A fine mechanical analysis of a polycrystalline material subjected to large stresses must distinguish between intergranular and crystalline matter because they have different mechanical properties. Homogeneity was an illusion at the grain level. It was shown that a grain boundary under the action of a strong enough in-plane shear stress became unstable, buckling into periodic trenches or a corrugated profile. The former should always occur; the latter demands the existence of steps, intersecting hard particles or triple junctions. Strongly varying stress fields, spontaneously induced to preserve mechanical equilibrium at the grain scale, cause intergranular matter to begin to release and capture vacancies in alternate sectors. The subsequent active lattice diffusion near the buckled boundary causes adjacent crystallites to slide. The effect was translated into the macroscopic scale to derive a closed-form constitutive equation relating stress, strain rate, temperature, grain size, and grain boundary thickness, without undetermined parameters. The agreement with available experimental data on the superplastic deformation of alloys, over the whole range of strain rates and temperatures, was remarkable. Applications to Al-8090 SPF, Al-7475, and Ti-6Al-4V were shown. The degradation of superplastic properties at high strain rates or temperatures was explained.

Theory of Superplasticity in Polycrystalline Materials - Stress-Induced Structural Instabilities of Grain Boundaries. M.Lagos: Physical Review B, 2005, 71[22], 224117 (15pp)