Jin Y, Yuan F G
Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC 27695-7921, USA.
J Nanosci Nanotechnol. 2005 Dec;5(12):2099-107. doi: 10.1166/jnn.2005.414.
The J-integral is investigated in discrete atomic systems using molecular mechanics simulations. A method of calculating J-integral in specified atomic domains is developed. Two cases, a semiinfinite crack in an infinite domain under the remote K-field deformation and a finite crack length in a finite geometry under the tensile and shear deformation prescribed on the boundary, are studied in the two-dimensional graphene sheets and the values of J-integral are obtained under small-strain deformation. The comparison with energy release rates in Mode I and Mode II based on continuum theory of linear elastic fracture mechanics show good agreements. Meanwhile, the nonlinear strain and stress relation of a 2D graphene sheet is evaluated and is fitted with a power law curve. With necessary modifications on the Tersoff-Brenner potential, the critical values of J-integral of 2D graphene systems, which denoted as Jc, are eventually obtained. The results are then compared with those from the relevant references.
利用分子力学模拟研究了离散原子系统中的J积分。开发了一种在指定原子域中计算J积分的方法。研究了两种情况：在无限域中远程K场变形下的半无限裂纹，以及在边界规定的拉伸和剪切变形下有限几何形状中的有限裂纹长度，在二维石墨烯片中进行了研究，并在小应变变形下获得了J积分值。与基于线弹性断裂力学连续介质理论的I型和II型能量释放率的比较显示出良好的一致性。同时，评估了二维石墨烯片的非线性应变和应力关系，并拟合了幂律曲线。对Tersoff-Brenner势进行必要修改后，最终获得了二维石墨烯系统J积分的临界值，记为Jc。然后将结果与相关参考文献的结果进行比较。
