Molecular dynamics calculation of the J-integral fracture criterion for nano-sized crystals

Abstract

The critical J-integral is recognized as a valuable criterion for evaluating elastic-plastic fracture behavior of materials. It is, however, computationally complicated at the atomic scale for a nano-sized crystal when using the traditional integral method to reckon the traction force, strain, strain energy, etc. atom by atom. This paper attempts to propose an effective J-integral calculation method based on molecular dynamics (MD) simulations. The proposed method takes advantage of the potential energy interpretation of the J-integral, the main task in which is to calculate the potential energy difference of two identical crystal models with the neighboring crack length. As the potential energy of crystals at the atomic scale can be obtained easily from molecular dynamics simulations, the proposed method is thus computationally simple and especially applicable to complex crystal structures. A nickel crystal having an opening model I crack is investigated using this method. The critical J-integral in the ductile fracture plane (1\bar10) is calculated to be 4.424 Jm−2. It is also found in this study that the onset of crack propagation does not coincide with the occurrence of the maximum tension stress for nano-sized crystals, which is different from conventional fracture mechanics observation.