René Billardon

Effect of punching on electrical steels: Experimental and numerical coupled analysis

Punching electrical steels drastically alters their magnetic properties near the cutting edges, which should be accounted for when designing machines. A simple magneto-mechanical coupled finite element analysis, suitable for fully processed grades, is proposed in order to model the consequences of this local degradation of the material on the global behavior of a machine. The model is used to study the effective section of the teeth of a punched stator; calculated results are compared with experimental data and a good agreement is found.

Continuum damage mechanics and local approach to fracture: Numerical procedures

Abstract In this paper, continuum damage mechanics is applied to the prediction of the failure of structures. The numerical implementation of this theory within the framework of the finite element method is described in details for both initiation and propagation problems. Practical examples are given to demonstrate the usefulness of this so-called ‘local approach to fracture’ in the case of creep and ductile damages.

Investigation of localization due to damage in elasto-plastic materials

Abstract Localization due to damage is investigated for rate-independent plasticity. A general class of elasto-plastic models is presented and analyzed in detail. Analytical localization results for homogeneous plane problems are derived and discussed. A J 2 plasticity model exhibiting nonlinear isotropic hardening, Chaboche-Marquis nonlinear kinematic hardening and Lemaitre-Chaboche ductile damage is thoroughly studied. Analytical results for softening and localization are derived and discussed. A numerical study of homogeneous plane stress states under monotonic biaxial loadings is conducted. Experimental results and numerical predictions for a notched plate with a macro-defect are presented.

Experimental analysis of the magnetoelastic anisotropy of a non-oriented silicon iron alloy

This paper deals with experimental measurements of the mechanical, magnetic and magnetostrictive behaviours of a non-oriented 3%SiFe alloy. The results show that the low crystallographic texture of the material brings important anisotropic effects and that the coupled magnetomechanical properties are much more sensitive than uncoupled ones.

Bifurcation and Localization in Rate-Independent Materials. Some General Considerations

This work deals with some aspects of bifurcation and localization phenomena for solids made of rate-independent materials. Only the theoretical developments are presented. Physical non-linearities (plasticity, damage, ...) and geometrical non-linearities are taken into account. The analysis is limited to quasi-static loadings. A full and complete analysis of the rate problem for incrementally linear solids is carried out. The first order rate problem is formulated and analysed in the framework of modern theory of linear elliptic boundary value problems. Three conditions are necessary and in the same time sufficient for this problem to be well-posed. These conditions are local in nature and are used to describe localization phenomena.

Residual stresses in punched laminations: Phenomenological analysis and influence on the magnetic behavior of electrical steels

The magnetic properties of laminated electrical steels are degraded by punching because of plasticity localized along the cutting edge, but also because of residual stresses, which may spread over the whole lamination. In this article, long-range residual stresses are analyzed via a simplified mechanical analysis. Then, their effect on the global magnetic behavior of the lamination is calculated by a magnetoelastic coupled model. It is found that the relative influence of residual stress is as important as the one of plasticity alone.

A two-field finite element formulation for elasticity coupled to damage

A two-field variational formulation is proposed for continuum damage mechanics problems. This formulation is applied to the numerical solution, via the finite element method, of initial boundary value problems arising in elasticity coupled to damage; the nodal variables are the displacement and damage fields. Simple examples are presented to demonstrate the advantages and limitations of this formulation.

Homogenisation of magneto-elastic behaviour: from the grain to the macro scale

The prediction of the reversible evolution of macroscopic magnetostriction strain and magnetisation in ferromagnetic materials is still an open issue. Progress has been recently made in the description of the magneto-elastic behaviour of single crystals. Herein, we propose to extend this procedure to the prediction of the behaviour of textured soft magnetic polycrystals. This extension implies a magneto-mechanical homogenisation. The model proposed is discussed and the results are compared to experimental data obtained on industrial iron-silicon alloys.

Numerical Analysis of the Resistance to Shear Test of Clinched Assemblies of Thin Metal Sheets

The work presented in this paper is part of a more extensive study the aim of which is to build a complete simulation of the clinching process and subsequent resistance tests. This paper focuses on finite element analyses ‐that are performed with the ABAQUS™ code‐ of the resistance of clinched points to shear test. These analyses are run up to propagation of metal sheet fracture. A simplified procedure is proposed to identify the fracture initiation and propagation models that are used to simulate this failure process. This identification process is based on Lemaitre’s ductile damage model. The numerical simulations of a shear test have been compared to experimental results.

Fatigue failure maps of heterogeneous materials

Abstract In this paper, so-called fatigue failure maps are studied as a function of initial flaw size distributions. The main cause of fatigue failure for brittle materials, and of fatigue initiation for ductile materials, is that initial flaws become critical. Fatigue failure maps where the number of cycles to initiation for a given failure probability is plotted for various flaw size distributions are a means of characterizing the influence of the initial flaw distribution on fatigue crack initiation. The results are applied to fatigue failure of austempered spheroidal graphite cast iron.