LAUSR

Abstract The purpose of this study is to quantitatively analyze the effect of strain path on roughness evolution of free surface during plastic deformation. Firstly, the crystal plastic finite element model for a representative volume element (RVE) of polycrystalline is established, including the polycrystalline geometric model and initial topography model. Next, based on two groups of strain path including five typical strain paths, i.e., uniaxial tension (UT), biaxial tension (BT), plane strain tension (PST), plane strain compression (PSC) and in-plane pure shear (PPS), the 3D surface roughness of free surface after the plastic deformation is presented quantitatively. The total change of surface topography can be divided into two parts, which relate to the homogenous deformation and inhomogeneous deformation. In a simple manner, the homogenous deformation and inhomogeneous deformation can correspond with the elastic deformation and plastic deformation respectively. As in the elastic deformation, the effect of the misorientation of the adjacent grains and strain localization in the polycrystalline material on the surface topography has no chance to exert on the very small strain. So the inhomogeneity of polycrystalline material has been ignored in the elastic deformation. For the effect of homogeneous deformation, the relationship between the surface roughness of the deformed surface, initial roughness and strain path is analytically derived. For the contribution of the inhomogeneous deformation to surface roughening, the quantitative relationship between surface roughness of the deformed surface and the strain path is acquired by the mathematical fitting based on hundreds of crystal plasticity finite element simulations. The final surface roughness of the deformed surface is obtained by combining these two parts. Then the experiment of biaxial tension on 6061 aluminum alloy sheet is taken as an example to verify the accuracy of surface roughness calculation. The comparison of experimental results and calculated results shows good consistency. Thereafter the surface roughening phenomena in the plastic deformation are observed at three different scales. The homogeneous deformation does not form additional peaks and valleys but changes the spacing and height of peaks and valleys of the initial surface topography, which brings about the surface roughening at macroscale level. In inhomogeneous deformation, the misorientation of the adjacent grains in the polycrystalline material is taken into consideration, which leads to the grain rotation and generates the additional peaks and valleys of the initial surface topography. The surface roughening due to this part can be seen at the mesoscopic scale. And the step phenomenon caused by slip bands inner the grains is the microscopic scale roughening behavior. This work is beneficial to understand the roughness evolution of free surface quantitatively with the effect of strain path and make out the surface roughening phenomena at different scales.