New generalised plasticity equation for compressible powder metallurgy materials: a new parallel RK-Butcher method

Abstract

In this paper, we propose a highly non-linear mathematical expression for characterising the flow behaviour of partially dense P/M materials during the case of simple upsetting – compression test, taking functional dependence of strain hardening index on a matrix strain and yield matrix (of partially dense material) on a mixed combination of matrix strain and strain sensitivity into account. Equivalent flow stress of matrix is considered to be a function of relative density, matrix strain and strain rate sensitivity parameters. A new parallel Runge-Kutta-fifth order algorithm with adaptive step-size control has been proposed for numerical integration of the resultant mathematical expression to compute the value of yield stress of partially dense P/M porous materials. Furthermore, a modest effort has been made to bring out the effectiveness of the adaptive step-size control. Numerical results show that the proposed parallel Runge-Kutta-fifth order algorithm with the adaptive step-size control increases the computational speed by more than eight times in an interval when solving the highly non-linear prevailing equation in comparison with the above algorithm with the fixed constant step-size.