Effect of extensional viscosity and wall quenching on modeling of mold fillings

Abstract

A combined finite element and finite difference approach has been developed to include the capability to model fluid and thermal transport for the filling of a die cavity by a fluid that has differing sensitivities to extensional and shear deformation rates. This is referred to here as a dual viscosity fluid. For the case of mildly convergent or divergent quasi two‐dimensional flows, a viscosity model is described that has such a dual‐viscosity character and in which shear and extension rate sensitivities are nearly separated. Filling simulation results can be generated rapidly in a modest computational environment. The range of cavities and molding materials that may be modeled realistically is widened by the inclusion of a dual viscosity model. The effect of wall quenching (freezing) increased with decreasing filling rate, while the effect of dual viscosity increased with increasing filling rate.

Further Investigation of the Effect of Elongational Viscosity on Entrance Flow

“…Since the third invariant of the strain-rate tensor is zero for a simple shear, but is (3/4 × elongation rate) for an axisymmetric elongation, equations depending upon the second (e II ), and third (e III ) invariants of the strain rate tensor have been used for such a composite viscosity model [19][20][21]. Since the third invariant of the strain-rate tensor is zero for a simple shear, but is (3/4 × elongation rate) for an axisymmetric elongation, equations depending upon the second (e II ), and third (e III ) invariants of the strain rate tensor have been used for such a composite viscosity model [19][20][21].…”

“…However, this approach cannot be extended to a planar extension or three-dimensional extension because in a planar extension e III = 0. To include the effect of elongational viscosity in a mold filling simulation, Moller et al [19] used an equation for viscosity which depends upon an eigenvalue of the strain-rate tensor in the plane of a thin shell finite element. Again, this approach cannot be extended to a three-dimensional flow.…”

“…To circumvent the complexities of a viscoelastic flow simulation, several authors have attempted to develop a composite viscosity model combining the shear and elongational viscosities in the generalized Newtonian formulation. Since the third invariant of the strain-rate tensor is zero for a simple shear, but is (3/4 × elongation rate) for an axisymmetric elongation, equations depending upon the second (e II ), and third (e III ) invariants of the strain rate tensor have been used for such a composite viscosity model [19][20][21]. However, this approach cannot be extended to a planar extension or three-dimensional extension because in a planar extension e III = 0.…”