A robust approach to model densification and crack formation in powder compaction processes

Abstract

This paper deals with the question of how to efficiently integrate a constitutive model that describes the densification of powders and the potential formation of cracks in Powder Metallurgy (P/M) cold compaction processes. The analyzed model is a large strain, elastoplastic model of the Drucker–Prager/Cap type, refined to cover also the prediction of crack formation, and featuring non-conventional elements such as a density-dependent Von Mises yield surface; a parabolic plastic potential function for the Drucker–Prager envelope; and a softening law whose softening modulus is dependent on the level of densification. The employed integration procedure is a non-conventional hybrid or IMPLicit–EXplicit (IMPL-EX) scheme, whose essence is to solve explicitly for some variables and implicitly for others, with the peculiarity of the ‘explicit’ variables being but extrapolated values of the same quantities computed, at previous time steps, by means of a fully implicit scheme. The return-mapping equations stemming from this implicit scheme are solved using an unconditionally convergent, fractional step method-based iterative procedure. The performance of the IMPL-EX integration algorithm is critically assessed in two different situations: the densification of a cylindrical specimen, and the fracture process in a diametral compression test. Results obtained show conclusively that the proposed hybrid integration strategy offers an efficient solution to the trade-off between robustness and computational time requirements.