Finite element analysis of sintering deformation using densification data instead of a constitutive law

Various forms of constitutive laws have been developed for use in the finite element analysis of sintering deformation. Some of these were based on micromechanical models and others were based on empirical fitting of experimental data. The mechanism-based constitutive laws differ from each other widely and it can be difficult to know which one to use. On the other hand, obtaining fitting functions for an empirical constitutive law is very time consuming. In this paper, an empirical finite element method is presented which does not require a constitutive law; rather the densification data (density as a function of time) is used to predict sintering deformation. The densification data can be obtained by sintering a relatively small number of samples of the powder or derived from the master sintering curve. Different sintering mechanisms and non-linearity pose no difficulty to the method. The method is, however, limited to pressureless sintering. To verify the densification-based finite element method, three case studies are presented. The numerical predictions were compared with experimental measurement for two different cases. It is shown that the accuracy of the prediction is well within the experimental uncertainties and comparable to previous finite element analyses using full constitutive laws.