We propose a 3D h-adaptive FE methodology to represent the initiation and propagation of cracks in ductile materials during metal forming process. A fully coupled elasto-plastic behavior model is used to describe the material. It is then implemented into ABAQUS/Explicit FE code using a user defined subroutine VUMAT. The methodology is validated by simulating a tensile test in which the whole loading process is divided into multiple loading sequences. The 10-node quadratic tetrahedral element (C3D10M) provided by ABAQUS is used to discretize the specimen.

In each loading sequence, the behavior model is solved with the updated boundary condition and initial condition. The adaptive process is then performed to deal with meshing and remeshing aspects. The cracks are represented as locations of all the fully damaged elements which are deleted from the mesh. The mesh size is then driven by an empirical size indicator based on values of the cumulative plastic strain and an appropriate measure of ductile damage. According to this size indicator, the mesh is first refined locally using a 3D bisection technique, and then optimized in terms of its shape quality. A hybrid field transfer procedure which includes both finite element shape function interpolation and Diffuse Approximation in its interpolating form (Diffuse Interpolation) is proposed to project the physical fields from the old the mesh to the adapted mesh. The selection of information points which are used to build the objective function is improved to consider both direction and distance between the evaluation point and its neighboring points. The number of selected information points is controlled as well. This hybrid operator prevents peak value from declining and limits the numerical diffusion during field transfer process which guarantee the accuracy of field transfer in a 3D context, even with highly localized fields (stress, damage, plastic strain). The length of the loading sequences is also adapted according to the plastic strain rate and severe distortion of the elements.

We then provide 3D numerical examples to show how our proposed approach is able to predict the initiation of damage and the propagation of macroscopic cracks inside plastic structures. From the results, we can see that due to the empirical size indicator, the gradation of the mesh captures the evolution of the plastic flow which allows the fully damaged zones (within shear bands) to be discretized with the elements having a minimum size. Meanwhile, the adjacent elements size ratio is controlled lower than 2 which avoids the ill-shaped elements to being generated and guarantees the accuracy of the field transfer process. These 3D numerical examples are compared with the experimental results. The initiation of the damage and propagation of the cracks give a good agreement between experimental results and numerical results.