A two-scale model for sintering damage in powder compact containing inert inclusions

This paper presents a numerical model for the early stage sintering of powder compact taking into account of the separation of contact necks. The neck separation or damage may occur in a powder matrix which contains large second phase inclusions. A damage parameter is introduced and a variational principle for the sintering deformation of the matrix is developed using the damage parameter as a control variable. The sintering problem is therefore modelled by the minimisation of a quadratic functional under the control of a Kuhn–Tucker condition of damage growth. A sequential quadratic programming algorithm is used to solve the minimisation problem, giving temporal evolution of the stresses, strains, damage parameter and deformation of the matrix material. A range of numerical examples are given and the results are qualitatively compared with experimental observations made by Sudre et al. [Sudre, O., Bao, G., Fan, B., Lange, F.F., Evans, A.G., 1992. Effects of inclusions on densification. II: Numerical model. Journal of the American Ceramic Society 75, 525–531] and by Lange [Lange, F.F., 1989. Densification of powder ring constrained by dense cylindrical core. Acta Metallurgica 37, 697–704].