The GTN Damage Model With Combined Hardening Rule

ABSTRACT:GTN (Gurson-Tvergaard-Needleman) damage model can simulate visually the process of steel ductile failure at a microscopic level. However, the model described a perfect plastic behavior when proposed and could’t describe Bauschinger effect of steel under low cyclic loading. In this paper, referring to previous research results, isotropic hardening rule and kinematic hardening rule are incorporated into the classic GTN damage model. The GTN damage model with combined hardening is implemented in ABAQUS by using the UMAT subroutine of ABAQUS.By using numerical tests of unit cell model, cell model and reference example under low cyclic loading, the validity of the UMAT subroutine is verified. The unit cell model test conceptually demonstrates that the subroutine can not only simulate qualitatively the process of steel ductile failure, but also reflect the expansion and move of yielding surface under loading after yielding. The cell model test verifys the correctness of evolution tendency of the void volume fraction of the UMAT subroutine. The reference example test shows that the UMAT subroutine can get correct result and be applied to practical problem.Smooth and notched specimens extracted from construction steels under low cyclic loading are simulated by using the UMAT subroutine. Study the evolution of void volume fraction f of GTN model under loading and compare the influences of different mesh sizes and different damage parameters on the crack initiation point of notched specimen.Compared to the result of combined module, the UMAT subroutine can reflect the damage accumulation of steel caused by micro-void and realize crack initiation prediction of notched specimen. However, there is a big difference between the result of experiment and prediction when damage parameters of GTN model, identified from uniaxial tensile material test, and combined hardening parameters, identified from low cyclic loading test, are applied together. The void volume fraction f is steppedly increased during early low cyclic loading. However, when matrix accumulated equivalent plastic strain reaches a certain value, the void volume fraction due to nucleation does’t grow and the void volume fraction rises and fails with the void volume fraction due to growth until it grows to the void volume fraction of material failure fF and the specimen comes into being crack initiation. Decreasing the mesh size can expedite the onset of crack initiation. However, when the mesh size is refined to a certain extent, the influence of mesh size can be negligible. Compared to the initial void volume fraction f0, the influence of nucleation void volume fraction fN and the void volume fraction of material failure fF on the crack initiation point of notched specimen is more obvious. Increasing fF can delay the onset of crack initiation, and increasing fN can expedite the onset of crack initiation.