Viscoplasticity: A thermodynamic formulation

A thermodynamic foundation using the concept of internal state variables is given for a general theory of viscoplasticity, as it applies to initially isotropic materials. Three fundamental internal state variables are admitted. They are: a tensor valued back stress for kinematic effects, and the scalar valued drag and yield strengths for isotropic effects. All three are considered to phenomenologically evolve according to competitive processes between strain hardening, strain induced dynamic recovery, and time induced static recovery. Within this phenomenological framework, a thermodynamically admissible set of evolution equations is put forth. This theory allows each of the three fundamental internal variables to be composed as a sum of independently evolving constituents

Finite strain viscoplasticity with nonlinear kinematic hardening: phenomenological modeling and time integration

This article deals with a viscoplastic material model of overstress type. The model is based on a multiplicative decomposition of the deformation gradient into elastic and inelastic part. An additional multiplicative decomposition of inelastic part is used to describe a nonlinear kinematic hardening of Armstrong-Frederick type. Two implicit time-stepping methods are adopted for numerical integration of evolution equations, such that the plastic incompressibility constraint is exactly satisfied. The first method is based on the tensor exponential. The second method is a modified Euler-Backward method. Special numerical tests show that both approaches yield similar results even for finite inelastic increments. The basic features of the material response, predicted by the material model, are illustrated with a series of numerical simulations.Comment: 29 pages, 7 figure

On the thermodynamics of stress rate in the evolution of back stress in viscoplasticity

A thermodynamic foundation using the concept of internal state variables is presented for the kinematic description of a viscoplastic material. Three different evolution equations for the back stress are considered. The first is that of classical, nonlinear, kinematic hardening. The other two include a contribution that is linear in stress rate. Choosing an appropriate change in variables can remove this stress rate dependence. As a result, one of these two models is shown to be equivalent to the classical, kinematic hardening model; while the other is a new model, one which seems to have favorable characteristics for representing ratchetting behavior. All three models are thermodynamically admissible

A low cycle fatigue model for low carbon manganese steel including the effect of dynamic strain aging

International audienceCarbon manganese steel A48 (French standards) is used in steam generator pipes of the nuclear power plant where it is subjected to the cyclic thermal load. The Dynamic Strain Aging (DSA) influences the mechanical behavior of the steel in low cycle fatigue (LCF) at favourable temperature and strain rate. The peak stress of A48 steel experiences hardening–softening–hardening (HSH) evolution at 200°C and 0.4% s-1 strain rate in fatigue loading. In this study, isotropic and kinematic hardening rules with DSA effect have been modified. The HSH evolution of cyclic stress associated with cumulative plastic deformation has also been estimated

Cyclic calculations and life estimation in thermomechanical fatigue

International audienceThe present paper describes a new numerical procedure devoted to the calculation of aeronautic engines and to the fatigue life assessment evaluation. The original aspects consists (1) in a new method used to determine the mechanical steady state of a structure under thermomechanical loading, (2) in a short review of an advanced fatigue model which can reproduce the Woehler curve, including the influence of the mean stress

Thermodynamics of Local State: Overall Aspects and Micromechanics Based Constitutive Relations

The thermodynamics of irreversible processes, based on a set of internal state variables, is revisited, paying attention on two complementary aspects:- The Generalized Standard Models are shown to introduce too stiff constraints, both for kinematic hardening and for damage modellings. A slightly less restrictive approach is then considered, based on several independent  potentials and several independent multipliers;- The micro-macro approach of elastoplasticity is formulated through the Transformation Field Analysis of Dvorak and the use of a correction method. Moreover, based on previous works of Suquet and Nguyen, the approach is generalized with energy considerations, incorporating continuous fields of eigenstrains

A plain linear rule for fatigue analysis under natural loading considering the sequence effect

Fatigue under variable amplitude loading is currently assessed with the Palmgren-Miner rule in structural standards, ignoring the order of loading, which would require non-linear or mixed rules, especially for the random loading sequences applied to certain structures. Therefore, the goal is to develop a practical and simple correction factor ensuring the linear summation of damage is conservative, so as to take the sequence effect into account in random loading from natural sources. The theoretical consistency of this approach is demonstrated and a case study is developed to test the feasibility of the new rule and its simplicity

Low cycle fatigue life prediction in shot-peened components of different geometries—part I: residual stress relaxation

In this study, the residual stress relaxation behaviour occurring during low-cycle fatigue in shot-peened specimens with either a flat or a notched geometry has been studied. A representative low-pressure steam turbine material, FV448, was used. The residual stress and strain hardening profiles caused by shot peening were measured experimentally and were then incorporated into a finite element model. By allowing for both effects of shot peening, the residual stress relaxation behaviour was successfully simulated using this model and correlated well with the experimental data. Although more modelling work may be required to simulate the interaction between shot peening effects and external loads in a range of notched geometries, the model predictions are consistent with the specimens tested in the current study. The novelty of this study lies in the development of such a modelling approach which can be used to effectively simulate the complex interaction between shot peening effects and external loads in notched regions. Compared with the un-notched geometry, the notched geometry was found to be more effective in retaining the improvement in fatigue life resulting from shot peening, by restricting the compressive residual stress relaxation during fatigue loading

Les dimensions culturelles, discursives et territoriales de production et de marchandisation d’un mythe moderne

La globalisation culturelle du sport est‑elle compatible avec le caractère mythique de certains clubs professionnels de football ? Cet article vise à interroger les dimensions culturelles, discursives et territoriales de production et de marchandisation du mythe moderne que constituerait le FC Barcelone (Barça), qui dit être plus qu’un club (Més que un club). S’interrogeant sur l’interaction entre mythe et globalisation sportive, on fait l’hypothèse que le système de mythification du Barça lui permet de transcender l’apparente antinomie entre son nationalisme revendiqué et sa globalisation recherchée. L’examen des éléments sportifs, organisationnels et identitaires de construction de ce mythe moderne combiné à l’analyse des modalités de son exploitation marchande et du rôle catalyseur de la culture barcelonista permet d’éprouver et de valider l’hypothèse initiale.Is the cultural globalisation of sport compatible with the mythical character of some professional football clubs? This article discusses the cultural, discursive and territorial dimensions of the production and commodification of the modern myth that FC Barcelona (Barça) is supposed to represent. Indeed, Barça claims to be « more than a club » (Més que un club). Reflecting on the interaction between myth and the globalisation of sport, our hypothesis is that the system of mythification of Barça allows the club to transcend the apparent antinomy between its proclaimed nationalism and its desired globalisation. The study of the sports, organisational and identity aspects that have helped to build this modern myth combined with the analysis of its marketing methods and the catalysing role played by the barcelonista culture will help us to test out and validate the initial hypothesis