Dislocation Microstructures and the Effective Behavior of Single Crystals
Dislocation Microstructures and the Effective Behavior of Single Crystals
复制标题
位错微观结构和单晶的有效行为
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
M. Ortiz
中科院分区：
文献类型：
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作者：
S. Conti;M. Ortiz
摘要：我们考虑无限潜在硬化极限情况下的单晶塑性，这意味着晶体必须在所有材料点上以单滑移变形。这一要求引入了非凸约束，从而诱导形成精细尺度结构。我们限制注意力在整个线性化运动学和塑性变形理论，这是适当的单调比例加载和赋予塑性边值问题的定义良好的变分结构类似elastics.We首先研究的规模不变（本地）的问题。我们表明，通过以有限深度的顺序层压板的形式发展微结构，晶体可以击败单滑移约束，即，宏观（松弛）本构行为与多滑移理想塑性是不可区分的。在第二步中，我们包括位错线能量，因此长度尺度，到模型中。不同的制度导致几种可能类型的微观结构模式。我们目前的建设，实现各种最佳的标度律，并讨论与实验已知的标度，如霍尔-佩奇定律的关系。
Abstract.We consider single-crystal plasticity in the limiting case of infinite latent hardening, which signifies that the crystal must deform in single slip at all material points. This requirement introduces a nonconvex constraint, and thereby induces the formation of fine-scale structures. We restrict attention throughout to linearized kinematics and deformation theory of plasticity, which is appropriate for monotonic proportional loading and confers the boundary value problem of plasticity a well-defined variational structure analogous to elasticity.We first study a scale-invariant (local) problem. We show that, by developing microstructures in the form of sequential laminates of finite depth, crystals can beat the single-slip constraint, i.e., the macroscopic (relaxed) constitutive behavior is indistinguishable from multislip ideal plasticity. In a second step, we include dislocation line energies, and hence a length scale, into the model. Different regimes lead to several possible types of microstructure patterns. We present constructions which achieve the various optimal scaling laws, and discuss the relation with experimentally known scalings, such as the Hall-Petch law.