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本文研究准静态扩展裂纹尖端附近场的渐近分析。所考虑的材料是服从Mises屈服判据及其相关连的流动律的弹性-幂硬化律塑性材料。注意力集中于尖端附近场奇性阶的确定。基于基本方程组和高玉臣、黄克智提出的应力场的渐近展开式作了渐近分析。分析包括了平面应变、平面应力和出平面应变剪切三种情况。主要结果如下: (1)当充分接近裂纹尖端时,流动应力必须与角度无关; (2)所有考虑的三种情况中,应力为(1nr)~(2/(n-1))阶奇性,而应变为(1nr)~((n+1)/n-1)阶奇性; (3)为完全确定应变场的主项,须考虑应力场次主项对应变场主项的贡献; (4)假如不考虑应力场次主项对应变场主项的贡献,则可得出幂硬化材料中尖端邻近场的角变化将与理想塑性情况中的一样的结论。 文中还讨论了上面提到的应力场渐近展开式应用的局限性。
In this paper, we study the asymptotic analysis of the quasi-static extended crack near the field. The material under consideration is elastic-power-law plastic material subject to the Mises yield criterion and its associated flow laws. Attention is focused on the determination of the field singularity near the tip. Based on the basic equations and Gao Yuchen, the asymptotic expansion of the stress field proposed by Huang Kezhi is asymptotically analyzed. The analysis includes three cases: plane strain, plane stress and plane strain shear. The main results are as follows: (1) The flow stress must be angle-independent when sufficiently close to the crack tip; (2) the stress is (1nr) ~ (2 / (n-1)) order singular in all three considered cases (3) In order to completely determine the main field of the strain field, the contribution of the sub-field of the stress field to the main field of the strain field should be considered. 4) If we do not consider the main contribution of the stress field to the main field of the strain field, we can get the conclusion that the change of the angle near the field in the power hardening material will be the same as in the ideal plastic case. The paper also discusses the limitations of the asymptotic expansion of the stress field mentioned above.