meaning, that have to be identified using coupled numerical simulation and experiments. On the other side, CDM model performance depends on the assumed form for the dissipation potential from which damage evolution law can be derived by normality rule. All the models proposed in the literature show material dependency, lack of performance under multi-axial state of stress conditions and temperature and strain rate effect is usually neglected. In 1997 Bonora [1] proposed a new non-linear CDM model for ductile failure that overcome material dependency and stress triaxiality effects. The model resulted successful in predicting notched and cracked components response using only information, such as damage parameters, identified in simple uniaxial state of stress condition, [2]. Later, Bonora and Milella [3] extended the damage model in order to incorporate temperature and strain rate effects. Up to now, very little attention have been given to the mechanics of ductile deformation and damage under compressive state of stresses. This issue becomes very important in order to understand and predict component life under low cycle fatigue regime or under intense dynamic loading in which damage accumulation is related to the bouncing motion of strain waves into the body. Bonora and Newaz [4] demonstrated the possibility to predict low cycle fatigue life at ductile crack growth initiation discussing possible integration scheme for the non-linear damage law. At the moment, as far as the authors are aware of, no attempt to extend CDM model formulation to cyclic loading under variable stress triaxiality loading conditions has been made. In this paper, for the first time, the non-linear damage model proposed by Bonora has been extended to negative stress triaxiality loading condition, based on simple physical considerations, introducing a new internal variable associated to damage D. The model, implemented in form of user subroutine in the finite element code MSC/MARC, has been tested on single FEM element under simple loading conditions such a as normal and shear stress. Successively, it has been applied to round notched bar specimens loaded in tension. At the present time, an extensive experimental program is under investigation. Here, the promising preliminary results are presented and discussed. NON-LINEAR CDM MODEL FOR DUCTILE FAILURE Lemaitre [5] firstly defined the CDM framework for plasticity damage. Damage accounts for material progressive loss of load carrying capability due to irreversible microstructural modifications, such as microvoids formation and growth, microcracking, etc. From a physical point of view, damage can be expressed as D A A n eff n n ( ) ( ) ( ) = -1 0 (1) where, for a given normal n, An 0 ( ) is the nominal section area of the RVE and Aeff n( ) is the effective resisting one reduced by the presence of micro-flaws and their mutual interactions. Even though this definition implies a damage tensor formulation, the assumption of isotropic damage leads to a more effective description where the scalar D can be simply experimentally identified. Additionally, this assumption is not too far from reality as a result of the random shapes and distribution of the included particles and precipitates that trigger plasticity damage initiation and growth. The strain equivalence hypothesis gives the operative definition of damage as: D E E eff = -1 0 (2) where E0 and Eeff are the Young’s modulus of the undamaged and damaged material, respectively. The complete set of constitutive equation for the damage material can be derived assuming that: - a damage dissipation potential fD, similarly to the one used in plasticity theory, exists; - no coupling between damage and plasticity dissipation potentials exists; - damage variable, D, is coupled with plastic strain; -the same set of constitutive equations for the virgin material can be used to describe the damaged
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