Fundamentals of viscoelastoplasticity and hardening theory revisited

Abstract

Thermodynamic and statistical methods for setting up the constitutive equations describing the viscoelastoplastic deformation and hardening of materials are proposed. The thermodynamic method is based on the law of conservation of energy, the equations of entropy balance and entropy production in the presence of self-balanced internal microstresses characterized by conjugate hardening parameters. The general constitutive equations include the relationships between the thermodynamic flows and forces, which follow from nonnegative entropy production and satisfy the generalized Onsager's principle, and the thermoelastic relations and the expression for entropy, which follow from the law of conservation of energy. Specific constitutive equations are derived by representing the dissipation rate as a sum of two terms responsible for kinematic and isotropic hardening and approximated by power and hyperbolic-sinus functions. The constitutive equations describing viscoelastoplastic deformation and hardening are derived based on stochastic microstructural concepts and on the linear thermoelasticity model and nonlinear Maxwell model for the spherical and deviatoric components of microstresses and microstrains, respectively. The problem of determining the effective properties and stress-strain state of a three-component material found using the Voigt-Reuss scheme leads to constitutive equations similar in form to those produced by the thermodynamic method Introduction. For theoretical descriptions of the viscoelastoplastic behavior of structural members under mechanical and thermal loads to be reliable, it is first necessary to set up appropriate constitutive equations or to establish relationships between the dynamic and kinematic parameters, taking into account the physical phenomena accompanying viscoelastoplastic deformation. Such phenomena include conversion of work into heat and strain energy, hardening, Bauschinger effect, aftereffect, relaxation, and dependence of hardening on inelastic strain rate. One of the most significant criteria that a complex model is adequate and correct is its consistency with the simpler models generalized by it. In our case, this means that the constitutive equations describing elastic deformation, viscous flow, and plastic deformation should follow, as partial or limiting cases, from the constitutive equations of viscoelastoplasticity.Recently, the theory and problems of viscoelastoplasticity have widely used the Bodner-Partom model [7,8,[12][13][14][15][20][21][22][23], which, along with stresses and strains, uses internal variables describing isotropic and kinematic hardening for which evolutionary equations are formulated. In this model, strains have elastic and inelastic components, and inelastic strain rates are specified as a negative exponential function of the ratio of the sum of hardening parameters to stresses. A serious shortcoming of this model is inconsistency-in the specific case of zero hardening parameters, the law of viscous flow does not follow from the constitutive equ...

Calculating creep strains in linear viscoelastic materials under nonstationary uniaxial loading

“…Such theories are usually validated by comparing theoretical and experimental relaxation and creep curves for nonstationary loading. Problems of relaxation and nonstationary creep are of practical interest as describing the real service conditions of many materials and structural members.To describe the relationship among strains, stresses, and time, widespread use is made of hereditary creep theories that take the loading history into account [7,11,12,[22][23][24]. The chief difficulties faced when using a hereditary theory are to choose a kernel for the integral equation, to find the associated resolvent, and to determine the parameters of the kernel.…”

“…To describe the relationship among strains, stresses, and time, widespread use is made of hereditary creep theories that take the loading history into account [7,11,12,[22][23][24]. The chief difficulties faced when using a hereditary theory are to choose a kernel for the integral equation, to find the associated resolvent, and to determine the parameters of the kernel.…”

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