Dislocation shielding of a cohesive crack
Dislocation shielding of a cohesive crack
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DOI：
10.1016/j.jmps.2010.01.008
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发表时间：
2010-04
影响因子：
5.3
通讯作者：
T. Bhandakkar;Audrey C. Chng;W. Curtin;Huajian Gao
中科院分区：
文献类型：
--
作者：
T. Bhandakkar;Audrey C. Chng;W. Curtin;Huajian Gao
位错与内聚裂纹的相互作用对于约束结构和循环疲劳条件下裂纹的形核/扩展及其相关增韧机制的计算模拟越来越重要。本文研究了用矩形牵引分离定律描述的Dugdale内聚裂纹的位错屏蔽问题。屏蔽完全由三个无量纲参数表征，它们分别代表有效断裂韧性、结合强度和位错到裂纹尖端的距离。封闭形式的解析解表明，虽然经典的奇异裂纹模型预测位错可以屏蔽或反屏蔽裂纹，但在低结合强度时，位错总是屏蔽内聚裂纹，而与Burgers矢量无关。数值研究表明，屏蔽问题从高强度极限下的Lin和Thomson(1986)经典解过渡到低强度极限下的解。渐近分析给出了在整个内聚强度范围内屏蔽的近似分析模型。离散位错(DD)模拟了由梯形牵引分离定律描述的大量(>；103)刃位错与内聚裂纹的相互作用，证实了屏蔽的转变，表明内聚裂纹在很高的内聚强度(∼7 Gpa)下确实表现为单裂纹，但在内聚强度约1 GPa时，奇性裂纹和内聚裂纹之间的屏蔽出现了显著的偏差，与分析模型一致。分析和数值研究都表明，一个合适的裂纹尖端模型对于在GPA范围内准确地量化位错屏蔽内聚力是必不可少的。
Dislocation interaction with a cohesive crack is of increasing importance to computational modelling of crack nucleation/growth and related toughening mechanisms in confined structures and under cyclic fatigue conditions. Here, dislocation shielding of a Dugdale cohesive crack described by a rectangular traction-separation law is studied. The shielding is completely characterized by three non-dimensional parameters representing the effective fracture toughness, the cohesive strength, and the distance between the dislocations and the crack tip. A closed form analytical solution shows that, while the classical singular crack model predicts that a dislocation can shield or anti-shield a crack depending on the sign of its Burgers vector, at low cohesive strengths a dislocation always shields the cohesive crack irrespective of the Burgers vector. A numerical study shows the transition in shielding from the classical solution of Lin and Thomson (1986) in the high strength limit to the solution in the low strength limit. An asymptotic analysis yields an approximate analytical model for the shielding over the full range of cohesive strengths. A discrete dislocation (DD) simulation of a large (>103) number of edge dislocations interacting with a cohesive crack described by a trapezoidal traction-separation law confirms the transition in shielding, showing that the cohesive crack does behave like a singular crack at very high cohesive strengths (∼7GPa), but that significant deviations in shielding between singular and cohesive crack predictions arise at cohesive strengths around 1GPa, consistent with the analytic models. Both analytical and numerical studies indicate that an appropriate crack tip model is essential for accurately quantifying dislocation shielding for cohesive strengths in the GPa range.