André Dragon

A Model of Anisotropic Damage by Mesocrack Growth; Unilateral Effect:

A three-dimensional model of anisotropic damage by mesocrack growth is first described in its basic version, employing a second-order tensorial damage variable. The model—concerning rate-independent, small strain, isothermal behaviour—allows to take into account residual effects due to damage and reduces any system of mesocracks to three equivalent orthogonal sets. This first version is then extended to account for elastic moduli recovery due to crack closure. Micromechanical considerations impose to employ a fourth-order crack-related tensor when the mesocracks are constrained against opening. Unlike some models which do not avoid (or rectify a posteriori) discontinuities of the stress-strain response, the approach herein ensures a priori the stress continuity and allows to express a convenient macroscopic opening-closure criterion. Nevertheless, the new formulation maintains the orthotropy of the effective properties (instead of an eventual, more general form of anisotropy). Finally, it appears that the extended version does not introduce additional material constants compared to the basic version. The model is tested by simulating the behaviour of Fontainebleau sandstone.

Coupling Between Mesoplasticity and Damage in High-cycle Fatigue

The multiaxial fatigue loading in the high-cycle regime leads to localized mesoscopic plastic strain that occurs in some preferential directions of individual grains for most metallic materials. Crack initiation modeling is difficult in this fatigue regime because the scale where the mechanisms operate is not the engineering scale (macroscopic scale), and local plasticity and damage act simultaneously. This article describes a damage model based on the interaction between mesoplasticity and local damage for the infinite and the finite fatigue life regimes. Several salient effects are accounted for via a simple localization rule, which connects the macroscopic scale with the mesoscopic one, and by the model presented here, which describes the coupled effects of mesoplasticity and damage growth. Irreversible thermodynamics concepts with internal state variables are used to maintain a balance between extensive descriptions of plastic flow and damage events. Cyclic hardening behavior is described by a combined isotropic and kinematic hardening rule while the damage evolution is governed notably by the accumulated plastic mesoscopic strain. In this study, predictions are compared to fatigue tests performed on a mild steel (C36) under different loading modes. All the experiments are carried out under in-phase loading conditions: reversed tension, torsion, and combined tension—torsion. The mean stress effect is also studied through tests conducted under tension. The predicted Wöhler curves under any loading mode can be readily obtained with this model, but the main feature of this approach is to ensure a clear link between the mesoscopic parameters like the hardening behavior of individual grains and the subsequent local damage.

A constitutive high cycle fatigue damage model – based on the interaction between microplasticity and local damage*

Abstract This paper presents a new model that accounts, on a local scale, for the coupling between plasticity due to gliding in shear bands and damage occurring when the accumulated plastic strain has reached a threshold value. The irreversible thermodynamics with internal state variables is employed to keep a middle way between extensive description of plastic and damage flow and application of accessibility requirements. Plasticity and damage are governed by their proper complementary rules (yield functions and potentials). At the same time, a coupling occurs between the damage variable and the hardening parameters. A large experimental database relative to the fatigue behavior of a mild steel C36 submitted to different loading modes (tension, torsion, combined proportional tension and torsion) proves the efficiency of such a model. The prediction of Wöhler curves for cyclic complex stress states can be readily done, but the main feature of this approach is to ensure a clear link between mesoscopic parameters like the hardening behavior of individual grains and the subsequent local damage.

Comparaison des concepts et prédictions des modèles

ABSTRACT Different models presented in this volume are compared. This comparision concerns their concepts and procedures of parameters determination, as well as their predictions.

Modelling of coupled effects of damage by microcracking and friction in closed cracks

The paper addresses crucial issues concerning inelastic behaviour of quasi-brittle solids, principally rock-like materials. Inelastic response for this class of solids results from the evolution of a large number of micro- and mesocracks accompanied with frictional effects regarding closed cracks for complex compression-dominated loading paths. Progressive microcracking and frictional blocking/sliding induce anisotropic behaviour, volumetric dilatancy and complex hysteretic effects due to crack opening/closure transition and plasticity-like sliding evolution. These problems are explored and modelled in the framework of rate-type constitutive theory with internal variables. The model is three-dimensional and micromechanically motivated in its essential ingredients. Meanwhile it is built to provide a tool for efficient structural analysis and, as such, represents a continuum damage approach coupled with a form of plasticity. The settlement between apparently conflicting requirements of physical pertinency on the one hand and of applicability of the model on the other hand, is attempted through relative simplicity of the approach (a small number of material constants to identify) and its modular character involving three increasing levels of complexity. The first, ‘basic’ level, concerns modelling of anisotropic degradation by multiple microcrack growth generating volumetric dilatancy and permanent strain. The second level consists in accounting for the ‘normal’ moduli recovery due to crack closure under predominantly compressive loads (unilateral effect). These two levels are outlined briefly at the beginning of the paper. The text focuses on the third level of modelling involving concomitant dissipative phenomena of damage by microcracking and frictional sliding leading to complex hysteretic effects such as inelastic unloading. The interaction of the two phenomena is successfully managed by the coupled model.