Sandia National Laboratories, Livermore, CA 94551-0969, USA.
J Phys Condens Matter. 2011 Jan 12;23(1):015002. doi: 10.1088/0953-8984/23/1/015002. Epub 2010 Nov 26.
In this work we apply a material-frame, kernel-based estimator of continuum fields to atomic data in order to estimate the J-integral for the analysis of an atomically sharp crack at finite temperatures. Instead of the potential energy appropriate for zero temperature calculations, we employ the quasi-harmonic free energy as an estimator of the Helmholtz free energy required by the Eshelby stress in isothermal conditions. We employ the simplest of the quasi-harmonic models, the local harmonic model of LeSar and co-workers, and verify that it is adequate for correction of the zero temperature J-integral expression for various deformation states for our Lennard-Jones test material. We show that this method has the properties of: consistency among the energy, stress and deformation fields; path independence of the contour integrals of the Eshelby stress; and excellent correlation with linear elastic fracture mechanics theory.
在这项工作中，我们应用连续场的基于材料框架、内核的估计器来处理原子数据，以便在有限温度下分析原子级尖锐裂纹时估算 J 积分。我们使用准谐自由能作为埃谢里比应力所需的亥姆霍兹自由能的估算值，而不是适用于零温计算的位能。我们采用了 LeSar 及其同事的最简单的准谐模型，即局部谐模型，并验证了它对于我们的 Lennard-Jones 测试材料的各种变形状态下修正零温 J 积分表达式是足够的。我们表明，该方法具有以下特性：能量、应力和变形场之间的一致性；埃谢里比应力的轮廓积分的路径独立性；以及与线弹性断裂力学理论的极好相关性。
