任意载荷下，材料失效的临界应力具有很大的不同，例如静水压下，材料失稳的压强可以到100 GPa，而在多方向剪切应力下材料失稳可能只需100~200 MPa，可以达到3个量级差。然而目前针对材料失稳的连续介质模型大多基于能量或者最大剪切应力，并不能完全覆盖材料任意的载荷。该研究基于连续介质理论提出了基于拉格朗日应变的五阶大变形模型，该模型能够准确获得硅在任意载荷下的材料失效应力。来自中国华东理工大学的陈浩博士和美国爱荷华州立大学航空航天工程和机械工程系的Valery I. Levitas教授团队，以及爱荷华州立大学材料学院的Duane D. Johnson教授团队合作，采用第一性原理计算得到了单晶硅材料在任意载荷下的失稳应力，拟合了提出的大变形弹性理论，发现该弹性理论可以精确给出硅材料任意载荷下的失稳应力。该研究为在连续介质框架下研究精确模拟材料在任意载荷下的失稳条件提供了理论基础，由于不同载荷可以导致不同的失稳模式，比如剪切应力下发生塑性变形，而在正应力下发生相变。因此该模型为连续介质力学提供了模拟任意载荷下导致不同失效模式的可能性。该文近期发布于npj Computational Materials 6: 115 (2020)。
Editorial Summary
Accurate prediction: continuum stress-strain relations and elastic instabilities
Materials under complex loading develop large strains and often phase transformation via an elastic instability, as observed in both simple and complex systems. This represents a material (exemplified for Si I) under large Lagrangian strains within a continuum description by a 5th-order elastic energy found by minimizing error relative to density functional theory (DFT) results. The Cauchy stress-Lagrangian strain curves for arbitrary complex loadings are in excellent correspondence with DFT results, including the elastic instability driving the Si I to Si II phase transformation and the shear instabilities. Phase transformation conditions for Si I to Si II under action of cubic axial stresses are linear in Cauchy stresses in agreement with DFT predictions. Such continuum elastic energy permits study of elastic instabilities and orientational dependence leading to different phase transformations, slip, twinning, or fracture, providing a fundamental basis for continuum physics simulations of crystal behavior under extreme loading. This article was recently published in npj Computational Materials 6,: 115 (2020).
原文Abstract及其翻译
Fifth-degree elastic energy for predictive continuum stress-strain relations and elastic instabilities under large strain and complex loading in silicon (大变形任意载荷下可预测材料不同失稳条件的五阶连续介质模型)
Hao Chen, Nikolai A. Zarkevich, Valery I. Levitas, Duane D. Johnson & Xiancheng Zhang
Abstract Materials under complex loading develop large strains and often phase transformation via an elastic instability, as observed in both simple and complex systems. Here, we represent a material (exemplified for Si I) under large Lagrangian strains within a continuum description by a 5th-order elastic energy found by minimizing error relative to density functional theory (DFT) results. The Cauchy stress—Lagrangian strain curves for arbitrary complex loadings are in excellent correspondence with DFT results, including the elastic instability driving the Si I → II phase transformation (PT) and the shear instabilities. PT conditions for Si I → II under action of cubic axial stresses are linear in Cauchy stresses in agreement with DFT predictions. Such continuum elastic energy permits study of elastic instabilities and orientational dependence leading to different PTs, slip, twinning, or fracture, providing a fundamental basis for continuum physics simulations of crystal behavior under extreme loading.
摘要 材料在复杂载荷下会有大变形，并经常伴有弹性失稳的相变过程。这种过程在简单体系和复杂体系内都被观察到。这里，基于对大量DFT计算结果的拟合，五阶连续介质力学模型被发展来拟合任意载荷下材料失稳条件。该模型的柯西应力-拉格朗日应变曲线可以很好重现第一性原理计算结果。并且该模型准确的预测了任意载荷下材料的临界失稳应力，包括多轴正应力和剪切应力下的失稳应力。这个模型将为连续介质力学模拟材料在任意载荷下大变形失稳提供了理论基础。
【文献来源】 npj计算材料学
