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.

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The objective of the paper is the analysis of various effects in fatigue damage in plastic flow of solids under dynamic cyclic loading. Attention is focused on the investigation of the following effects: (i) influence of the shape of the loading pulse; (ii) softening generated by thermomechanical coupling; (iii) softening generated by microdamage; (iv) plastic strain-induced anisotropy caused by kinematic hardening; (v) plastic spin; (vi) strain-rate sensitivity; (vii) covariant terms.Experimental motivations are given. Based on observations on cyclic fatigue damage in metals at high temperatures we can suggest that intrinsic microdamage processes very much depend on the strain-rate effects as well as on the pulse-shape effects. A microdamage process is treated as a sequence of nucleation, growth and coalescence of microcracks. Microdamage kinetics interacts with thermal and load changes to make the failure of a solid a highly ratetemperature-and history-dependent, nonlinear process. 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. Kinetics of the microdamage and the kinematic hardening law are modified in order to describe suitably the time-and temperature-dependent effects. Relaxation time is used as a regularization parameter. Rate-independent elastic-plastic response is obtained when the relaxation time tends to zero.Viscoplastic regularization procedure assures a stable integration algorithm by using the finite difference method. Attention is focused on the well-posedness of the evolution problem (the initial-boundary value problem) as well as on its numerical solutions. The Lax-Richtmyer equivalence theorem is used, and conditions under which this theory is valid are examined. The identification procedure is developed. Utilizing the finite difference method for a regularized elasto-viscoplastic model, a numerical investigation of a dynamic adiabatic deformation under cyclic loading condition is presented. Particular examples are: dynamic, adiabatic and isothermal cyclic loading processes for a thin steel plate with a rectangular hole located in the center. Two regions undergoing significant deformations and a temperature rise are determined. Their evolution until the occurrence of a final fracture simulated together with the accumulation of damage and equivalent plastic deformation at each cycle. It is found that this accumulation depends on the pulse shape of the assumed loading cycle. The nucleation of the macrocrack is examined and the propagation of the macrocrack during the cyclic dynamic process is described. The influen...

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