Analytic study of the onset of plastic instabilities during plane tension and compression tests on metallic plates

•We model the onset of plastic instabilities in plane tension and compression tests.•We carry out a linear stability analysis.•We consider symmetric and antisymmetric periodic modes (λ: wavelength).•The material is a metal satisfying Von Mises criterion and normality flow rule.•We propose an approximate analytic formulation of the growth-rates, for λ ≥ thickness.

In this article, we propose an approximate analytic formulation of the growth-rate of plastic instabilities (symmetric and antisymmetric modes with respect to the median plane of the plate) during plane tension or compression tests on metals supposed to satisfy the Von Mises plasticity criterion, valid for any elastoviscoplastic constitutive law, and long and medium wavelengths λ (in comparison with thickness e) along the loading direction (typically e ≤ λ, and even e/3 ≤ λ in the absence of viscous effects). This work generalizes important published results. For static tests, or dynamic ones in the field of long wavelengths, this formulation retrieves the formulae proposed by Fressengeas and Molinari (Instability and bifurcation in the plane tension test, 1992, Archives of Mechanics44 (1), 93; Fragmentation of rapidly stretching sheets, 1994, European Journal of Mechanics A/Solids, 13 (2), 251) for the development of plastic necking instabilities during plane tension tests on rigid viscoplastic materials obeying Norton's constitutive law. In the absence of viscosity, for static tests, it retrieves the bifurcation stress proposed by Hill, Hutchinson (Bifurcation phenomena in the plane tension test, 1975, Journal of the Mechanics and Physics of Solids23, 239) and Young (Bifurcation phenomena in the plane compression test, 1976, Journal of the Mechanics and Physics of Solids24, 77).