The plastic flow of polycrystalline solids

Abstract

A polycrystalline solid is modelled as an ensemble of random irregular polyhedra filling the entire space occupied by the solid body, leaving no voids or flaws between them. Adjacent grains can slide with a relative velocity proportional to the local shear stress resolved in the plane common to the two sliding grains, provided it exceeds a threshold. The local forces associated to the continuous grain shape accommodation for preserving matter continuity are assumed much weaker. The model can be solved analytically and for overcritical conditions gives two regimes of deformation, plastic and superplastic. The plastic regime, from yield to fracture, is dealt with. Applications to nickel superalloys and stainless steels give impressive agreement with experiment. Most work of the last century relies on postulating pre--existent cracks and voids to explain plastic deformation and fracture. The present model gives much better results.

Figures (6)

• Figure 1: Functions $f_s$ and $g_s$. Lévy--Mises Eqs. (\ref{['E6']}) are exact when $f_s(2\theta_c)=g_s(2\theta_c)$.
• Figure 2: Discrete symbols represent experimental data for the stress--strain rate for the nickel superalloy Inconel X750 at room and lower temperatures Wolf. Solid lines are the predictions of Eq. (\ref{['E10']}) with the parameters of Table \ref{['table1']} and Fig. \ref{['Fig3']}.
• Figure 3: Graphical display of the constants in Table \ref{['table1']} showing their dependence on temperature.
• Figure 4: Tensile stress-strain behaviour of additively manufactured Inconel 718 bars after one hour heat treatment and ageing.
• Figure 5: Same as Fig. \ref{['Fig4']}, but previous to the ageing procedure.