Crack tip fields in ductile crystals
Crack tip fields in ductile crystals
复制标题
延性晶体中的裂纹尖端场
DOI：
10.1007/978-94-017-2444-9_20
复制
发表时间：
1990
影响因子：
2.5
通讯作者：
R. Asaro
中科院分区：
文献类型：
--
作者：
James R. Rice;D. E. Hawk;R. Asaro
本文给出了弹塑性单晶体裂纹尖端场的渐近分析结果，并总结了这类裂纹固体有限元解的一些初步结果。在所研究的理想塑性fcc和B cc晶体中的平面应变拉伸和反平面剪切裂纹的情况下，在常规的小位移梯度假设下分析，渐近分析揭示了裂纹尖端显著的不连续场。对于静止裂纹，发现裂纹尖端的应力状态在一族角扇区中的每一个中是局部均匀的，但在扇形边界处不连续地跳跃，这也是位移场中剪切不连续的表面。对于准静态增长的裂纹的应力状态是完全连续的，从一个近端角扇区到下一个，但现在的一些部门涉及弹性卸载，并重新加载，屈服状态，和剪切不连续的速度场发展在扇区边界。在反平面的情况下研究，列入惯性条款（动态）增长的裂纹恢复一个不连续的应力场的尖端移动通过材料的弹塑性冲击波。对于相对于晶体的高对称性裂纹取向，不连续表面有时与活动晶体滑移面重合，但通常垂直于活动滑移面族，使得不连续对应于剪切的扭折模式。似乎与渐近分析一致。小规模的解决方案确认预期的不连续性，在网格分辨率的限制，位移的一个固定的裂纹和准静态增长的速度。此外，不连续性显然延伸到近端塑性区。本文用一种适用于任意变形的有限元法求解了一个泰勒硬化晶体板的平面应变拉伸问题。这表明由于晶格旋转的影响，区分裂纹尖端松弛的常规与扭结剪切模式。并有望探索裂纹尖端张开的机理。
Results on the asymptotic analysis of crack tip fields in elastic-plastic single crystals are presented and some preliminary results of finite element solutions for cracked solids of this type are summarized. In the cases studied, involving plane strain tensile and anti-plane shear cracks in ideally plastic f c c and b c c crystals, analyzed within conventional small displacement gradient assumptions, the asymptotic analyses reveal striking discontinuous fields at the crack tip.For the stationary crack the stress state is found to be locally uniform in each of a family of angular sectors at the crack tip, but to jump discontinuously at sector boundaries, which are also the surfaces of shear discontinuities in the displacement field. For the quasi-statically growing crack the stress state is fully continuous from one near-tip angular sector to the next, but now some of the sectors involve elastic unloading from, and reloading to, a yielded state, and shear discontinuities of the velocity field develop at sector boundaries. In an anti-plane case studied, inclusion of inertial terms for (dynamically) growing cracks restores a discontinuous stress field at the tip which moves through the material as an elastic-plastic shock wave. For high symmetry crack orientations relative to the crystal, the discontinuity surfaces are sometimes coincident with the active crystal slip planes, but as often lie perpendicular to the family of active slip planes so that the discontinuities correspond to a kinking mode of shear.The finite element studies so far attempted, simulating the ideally plastic material model in a small displacement gradient type program, appear to be consistent with the asymptotic analyses. Small scale yielding solutions confirm the expected discontinuities, within limits of mesh resolution, of displacement for a stationary crack and of velocity for quasi-static growth. Further, the discontinuities apparently extend well into the near-tip plastic zone. A finite element formulation suitable for arbitrary deformation has been used to solve for the plane strain tension of a Taylor-hardening crystal panel containing, a center crack with an initially rounded tip. This shows effects due to lattice rotation, which distinguishes the regular versus kinking shear modes of crack tip relaxation. and holds promise for exploring the mechanics of crack opening at the tip.