【作者】 张林；

【导师】 黄克智；

【作者基本信息】 清华大学 ， 固体力学， 1993， 博士

【摘要】 本文研究了理想弹塑性材料中Ⅰ型平面应变准静态定常扩展裂纹尖端场的高阶渐近解。 对不可压缩材料,本文假定裂纹前方速度具有奇异性,建立了一个应力和速度在裂尖附近全连续的高阶渐近解,导出了相应的裂纹稳定扩展准则,并与修正Prandtl场进行了比较。 对可压缩材料,本文首先采用非规则的对数幂级数渐近展开方法,克服了过去研究中存在的中心扇形区变形率协调方程的高次渐近式不能被满足的困难,并得到了一个切向速度在裂尖前方存在间断的高阶渐近解,该解的主项就是目前被广泛接受的关于可压缩材料的尖端场解。由于上述尖端场的应力渐近解不满足允许发生切向速度间断的条件,本文分析了构造应力和速度全连续的渐近解的各种可能方案。最后,通过在裂尖前方引人一快变化区,本文得到了一个在裂尖周围应力和速度全连续的渐近解。更多还原

【Abstract】 The higher-order asymptotic solutions of a quasi-static, steadily propagating Mode I plane strain crack in an elastic perfectly plastic material are studied.For the incompressible materials, with the velocities ahead of the crack tip supposed to be singular, a higher-order asymptotic solution with fully continuous stress and velocity fields around the crack tip is obtained and the corresponding stable crack growth criterion is constructed. The detailed comparisons between the higher—order near tip solution and the well—known modified Prandtl field are also given in this paper.For the compressible materials, in order to satisfy the higher-order compatibility equation of the rate of deformation in the centered fan sector, which is a quite difficult problem unresolved in the previous studies, a particular term must be added to the expansions of the stress components in the regular logarithmic power series adopted by many researchers before. A higher-order near tip field with tangential velocity jump ahead of the crack tip is derived first, of which the dominant terms are the solution widely accepted. Unfortunately, there is a loophole in this asymptotic solution due to the discontinuity of the tangential velocity, which suggests us to study the solutions without any discontinuities of all the components of the stress and velocity fields. Finally, with the introduction of a fast varying zone ahead of the crack tip, a solution with fully continuous stress and velocity fields is obtained.更多还原