Jean-Louis Chaboche

Constitutive equations for cyclic plasticity and cyclic viscoplasticity

Abstract The cyclic constitutive equations developed and used at ONERA and LMT-Cachan are presented in detail in terms of a hierarchy of various models. Both the time-independent and the viscoplasticity versions of the equations are discussed, as well as their ability to describe correctly most of the experimentally observed effects under monotonic or cyclic loading, constant or variable temperature, including strain hardening and time recovery effects. The reported experimental data concerns stainless steels and have been published previously. Four other theories are then presented and compared in a systematic way. They include the Ohno-Kachi time-independent plasticity theory, two unified viscoplastic models by Walker and by Krempl and Yao, the new developments of the endochronic theory by Watanabe and Atluri. All these approaches show some similarities with the first one, especially i that concerns the non-linearity of kinematic hardening, which represents the key for describing the cyclic behaviour of metallic materials.

On some modifications of kinematic hardening to improve the description of ratchetting effects

Abstract The constitutive modeling of cyclic plasticity has made great progress durinr the past 20 years. One of the unsolved difficulties concerns the problem of ratchetting, that is, the progressive strain accumulation, cycle-by-cycle, induced by the superposition of a cyclic secondary load to a constant primary load (the mean-stress in the tension-compression case). This paper consider several special kinematic hardening rules and their properties in tension-compression. One particular rule is selected which offers a good compromise, describing both the shape of the normal cyclic stress-strain relations and the ratchetting results. A complete model is then developed including isotropic hardening, which describes fairly well the monotonic, cyclic and ratchetting behaviour of type 316 L stainless steel at room temperature.

Continuous damage mechanics — A tool to describe phenomena before crack initiation

Abstract The classical structural life predictions are based on stabilized stress-strain analysis and some parametric relations with the number of cycles to failure. During the last ten years a different approach, initiated by the works of Kachanov and Rabotnov for creep rupture, has been developed by different laboratories. This continuous Damage Mechanics, treating the damaged material as a macroscopically homogeneous one, leads to the possibility of globally modelling the nucleation and the propagation of microdefects including their effect on the stress-strain behaviour. This paper presents the general theory and several applications to a turbine blade refractory alloy. It includes the description of sequence effects and creep-fatigue interaction. The generalization for three-dimensional conditions, where anisotropic damage effects are possible, is discussed and some new proposals are given for the determination of simple anisotropic damage equations.

Towards a micromechanics based inelastic and damage modeling of composites

Abstract Micromechanics based models are considered for application to viscoplasticity and damage in metal matrix composites. The method proposes a continuation and development of Dvoraks transformation field analysis, considering piecewise uniform eigenstrains in each material phase. Standard applications of the method for a two-phase model (only one sub-volume per phase) deliver too stiff responses. Two modifications are proposed that improve considerably the overall stress–strain response, at least for materials sustaining a linear hardening under large strains. Introduction of damage effects in the TFA method is considered, within the CDM framework, using two modeling approaches: the “Direct Simplified Model”, using only two damaged phases, and the “Generalized Eigenstrain Model”, with more degrees of freedom, that allows the description of interfacial damage. The different aspects of the proposed methods are systematically checked by comparing with finite element unit cell analyses, made through periodic homogenization assumptions, for a SiC/Ti unidirectional MMC.

Thermodynamic formulation of constitutive equations and application to the viscoplasticity and viscoelasticity of metals and polymers

Abstract Elastoviscoplasticity for metallic materials and viscoelasticity for polymers are generally treated as completely independent processes. In the present paper we intend to discuss some possible bridges between the two kind of constitutive theories. Two aspects are more specifically addressed: (i) the classical thermodynamics of irreversible processes, using material state variables, is further extended in order to incorporate more easily dynamic and static recovery effects in the kinematic hardening evolutionary equations; (ii) the qualitative and quantitative equivalence between elasto-viscoplasticity and viscoelasticity is discussed both in terms of the simplest linear model and for a more complicated non-linear situation. In fact, it is demonstrated that superposing several non-linear kinematic hardening and static recovery rules allows to model a viscoelastic behavior. One of the advantages of the approach is to describe easily the cyclic loading situations, as shown by comparison with experiments made on a glass-epoxy composite.

