Dynamic buckling of thin thermoviscoplastic cylindrical shell under radial impulsive loading

Abstract

The dynamic plastic buckling of a homogeneous and isotropic thin thermoviscoplastic cylindrical shell loaded radially is studied analytically by analyzing the stability of its stressed/deformed configuration under superimposed infinitesimal perturbations. The wave number of the perturbation that maximizes its initial growth rate is assumed to determine the buckling mode. Cubic algebraic equations are obtained for both the maximum initial growth rate of perturbation and the corresponding wave number. The buckled shape of a cylindrical shell is found to match well with that observed experimentally. The sensitivity of the buckled shape to the impact velocity, the hardening modulus, and the material viscosity has been delineated. For axially restrained shells, it is found that for materials exhibiting strain rate hardening only the maximum initial growth rate of the perturbation and the corresponding wave number vary as ( σ ¯ 0 / ρ β ) 1 / 3 h - 2 / 3 and ( ρ / σ ¯ 0 ) 1 / 6 R β - 1 / 3 h - 2 / 3 , respectively. For axially unrestrained cylindrical shells made of strain hardening only materials, the maximum initial growth rate of a perturbation and the corresponding wave number vary as ( σ ¯ 0 / h ) ( ρ E ) - 1 / 2 and ( R / h ( σ ¯ 0 / E ) ) 1 / 2 , respectively. Here σ ¯ 0 is the mean value of the generalized stress, ρ the mass density, β the material viscosity, h the shell thickness, and R the mean radius of the shell.