A large deformation analysis of crystalline elastic-viscoplastic materials

• Published in: Nuclear engineering and design 1974, Vol.29 (3), p.360-369
• Main Authors: Bhandari, D.R., Oden, J.T.
• Format: Article
• Language: English
• ISSN: 0029-5493; 1872-759X
• DOI: 10.1016/0029-5493(75)90046-1

The thermodynamics of crystalline elastic-viscoplastic materials developed earlier by the authors is extended to account for finite strains. The present theory utilizes the basic physical concepts derived from the theory of dislocations in crystals and the thermodynamics of continua with internal state variables. A crystalline simple solid is considered to be a homogeneous elastic-plastic continuum containing dislocations which constitute the intrinsic, internal mechanism of plasticity phenomena. The appropriate internal state variables and the basic constitutive relations for the description of the elastic-viscoplastic behavior are deduced from the consideration of dislocation dynamics. The theory proposed in the present paper is based on the assumption that both elastic and inelastic deformations take place at every stage of loading and unloading. This assumption has a definite physical basis and is the underlying consideration in the field of dislocation dynamics. Unlike other theories, the present one does not require the specification of a yield criterion or the prior determination of whether the material is loading or unloading. It can be shown that under appropriate assumptions on the constitutive laws the present theory reduces to the case of classical thermoelasticity or thermoplasticity. The general finite-element formulation of an initial boundary value problem is briefly presented. A specific example is carried out in detail which involves the solution of equations governing the coupled thermomechanical response of titanium. To demonstrate the effectiveness of the present formulation, a scheme for calculating the deformations, the stresses and temperature distribution is developed and applied to a three-dimensional structure subjected to high temperature, surface heat flux, volume heat supply as well as mechanical loading. The theory and the analysis should be beneficial in the study of the behavior of reactor materials at high temperatures.