线性硬化材料III型袭纹的弹塑性：解及向理想塑性解的过渡

An Analytical Solution for a Mode Ⅲ Crack in a Piece-Wise Linear Material and its Transition to the Perfectly Plastic One

本文论述了在小范围屈服条件下求得线性硬化弹塑性材料Ⅲ型裂纹问题的全场解,详细阐述了弱硬化时解的渐近性态.结果表明,在硬化参数α趋于零时,线性硬化材料的全场解趋于理想塑性的 Hult 和 McClintock 解,而主奇异解的适用区域尺寸趋于零.

An analytical solution for a mode Ⅲ crack in a piece-wise linear material under small scale yielding conditions is obtained.The asymptotic behavior of the solution in the case of weak strain hardening is carefally investigated.It is shown that the solution tends to the corresponding perfectly plastic one of Hult and Mc- Clintock when hardening parameter α(=G_t/G,G:shear elastic modulus;G_t: plastic tangential modulus)approaches zero.But,in this limiting process,the dominent zone of the near-tip singular solution becomes vanishingly small.