Anisotropic creep damage in the framework of continuum damage mechanics

Abstract For some years various works have shown the possibility of applying continuum mechanics to model the evolution of the damage variable, initially introduced by Kachanov. Of interest here are the complex problems posed by the anisotropy which affects both the elastic behaviour and the viscoplastic one, and also the rupture phenomenon. The main concepts of the Continuum Damage Mechanics are briefly reviewed together with some classical ways to introduce anisotropy of damage in the particular case of proportional loadings. Based on previous works, two generalizations are presented and discussed, which use different kinds of tensors to describe the anisotropy of creep damage: • - The first one, by Murakami and Ohno introduces a second-rank damage tensor and a net stress tensor through a net area definition. The effective stress-strain behaviour is then obtained by a fourth-rank tensor. • - The second theory, by Chaboche, uses one effective stress tensor only, defined in terms of the macroscopic strain behaviour, through a fourth-order non-symmetrical damage tensor. The two theories are compared at several levels: differences and similarities are pointed out for the damage evolution during tensile creep as well as for anisotropy effects. The possibilities are discussed and compared on the basis of some existing experimental results, especially for creep under tension-torsion, which leads to a partial validation of the two approaches.

Continuum damage mechanics: Present state and future trends

Abstract Continuum Damage Mechanics (CDM) has developed since the initial works of Kachanov and Rabotnov. The paper gives a review of its main features, of the present possibilities and of further developments. Several aspects are considered successively: • - damage definitions and measures, • - damage growth equations and anisotropy effects, • - use of CDM for local approaches of fracture. Various materials, loading conditions and damaging processes are incorporated in the same general framework. Particular attention is given to the possible connections between different definitions of damage, especially between the CDM definition and the information obtained from material science.

Continuum Damage Mechanics, Anisotropy and Damage Deactivation for Brittle Materials Like Concrete and Ceramic Composites

The main lines of a Continuum Damage Mechanics Modelling are reviewed, for applications to brittle materials treated as elastic damageable ones. The proposed damage models consider in the same framework the cases of initially isotropic materials like concrete and anisotropic composites. Attention is focused on the damage deactivation effects and on the possibility to describe irreversible strains directly associated to the damaging processes without any additional dissipation. Finally, the model is applied to two particular SiC/SiC and C/SiC composites.

On the Interface Debonding Models

Interface debonding models offer the possibility to simulate numerically the interface crack growth, and the eventual contact friction behaviour on the cracked area. The paper considers models in the framework of an Interface Damage Mechanics, relating displacement discontinuities across the interface to the corresponding tractions, through various constitutive and damage equations. The approach is based on the initial works by Needleman (1987) and Tvergaard (1990a, 1990b). After a brief review of the existing models, two new versions are proposed and discussed in detail, with the purpose of simulating mixed mode progressive decohesion, followed by a contact/friction behaviour after complete separation, and to guarantee the continuity between the two phases. The first modified model considers coupling terms in the elastic behaviour with damage. The second one introduces the possibility for sliding effects, obeying the Coulomb criterion, during the decohesion phase. The initial Tvergaard model and the second modified model are shown to be derivable from a state potential. Moreover, the thermodynamic framework is used to choose some characteristics of the Model II under a compressive behaviour. Under tension, the models reduce to the classical one. A three-dimensional generalization is given in the Appendix. In addition, the numerical simulation capabilities of the interface debonding models are illustrated by two examples: the fibre-matrix-interface decohesion in a Metal Matrix composite with a bridged matrix crack and the delamination of a DCB (Double Cantilever Beam) specimen.

A viscoplastic theory with thermodynamic considerations

SummaryA thermodynamic foundation using the concept of internal state variables is given for a general theory of viscoplasticity for initially isotropic materials. Three, fundamental, internal, state variables are admitted; they are: a tensorial back stress for kinematic effects, and scalar drag and yield strengths for isotropic effects. All three are considered to evolve phenomenologically according to competitive processes between strain hardening, deformation induced dynamic recovery, and thermally induced static recovery. Within this phenomenological framework, a thermodynamically admissible set of evolution equations is proposed. The theory allows each of the three internal variables to be composed as a sum of independently evolving constituents. The evolution of internal state can also include terms that vary linearly with the external variable rates, whose presence affects the energy dissipation properties of a material.