Mixed mode near-tip fields for cracks in materials with strain-gradient effects
Mixed mode near-tip fields for cracks in materials with strain-gradient effects
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DOI：
10.1016/s0022-5096(96)00089-0
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发表时间：
1997-03
影响因子：
5.3
通讯作者：
Yonggang Huang;Li-yuan Zhang;T. Guo;K. Hwang
中科院分区：
文献类型：
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作者：
Yonggang Huang;Li-yuan Zhang;T. Guo;K. Hwang
由于应力奇异性，裂纹尖端附近存在较大的应变梯度。当裂纹尖端周围的断裂过程区的尺寸与本征材料长度l相当时，应变梯度效应变得显著，通常在微米的量级上。Fleck和哈钦森[（1993）塑性中应变梯度效应的唯象理论。J.Mech.Phys.Solid41，1825-1857]，应变梯度塑性理论被应用于研究弹性以及具有应变梯度效应的弹塑性材料中的混合型裂纹尖端附近的渐近场。确定了主导应变场为无旋应变场。对于弹性材料，应力和力偶应力在裂纹尖端附近具有平方根奇异性，并且由三个变量控制（两个用于模式I和II应力场，第三个用于力偶应力场，由高阶应力产生）。在具有应变梯度效应的弹性材料中，裂纹尖端的应力可能比没有应变梯度效应的材料中的相应材料高50%以上。对于弹性幂硬化应变梯度材料，得到了一个解析解。应变梯度塑性中的混合型应力场是Ⅰ型和Ⅱ型应力场的线性叠加。几种近端模式混合物的应力和偶应力的角分布清楚地表明，应变梯度塑性中的新近端场与HRR场显着不同。在具有应变梯度效应的弹塑性固体中，裂纹尖端前的应力可能是HRR场中相应应力的2.5倍以上。渐近分析比较有利的有限元结果。这种解决方案的材料，特别是主导区的大小的相关性进行了讨论。
Large strain gradients exist near the tip of a crack due to stress singularity. The strain-gradient effect becomes significant when the size of the fracture process zone around a crack tip is comparable to the intrinsic material length, l, typically on the order of microns. Fleck and Hutchinson's [(1993) A phenomenological theory for strain-gradient effects in plasticity. J. Mech. Phys. Solid41, 1825–1857], strain-gradient plasticity theory is applied to investigate the asymptotic field near a mixed mode crack tip in elastic as well as elastic-plastic materials with strain-gradient effects. It is established that the dominant strain field is irrotational. For an elastic material, stresses and couple stresses have the square-root singularity near the crack tip, and are governed by three variables (two for mode I and II stress fields, and the third, resulting from higher order stresses, for the couple stress field). Stresses ahead of a crack tip in elastic materials with strain-gradient effects could be more than 50% higher than their counterparts in materials without strain-gradient effects. For an elastic-power law hardening strain-gradient material, an analytical solution is obtained. The mixed mode stress field in strain-gradient plasticity is the linear superposition of their counterparts in mode I and II. The angular distribution of stresses and couple stresses for several near-tip mode mixities clearly indicate that the new near-tip field in strain-gradient plasticity differs significantly from the HRR field. Stresses ahead of a crack tip in elastic-plastic solids with strain-gradient effects could be more than 2.5 times their counterparts in the HRR field. The asymptotic analysis compares favorably with available finite element results. The relevance of this solution to materials, in particular the size of the dominant zone, is discussed.