Rainer Sievert

Strain gradient crystal plasticity : thermomechanical formulations and applications

Since the pioneering work of [3] (see [4] for a review), strain gradient plasticity has aroused increasing interest in the mechanics of materials community, leading to a large panel of non local plasticity models. However, comparisons between these models remain seldom [19], and he full thermomechanical framework is usually not provided. The attention is focused here on models incorporating modified or additional balance equations and therefore additional boundary conditions in order to solve practical boundary value problems. The reader is referred to [1] for models sticking to classical structure of the boundary value problem. The aim of the present work is to bring together and to some extent reconcile three main trends of strain gradient plasticity models applied to metal single crystals : the gradient of internal variable, second grade and Cosserat approaches. In particular, the thermodynamical setting for all three models will be described in a unified way, in order to make actual differences between theories really visible. For simplicity and clarity, the analysis is restricted to single slip and rate–independent constitutive equations. Extensions to the general viscoplastic multislip case are straightforward, based on multicriterion elastoviscoplasticity. Each model presentation follows the three following main steps :

Hyperelastic models for elastoplasticity with non-linear isotropic and kinematic hardening at large deformation

Abstract This work is concerned with the formulation of hyperelastic-thermodynamic-based models for associated elastoplasticity with non-linear isotropic and kinematic hardening valid for both large elastic and large plastic deformation. On this basis, one can then introduce explicitly the assumptions of (1), small incremental plastic deformation, and (2), small elastic strain, into the general model and obtain special cases whose behaviour corresponds to that of various classical hypoelastic formulations. In particular, these are obtained on the basis of two different thermodynamic formulations for kinematic hardening with respect to the intermediate configuration. The simplest of these, in which the plastic part of the free energy does not depend explicitly on the plastic deformation, leads for example to Jaumann-or Green-Naghdi-hypoelastic-type behaviour for linear kinematic hardening in simple shear. In particular, the former case is obtained in this context when the plastic spin is assumed constant and equal to zero, and the latter case when the plastic rotation is assumed constant and equal to the identity. Allowing the plastic part of the free energy to depend explicitly on the plastic deformation yields the second thermodynamic model for kinematic hardening considered in this work. Here, again in the special case of linear hardening, Oldroyd-like behaviour for the shear stress and back stress, but not for the normal stress, is obtained in simple shear.

Thermoelasticity of second-grade media

The method of virtual power and continuum thermodynamics are used to incorporate temperature and temperature gradients into the theory of second grade solids settled by [Germain, 1973] in the isothermal case. In a second part, it is shown that heterogeneous classical materials submitted to slowly-varying mean fields can be replaced by a homogeneous equivalent medium including higher order gradients of displacement and temperature. For that purpose, an asymptotic analysis of thermoelastic heterogeneous periodic materials is performed. The form of the derived effective properties are compared to the previous phenomenological framework.

High-temperature behaviour of IN 738 LC under isothermal and thermo-mechanical cyclic loading

Abstract The temperature dependence of the cyclic behavior of IN 738 LC was studied. Cyclic iso- and non-isothermal tests were performed with proportional and non-proportional tension/torsion strain paths. It was shown that maximum and minimum stress values measured in isothermal strain controlled tests correspond quite well with results of non-isothermal tests. Thermal-mechanical constitutive equations based on the viscoplastic Chaboche model were used to describe the non-isothermal stress-strain behavior.

Multi-Axial Thermo-Mechanical Fatigue of a Near-Gamma TiAl-Alloy

A material family to replace the current superalloys in aeronautical gas turbine engines is considered to be that of gamma Titanium Aluminide (-TiAl) alloys. Structural components in aeronautical gas turbine engines typically experience large variations in temperatures and multiaxial states of stress under non-isothermal conditions. The uniaxial, torsional and bi-axial thermo-mechanical fatigue (TMF) behaviour of this -TiAl alloy have been examined at 400 – 800oC with strain amplitudes from 0.15% to 0.7%. The tests were conducted at both in-phase (IP) and out-of-phase (OP). The effects of TMF on the microstructure were also investigated. For the same equivalent mechanical strain amplitude uniaxial IP tests showed significantly longer lifetimes than pure torsional TMF tests. The non-proportional multiaxial OP test showed the lowest lifetimes at the same equivalent mechanical strain amplitude compared to the other types of tests.

The Stress-Strain Behaviour of IN738LC under Thermomechanical Uni- and Multiaxial Fatigue Loading

High temperature components such as cooled or uncooled first stage turbine blades are subjected to triaxial stress fields, mainly induced by constrained thermal strain fields during service. The steepest temperature gradients and consequently the largest thermoinduced stresses are generated during start-up and shut-down phases of turbine operation.

Failure estimation of thermo-mechanically loaded hot parts in turbochargers

Components directly exposed to the exhaust-gas streams of combustion engines are increasingly thermo-mechanically loaded. A keystone for dimensioning is the calculated failure prediction. Within the FVV research project No. 916 (“Hot Parts”), a model for the calculated simulation of thermo-mechanical fatigue was developed for the cast iron material SiMo 4.05 in the division Mechanical Behaviour of Materials at the Federal Institute for Material Research and Testing (BAM). Using this model, the location and the time of the occurrence of first cracks in exhaust-gas turbocharger housings may be estimated in good approximation.