Rheological behavior of Al-Cu alloys during solidification constitutive modeling, experimental identification, and numerical study

Abstract

The rheological behavior of a solidifying alloy is modeled by considering the deforming material as a viscoplastic porous medium saturated with liquid. Since the solid grains in the mush do not form a fully cohesive skeleton, an internal variable that represents the partial cohesion of this porous material is introduced. The model parameters are identified using shear and compressive stress states under isothermal conditions on an Al-Cu model alloy. The model is partially validated with nonisothermal conditions and we complete this study with tensile conditions. Such conditions, when applied on the mush, may lead to severe defects in many casting processes. The model has been implemented into a commercial finite-element code to simulate a tensile test. Comparison with experimental data shows that the model is able to reproduce the main features of a solidifying alloy under tension, although fracture is not directly addressed here. We show that two critical solid fractions must be introduced in the model to account for the rheology: the coherency solid fraction at which the mush acquires significant strength and the coalescence solid fraction at which solid grains start to form solid bridges.

Simulation of Semi-Solid Material Mechanical Behavior Using a Combined Discrete/Finite Element Method

“…This simplified constitutive description has been used previously for examining the mechanical behavior of Al-Cu alloys. [5,8,41,42] The isotropic elastic modulus E = 10 GPa and isotropic Poisson coefficient m s = 0.30 are taken from Reference 8. As no hardening is observed in the experimental results of the Al-Cu alloy at high temperature, [41,42] the flow stress behavior of each grain beyond the elastic limit is assumed to be perfectly plastic and based on the following Norton-Hoff law:…”

“…First, stress-strain curves obtained from a series of tensile deformation simulations were generated for a given g s , strain rate, and different values of C and K. Second, these stress-strain curves were compared with semisolid tensile test experimental results. [8] The values of C and K giving the best fit were determined and then used for all other simulation results. More details on this fitting procedure are provided in Section III.…”

“…[8][9][10][11] In these works, a representative volume element (RVE) is assumed to contain a mixture of solid and liquid with local volume fractions g s and g l , respectively, interacting through the averaged conservation equations. [12] Unfortunately, such approaches are unable to describe any strain inhomogeneity at the grain level, particularly at grain boundaries where hot tears form.…”

“…[8,10] The mechanical behavior of the solid grains is modeled using a simple viscoplastic law, while the intergranular liquid has been replaced by connector elements. First, the methodology for generating the granular grain structure based on a solidification model is briefly described.…”

“…[32] Third, the deformation results from the FE/DEM simulation are discussed and validated against experimental data from the literature. [8,10] II. MODEL DEVELOPMENT…”