Numerical investigation of the effect of non-local plasticity on surface roughening in metals

A non-local crystal plasticity theory that incorporates strain gradients in the hardening moduli has been implemented in a finite element program. It is proposed that a gradient term enters the hardening modulus through a square-root dependence, which introduces an internal length scale. The relation has resemblance to the Hall–Petch relation. Simulations of polycrystalline materials are performed through a numerical finite element model that partition the mesh into grains through a discrete version of the Voronoi algorithm. Numerical simulations are performed and the surface roughness of an initially flat free surface is evaluated. The effects of microstructure, the internal length scale, anisotropy and hardening are presented. It is shown that the local surface roughness decreases as the ratio between internal length scale and grain size increases, since the non-local term accelerates hardening. By studies of three different materials (Al, Cu and Pu) with varying degree of anisotropy and hardening it is shown that there is a more pronounced roughening effect in anisotropic materials, the same effect is also seen for material softening.