universality for the different materials.

Key words: Mixed mode crack Small scale yielding Crack tip plastic zone Unified strength theory

CLC No: TG111

教育部NECT和国家重大基础研究发展计划资助项目(61338). Received 20060218, received in revised form 20060904