Issue 49

H. Berrekia et alii, Frattura ed Integrità Strutturale, 49 (2019) 643-654; DOI: 10.3221/IGF-ESIS.49.58 649 D s D s    (1) If the damage is isotropic, D is a scalar; this allows the introduction of the notion of the effective stress: 1 D      (2) By considering the principle of deformation equivalence [13], the coupling deformation damage is done at two levels:  At the level of the elastic potential  ( e E , D) which leads to the law of elasticity of the damaged material : = e E     Or ij IJ e ij . 1+ E = - 1-D 1-D IJ E E        (3) Where E is Young’s modulus, and  , Poisson’s ration. The associated variable to D is defined by: D      ;   2 2 2 1 eq V R E D        (4) Y is the strain energy density release rate [14] defining the power dissipated in the damaging process where:     3 2 3 1 3 1 2 2 D D eq ij IJ H V eq D ij ij H ij R                                                       with: 1 3 H KK     At plastic yield function: 1 eq S f D      (5) Where: S  is the threshold of plasticity (defined previously). The condition eq s    deviates any plastic deformation and ensures a pure elastic deformation The zone in the vicinity of the corrosion defect (whose plasticity threshold S  ) undergoes a plastic deformation, therefore a damage, while the zones further from the corrosion defect (whose elastic limit is y  ) undergo only one elastic deformation. The kinetic law of damage for ductile damage derives from the dissipation potential F [15]: