An extended GTN model for ductile fracture under high and low stress triaxiality

• A network alteration theory for the Mullins effect, the permanent set and the stress-softening.
• Reconciliation between physical and phenomenological approaches.
• Normalized network parameter depends only on the normalized cycle number.

This contribution provides an improvement on GTN model upon the prediction of fracture location within low level of stress triaxiality. In the proposition, two distinct damage parameters are introduced as internal variables of the degradation process and an effective damage is calculated as a sum of both contributions in the post-processed step. In the beginning, the volume void fraction, based on conservation mass law, is assumed as the first damage parameter, similar to Gurson’s original model. This volumetric damage contribution is able to capture spherical void growth, which plays the main role in tensile loading condition. The second damage parameter is proposed as a new shear mechanism, based on geometrical and phenomenological aspects and is also a function of the equivalent plastic strain, Lode angle and stress triaxiality. The shear damage parameter is formulated independent of the volume void fraction and requires a new nucleation of micro-defects mechanism to trigger the shear growth contribution, and hence is able to capture elongated (and rotation) void growth which is present in simple shear and combined shear/tensile or shear/compression loading conditions. Furthermore, the first and the second damage parameters are coupled in the yield function in order to affect the hydrostatic stress and deviatoric stress contributions, separately. In the first part of this paper, a review of Gurson’s model and its most famous version as GTN’s model is done. After that, the new contribution is presented and an implicit numerical integration algorithm is determined, based on the operator split methodology. The calibration strategy is discussed for determination of material parameters. Numerical tests are performed for a butterfly specimen using two types of materials (aluminum alloy 2024-T351 and steel 1045) under ranges of stress triaxiality between-1/3<η<1/3-1/3<η<1/3 (shear/compression or shear/tensile). At the end, the behavior of internal variables is analyzed, such as: evolution of both damage parameters, evolution of the equivalent plastic strain, the reaction curve and the contour of the effective damage parameter. The results obtained are compared with experimental data and have shown that the present formulation performs well in the prediction of the fracture location and determination of the correct level of equivalent plastic strain at fracture under predominant shear loading condition.