Constitutive relations of the endochronic theory of thermoplasticity for high-temperature composites under plane stress state

Abstract

A variant of the constitutive relations of the endochronic theory of thermoplasticity for high-temperature composites is proposed. The relations for the plane stress state are considered. Examples of the use of the proposed relations in which the material behavior under complex loading is analyzed are given. The dependence of the elastic modulus of the material on the temperature of pre-heating is shown.

Application of the finite element method to the endochronic theory of thermoplasticity for isotropic materials in a plane stress state

“…where s ij are components of the stress deviator, e ij are components of the strain deviator, σ o is average stress, ε o is average strain, a = a(T ) is material parameter of the model, µ = E/[2(1+ν)], K = E/(1 − 2ν) are shear modulus and elastic bulk modulus, respectively, E = E(T ), ν = const 2 are normal elastic modulus and Poisson's ratio, α (T) is coefficient of linear thermal expansion; z is intrinsic time, defined as dz = dξ/f (ξ), f (ξ) ≥ 1, f (0) = 1, f (ξ) is temperature-dependent hardening function, dξ is the increment of intrinsic time measure are defined as [6]…”

“…In this study, a variant of the endochronic theory of plasticity for isotropic materials under non-isothermal loading conditions and a numerical algorithm based on finite element analysis are proposed. A characteristic feature of this theory is the use of intrinsic time to account for irreversible deformation processes [4][5][6]. The advantage of the endochronic theory of thermoplasticity is the relative simplicity of the governing equations and the ability to describe such features of plastic behavior as linear and nonlinear hardening, inelastic unloading, hysteresis, etc.…”