复合型裂纹小范围屈服下裂尖塑性区统一解

UNIFIED SOLUTIONS TO MIXED MODE CRACK TIP UNDER SMALL SCALE YIELDING

采用俞茂宏统一强度理论,推导Ⅰ、Ⅱ复合型裂纹在小范围屈服条件下裂尖塑性区尺寸的统一解析解。给出材料参数在不同拉压比a、泊松比v和中间主应力影响参数b下的一族裂尖塑性区形状与大小的轨迹。讨论以上参数对裂尖塑性区变化的影响,其中拉压比a对塑性区影响较大, a≠1导致塑性区在裂纹上下表面处不连续, b=0和b=1分别对应裂尖塑性区的上限、下限边界。同Tresca准则、Mises准则的解进行比较分析,已有解均是它的特例或线性逼近,该理论解具有理论的统一性和对不同材料的普适性。

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 α, poisson＇s ratio ν and material constant b are obtained. Furthermore the influences of the material parameters to the shapes and sizes of crack tip plastic zone are discussed essentially. Amongst them the α parameter effects much more than other parameters, it causes discontinuity in crack＇s up and down surface as α≠1, 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.