Effect of thermal history on the superplastic expansion of argon-filled pores in titanium: Part II modeling of kinetics

Abstract

Metals can be foamed to ca. 50% porosity in the solid state by the creation of gas-pressurized pores within the metal, followed by expansion of these pores at elevated temperatures. We present here models for the time-dependence of pore expansion during solid-state foaming performed under isothermal conditions, where the metal deforms by creep, and under thermal cycling conditions, where superplasticity is an additional deformation mechanism. First, a continuum-mechanics model based on the creep expansion of a pressure vessel provides good quantitative agreement with experimental data of isothermal foaming of titanium, and qualitative trends for the case of foaming under thermal cycling conditions. Second, an axisymmetric finite-element model provides predictions very similar to those of the pressure-vessel model, indicating that stress-field overlap is unimportant when pores are equidistant. Numerical modeling shows that stress-field overlap increases foaming rate when pores are clustered, and also cause anisotropic pore growth. However, a bimodal distribution of pore size was found to have little effect on pore growth kinetics.