Analysis of spurious image forces in atomistic simulations of dislocations

Molecular dynamics simulations of dislocation/obstacle interactions are enhancing our physical understanding of plasticity. However, despite increasing computational power, the interaction between simulation cell boundaries and the long ranged fields of dislocations make spurious image effects inevitable. Here, these image effects are examined in detail, providing a general map of the spurious image stress as a function of simulation cell size, aspect ratio and bow-out for both nominally edge and screw dislocations. This is achieved using an approximate image solution of the resulting boundary value problem as well as an analytic model that captures most of the spurious image effects. A unique simulation cell shape is found to minimize spurious image effects for a fixed simulation volume (i.e. fixed total number of atoms) and specified initial dislocation line length. The results are used to estimate image stress effects in various literature studies involving dislocation bow-out. The image effects are non-negligible. Several case studies involving simulation cell dimensions are shown to converge due to a near-zero scaling of the image stress with respect to the simulation cell dimensions used. Finally, a direct comparison is made between a dislocation bow-out configuration under an applied load in a finite simulation cell and an image-free multiscale simulation of the same problem and the difference is shown to be consistent with our estimated image stresses. Overall, the results here provide guidance for both the development and interpretation of quantitative molecular dynamics studies involving curved dislocation structures.