A nonlinear model for ductile damage accumulation under multiaxial non-proportional loading conditions

• A nonlinear ductile damage accumulation law is formulated.
• Several non-proportional multiaxial tests are devised and executed.
• Two plasticity formulations are used to describe the material constitutive behavior.
• Damage prediction using linear and different nonlinear approaches is discussed.

In this paper, a nonlinear model for ductile damage accumulation is presented and applied to predict failure under non-proportional loading conditions. To this purpose, several tension-torsion tests were executed on samples of an isotropic Grade X65 steel, using a custom biaxial equipment. The experiments were carried out on hollow cylindrical specimens with two different gauge axial lengths. Non-proportional loading paths were achieved changing the tension to torsion ratio during runs. The dependence of damage accumulation on the equivalent plastic strain was modelled by means of a nonlinear function of the triaxiality and the deviatoric component of the stress state. The devised model, suitable to predict failure under complex loading paths, was implemented in a commercial FE code. All experimental tests were simulated in order to monitor the stress and strain evolution within the specimen, and to determine the onset of fracture. In the numerical simulations, the constitutive behavior was described using both a J2 and a J2J3 plasticity models. Thanks to the applied testing conditions, different stress states were induced in the material. A straightforward calibration of the accumulation model was achieved from few experiments, then the transferability of the formulation was validated on different tests. The proposed method showed appreciable improvements in final fracture prediction over a linear approach, as well as over other nonlinear approaches from the literature.