Finite element analysis of time‐dependent inelastic deformation in the presence of transient thermal stresses

Abstract

A finite element formulation for the solution of time‐dependent inelastic deformation problems for metallic structures, in the presence of transient thermal stresses, is presented in this paper. A rate formulation of the equations is used and any of a number of recently proposed combined creep‐plasticity constitutive models with state variables can be adopted to describe material behaviour. The computer program developed can solve planar (plane strain and stress) and axisymmetric problems. Using one of the above‐mentioned constitutive models, numerical results are presented for several illustrative problems, and comparisons of results, using either the quasi‐steady or the unsteady diffusion equation for the determination of the temperature field, are carried out.

Stress Intensity Solutions of Thermally Induced Cracks in Combustor Liner Hot Spots Using Finite Element Analysis (FEA)

“…Morjaria and Mukherjee [40] were some of the first to model transient thermal stresses for inelastic boundary value problems.…”

A finite element analysis of metal‐forming problems with an elastic‐viscoplastic material model

“…The second stiffness matrix in equation (12), the geometric stiffness matrix [ k,], originates from the second term in equation ( 5 ) . This is a stress-dependent symmetric matrix which comes about as a consequence of including rotation effects in the stress rate equation (3).…”

“…A piecewise quadratic interpolation is used for vg on the die-material interface in order to determine the load correction matrix [ k,]. Integrals necessary to obtain terms in the various matrices and vectors in equation (12) are obtained numerically by Gaussian quadrature.…”

A flow formulation for rate equilibrium equations

“…The difference between the approaches used by these two groups of investigators is that the steady state formulations all use a weak form of the eqilation of equilibrium, while the transient formulations use incremental techniques which are essentially weak forms of rate equilibrium equations, e.g. see papers by S w e d l~w ,~~ Osias and S~e d l o w ,~~ McMeeking and Rice,34 Lee et u1.,37* 38 Morjaria and Mukherjee, 48 Nagtegaal and de J~n g~~ and Yamada and Hirakawa." Steady state solutions to metal forming problems have been obtained by conducting transient analyses until steady conditions are reached.…”