A further report on finite element analysis of sintering deformation using densification data—Error estimation and constrained sintering

In a previous paper, Kiani et al. [Kiani, S., Pan, J., Yeomans, J. A., Barriere, M. B. and Blanchart, P., Finite element analysis of sintering deformation using densification data instead of a constitutive law. J. Eur. Ceram. Soc., 2007, 27, 2377–2383] proposed an empirical numerical method to calculate the sintering deformation of ceramic powder compacts without knowing the viscosities and sintering potential. The method was validated by free sintering experiments using specimens with non-uniform initial densities. Two new developments are reported in this paper: (a) a method of error estimation is developed which can be used to check if the empirical analysis is valid after the analysis; (b) a range of case studies are presented showing that the empirical solutions provide very good approximations to the solutions obtained using full constitutive laws not only for free sintering but also for highly constrained sintering of single- or multi-layered films.