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Modeling of distortion after densification during liquid-phase sintering

“…The density also contributes to the speed of the slumping. Moreover, the density variation with time was observed by the formation of pores, even after full densification is reached, as reported by Wu et al [2,3] This effect makes the compact become larger and the mass is not conserved, in contrast to the current model. Finally, it is assumed that the surface tension will vary with time, since it is most likely to be affected by liquid formation and solid settling in the sample.…”

“…4. The density is constant and it has reached theoretical full density prior to distortion, as observed by Wu et al [2,3] 5. The model is axisymmetric (field quantities are independent of and u ϭ 0).…”

“…Continuity: [1] Momentum conservation: [2] In these equations, u is the velocity vector in the r and z coordinate directions, t is the time, is the density assuming that the density of the semisolid is constant and incompressible, is the compact viscosity, p is the static pressure, and g is the acceleration due to the gravity, which is represented as a vector.…”

“…The mesh was also created to take into account the anticipated total deformation usually observed in experiments. [2,3] Since these spines needed to be normal to the free surface, the meshing of a square section caused a difficulty because the square element normally used will be distorted tremendously in the far corner if the spines are kept on the total surface. To overcome this difficulty, a square section of the mesh was kept fixed in time and space.…”

“…A critical observation in recent years has been the recognition that LPS systems largely distort after densification. [2,3] Accordingly, it is appropriate to treat the problem as a viscous flow process involving the semisolid mixture of solid grains in a liquid phase. In this article, a finite-element approach is used to solve continuity and momentum equations for predicting distortion during LPS for low dihedral angle materials and after full densification.…”