# 可压缩理想弹塑性裂纹定常扩展尖端场 【作者】罗学富 【导师】黄克智

【作者】罗学富导师黄克智
【作者基本信息】清华大学，固体力学，1988年，博士

【中文摘要】 本文给出了可压缩(ν<1/2)理想弹塑性平面应变准静态定常扩展裂纹尖端分析的正确提法,并采用三种方法进行了求解。第一种方法以学术界普遍接受的高玉臣与Rice等的不可压缩(ν=1/2)理想弹塑性扩展裂纹尖端场为基础,以ε=1/2-ν为小参数作摄动展开,得到了直到ε2阶的渐近解。第二、第三种方法分别以Rice从及高玉臣和黄克智对裂尖场问题的理论提法框架直接求解裂尖场渐近解。并对各种解法进行了比较。分析表明,可压缩理想弹塑性扩展裂纹尖端场由五区构成。当ν→1/2时,该五区解可以退化到不可压缩扩展裂纹尖端场的四区解。本文指出,Orugan等对扩展裂纹尖端场的分析在数学上是不适定的,因而在他们所得解的部分塑性区中,出现塑性流动因子为负的情况,即塑性流动法则已遭破坏。

【英文摘要】 The solution of near-tip fields for crack growing quasi-statically and steadily in elastic perfectly-plastic compressible (v<1/2) materials is a difficult problem unresovled for a long time in Fracture Mechanics. This paper gives correct formulations of the problem, and the correct solution is obtained by using three different methods. In the first method, which is initiated by present author, the perturbations expansions with ∈=1/2-v as a small parameter are proposed. Based on the solution for incompressible materials, the asymptotic solution of the order up to ∈2 is obtained. In the second and third methods, the Near-tip solutions are obtained based on the frames of theoretical formulations by Rice, and Gao and Hwang, respectively. It turns out that the upper plane of the near-tip field is divided into 5 sectors for compressible materials. As ∈→ o , the 5-sector solutions degenerate to the well-known 4-sector solutions for incompressible materials. It is pointed out that, in the ...更多solutions by Drugan et al., the plastic flow factor turns out to be negative in part of the plastic sector, hence the plastic flow law is violated.  还原

TAG: 黄克智 尖端 裂纹 定常 罗学富
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