Multiscale modelling of ductile failure in metallic alloys

Micromechanical models for ductile failure have been developed in the 1970s and 1980s essentially to address cracking in structural applications and complement the fracture mechanics approach. Later, this approach has become attractive for physical metallurgists interested by the prediction of failure during forming operations and as a guide for the design of more ductile and/or high-toughness microstructures. Nowadays, a realistic treatment of damage evolution in complex metallic microstructures is becoming feasible when sufficiently sophisticated constitutive laws are used within the context of a multilevel modelling strategy. The current understanding and the state of the art models for the nucleation, growth and coalescence of voids are reviewed with a focus on the underlying physics. Considerations are made about the introduction of the different length scales associated with the microstructure and damage process. Two applications of the methodology are then described to illustrate the potential of the current models. The first application concerns the competition between intergranular and transgranular ductile fracture in aluminum alloys involving soft precipitate free zones along the grain boundaries. The second application concerns the modeling of ductile failure in friction stir welded joints, a problem which also involves soft and hard zones, albeit at a larger scale. (C) 2010 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved

Ductile damage and fracture in metallic alloys combining soft and hard phases

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Geometrical Picture of Third-Order Tensors

Abstract Because of its strong physical meaning, the decomposition of a symmetric second-order tensor into a deviatoric and a spheric part is heavily used in continuum mechanics. When considering higher-order continua, third-order tensors naturally appear in the formulation of the problem. Therefore researchers had proposed numerous extensions of the decomposition to third-order tensors. But, considering the actual literature, the situation seems to be a bit messy: definitions vary according to authors, improper uses of denomination flourish, and, at the end, the understanding of the physics contained in third-order tensors remains fuzzy. The aim of this paper is to clarify the situation. Using few tools from group representation theory, we will provide an unambiguous and explicit answer to that problem.