Micromechanical model of deformation-induced surface roughening in polycrystalline materials

A micromechanical model has been developed to describe deformation-induced surface roughening in polycrystalline materials. The three-dimensional polycrystalline structure is taken into account in an explicit form with regard to the crystallographic orientation of grains to simulate the micro- and mesoscale deformation processes. Constitutive relations for describing the grain response are derived on the basis of crystal plasticity theory that accounts for the anisotropy of elastic-plastic properties governed by the crystal lattice structure. The micromechanical model is used to numerically study surface roughening in microvolumes of polycrystalline aluminum and titanium under uniaxial tensile deformation. Two characteristic roughness scales are distinguished in the both cases. At the microscale, normal displacements relative to the free surface are caused by the formation of dislocation steps in grains emerging on the surface and by the displacement of neighboring grains relative to each other. Microscale roughness is more pronounced in titanium, which is due to the high level of elastic-plastic anisotropy typical of hcp crystals. The mesoscale roughness includes undulations and cluster structures formed with the involvement of groups of grains. The roughness is quantitatively evaluated using a dimensionless parameter, called the degree of roughness, which reflects the degree of surface shape deviation from a plane. An exponential dependence of the roughness degree on the strain degree is obtained.