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

Authors: R. Ponalagusamy, K. Ponnammal

Addresses: Department of Mathematics, National Institute of Technology, Tiruchirappalli – 620 015, India. ' Department of Mathematics and Computer Science, Government Arts College, Tiruchirappalli – 620 022, India

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.

Keywords: powder metallurgy materials; parallel Runge-Kutta-fifth order algorithm; adaptive control; step-size control; plasticity equations; flow behaviour; flow stress.

DOI: 10.1504/IJNM.2010.034799

International Journal of Nanomanufacturing, 2010 Vol.6 No.1/2/3/4, pp.395 - 408

Published online: 22 Aug 2010 *

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