Development of constitutive creep damage-based modified Robinson–Rousselier (MRR) model with XFEM for void-crack relation in ductile materials

In this work, we present the predictive modeling for ductile creep damage by implementing the modified Robinson–Rousselier constitutive relations and extended finite element method (XFEM) to treat creep rupture in the void-crack growth problem. We develop an attractive new model, called the modified Robinson–Rousselier (MRR) model, to predict the creep damage behavior in terms of micromechanical damage due to void growth in the ductile materials. The MRR model interface executes an implicit integration scheme in the UMAT subroutine of the Abaqus/Standard module. The radial return method is performed to integrate the viscoplastic constitutive equation in finite element formulation. The numerical models in 2D and 3D elements are implemented to identify the developed subroutines’ correctness, and the results are compared with the exact solution for verification. Furthermore, the tensile creep tests on the smooth bars specimen are modeled and tested at a constant temperature of 625 ∘C with different stress levels. The results show that the maximum values of stress, creep strain, and void damage are detected near the tensile specimen center, where the necking process is formed. Furthermore, the results are compared with the literature to verify and evaluate the developed model and show a reasonable agreement between both results. Then this analysis is extended by introducing crack development in the specimen based on the XFEM technique. As a result, a new model, called the modified Robinson–Rousselier XFEM (MRRX) model is proposed, and the results are compared with the results found in the literature, which showed the evolutions of void growth in the crack path. Therefore the MRRX model solution is proven to have the potential to predict the creep damage behavior in terms of the void-crack growth in the ductile material structures.