Proposal of Nonlinear Friction Law Taking Account of Frictional Work Quantity and Normal Pressure as State Variables

— Assessment of Sheet Formability by Nonlinear Friction Model II —

Abstract

Effects of coated-layer cracks on a coated layer on a change in friction coefficient are examined. Experimental results indicate that sliding distance influences friction coefficient rather than the cracks on a coated layer. To express the change in friction coefficient due to sliding, a frictional work parameter ω, which is derived as a summation of products of sliding distance and normal pressure, is proposed. In addition, it is demonstrated that ω is a state variable of friction coefficient, which has a sliding-history independence. It is shown that the subsequent friction coefficient during a sequential sliding test can be expressed in terms of two state variables, ω and normal pressure. Finally, a polynomial expression for the evolution of friction coefficient is introduced in contrast to a constant value typical for the Amontons-Coulomb laws.