This paper deals with the identification of an empirical equation for predicting free surface roughness evolution. The equation has been proposed elsewhere, and, in contrast to widely used equations, assumes that the evolution of free surface roughness is controlled by two kinematic variables, the equivalent strain, and the logarithmic strain normal to the free surface. Therefore, an experimental program is designed to account for the effect of the mode of deformation on free surface roughness evolution. Thin sheets of aluminum alloy A5052-O and pure copper C1220P-O alloys are used to conduct the experimental program. In addition, numerical simulation is performed to calculate the evolution of free surface roughness under the same conditions. Comparison of experimental and numerical results shows that the accuracy of the numerical results is good enough. Then, numerical simulation is extended to the domain in which no experimental results are available. Discrete functions so found are fitted to polynomials. As a result, continuous functions that represent the empirical equation for predicting free surface roughness evolution for A5052-O and C1220P-O alloys are determined. These equations can be used in conjunction with solutions to boundary value problems in plasticity for predicting the evolution of free surface roughness in metal forming processes.

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