Irreversible deformation with subsequent unloading of a spherical viscoelastoplastic layer

Abstract

Analytic solutions are obtained for a sequence of one-dimensional quasistatic problems describing viscoelastic deformation processes in the material of a hollow ball and the plastic flow nucleation and evolution processes occurring in the ball as the pressure on the outer boundary increases. The unloading process under slow removal of the loading pressure is considered as well. The stress fields and the elastic and plastic strain fields in the spherical layer material, the law of motion of the elastoplastic boundary, and the residual stress level and distribution are computed. It is assumed that at the stage preceding the plastic flow the material obeys the viscoelastic Voigt model and the loading surface is determined by the von Mises plastic flow condition.

On Finite Strains in Continua with Complex Rheology

“…The second problem is constitution of irreversible strain source. The mathematical model which was proposed in [5,8,12] is used throughout the paper. The problem of a spherically symmetric compression of the ball with micropore in the center is considered.…”

“…wherein w ij is the angular rate tensor and z ij (e ij , ε ij ) is the nonlinear part of the rotation tensor r ij (see in full in [5]). Thus, the components of the Almansi total strains d ij in terms of its parts e ij and p ij taking account of equations (1) and (3) are presented as follows…”

“…In this case, the effect of adaptability to periodic loading on the cycle "loading and unloading" was shown in [6]. Since classic work E. Lee [7], lots of plastic flow models with large reversible and irreversible deformations were developed [4][5][6][7][8][9][10][11][12][13][14]. Lot of them use a Lagrangian description [13,14].…”

“…Well known experiments [3,4] when the long-term strength of metal products after their treatment under hydrostatic pressure is significantly increased. Attempts to simulate such process of the micropores "healing" in the metal have been made repeatedly [4][5][6][7][8][9][10][11][12][13][14]. In [5] such problems are considered due to the model of large elastic-plastic deformation.…”

“…Attempts to simulate such process of the micropores "healing" in the metal have been made repeatedly [4][5][6][7][8][9][10][11][12][13][14]. In [5] such problems are considered due to the model of large elastic-plastic deformation. In this case, the effect of adaptability to periodic loading on the cycle "loading and unloading" was shown in [6].…”