Numerical Simulations of Thermo-Viscoplastic Flow Processes under Cyclic Dynamic Loadings

Abstract

Abstract. The main objective of the paper is the description of the behaviour and fatigue damage of inelastic solids in plastic flow processes under dynamic cyclic loadings.A general constitutive model of elasto-viscoplastic damaged polycrystalline solids is developed within the thermodynamic framework of the rate type covariance structure with a finite set of the internal state variables. A set of the internal state variables is assumed and interpreted such that the theory developed takes account of the effects as follows: (i) plastic nonnormality; (ii) plastic strain induced anisotropy (kinematic hardening); (iii) softening generated by microdamage mechanisms; (iv) thermomechanical coupling (thermal plastic softening and thermal expansion); (v) rate sensitivity.To describe suitably the time and temperature dependent effects observed experimentally and the accumulation of the plastic deformation and damage during dynamic cyclic loading process the kinetics of microdamage and the kinematic hardening law have been modified. The relaxation time is used as a regularization parameter. The viscoplastic regularization procedure assures the stable integration algorithm by using the finite difference method. Particular attention is focused on the well-posedness of the evolution problem (the initial-boundary value problem) as well as on its numerical solutions. Convergence, consistency, and stability of the discretised problem are discussed. The Lax-Richtmyer equivalence theorem is formulated and conditions under which this theory is valid are examined. Utilizing the finite difference method for regularized elasto-viscoplastic model, the numerical investigation of the three-dimensional dynamic adiabatic deformation in a particular body under cyclic loading condition is presented. Particular examples have been considered, namely a dynamic, adiabatic and isothermal, cyclic loading processes for a smooth cylindrical tensile bar. The problem is assumed as axisymmetrical. The accumulation of damage and equivalent plastic deformation on each considered cycle has been obtained. It has been found that this accumulation of microdamage distinctly depends on the wave shape of the assumed loading cycle.

Elasto‐plastic finite element analysis of shells with damage due to microvoids

“…The form of the yield condition given by Equation (55), can be easily derived from the von Mises function and the definition of normal stresses at the top and the bottom surfaces of the shell, as is shown in Reference [89]. Instead we use in this work the yield criterion for porous ductile metals as originally proposed by Gurson [65,66], and later modified by Perzyna [80] and Dornowski and Perzyna [93]. Although it is of a form similar to von Mises equation, it accounts for the isotropic damage effects through the dependence of the first invariant of stress and the evolution of porosity.…”

“…Although it is of a form similar to von Mises equation, it accounts for the isotropic damage effects through the dependence of the first invariant of stress and the evolution of porosity. The plastic potential function defined by Dornowski and Perzyna [93] can be written as…”

Analysis of various effects in dynamic cyclic fatigue damage

“…[16], [17], [18]. In this theory, experimentally observed time-and temperature-dependent effects as well as accumulation of plastic deformation and damage during dynamic cyclic loading have been suitably described.…”

“…Particular attention is focused in the analysis on the influence of (i) the shape of loading waves; (ii) softening generated by thermomechanical coupling; (iii) softening by microdamage mechanism; (iv) plastic strain-induced anisotropy as described by kinematic hardening; (v) plastic spin; (vi) strain-rate sensitivity; (vii) covariant terms. To describe these effects, a constitutive model of thermo-elasto-viscoplastic damaged polycrystalline solids developed in [22] was modified in [16], [17], [18]. The main modification concerns the kinetic of microdamage and the kinematic hardening law.…”

“…A general constitutive model of an elasto-viscoplastic damaged polycrystalline solid developed within the thermodynamic framework of the rate-type covariance structure with a finite set of internal state variables is assumed, cf. [18]. The internal state variables are postulated and interpreted such that the theory developed here takes account of (i) plastic nonnormality; (ii) plastic strain-induced anisotropy; (iii) microdamage softening; (iv) thermal-plastic softening and thermal expansion; (v) rate sensitivity; (vi) plastic spin.…”