Thermal stress analysis of sintering using a moving grid

Abstract

AbstractA moving finite element method that calculates the transient temperature distribution, the density distribution and the stress distribution during the sintering cycle has been developed. Coupled two‐dimensional axisymmetric energy, continuity and stress equilibrium equations along with a constraint, specifying the direction of the initial material velocity, are solved in a Lagrangian co‐ordinate system. The nodes move at the same speed as the material and therefore the convective terms in the differential equations drop out. At every time step, the energy equation is solved, and the computed temperatures are then used to find the densification rate. In two‐dimensional problems, the continuity equation is not sufficient to calculate the two components of material velocity. Here, it is assumed that the diffusion caused by the density gradient is the driving force. This implies that the velocity vector of the material is perpendicular to the lines of constant density. Therefore, the combination of the diffusion and continuity equations will generate the initial sintering strains. The elastic stress equilibrium equations are then solved using the thermal and initial sintering strains as the driving forces. As a result, the final shape of the material and the stresses are determined.