In this study, we follow the work of Tvergaard & Needleman (1995), Tvergaard & Needleman (1997) and Needleman & Tvergaard (1998) and present the numerical implementation and some initial applications of a non-local Gurson-Tvergaard-Needleman (GTN) model for explicit finite element (FE) analysis. The delocalization relates to the damage mechanism and is incorporated in terms of an integral condition on the rate of change of the porosity. In order to demonstrate the mesh independence during all stages of ductile damage and fracture, several material test specimens have been simulated until full fracture using different mesh sizes. For comparison purposes, results are also obtained for the corresponding local GTN model in all cases. The effect of the material characteristic length on the ductile damage and fracture behavior and on the mesh sensitivity of the results is discussed. It is shown that simulation results obtained in all stages of the ductile fracture process, including void growth, fracture initiation by coalescence and crack propagation all the way to a fully fractured specimen, are mesh independent from a certain ratio of mesh size relative to the material characteristic 2 length, provided the non-local integral is evaluated on the current configuration. This ratio is unique for each individual specimen simulated as it depends on the spatial gradients of the porosity and the material parameters adopted for the problem at hand. It is shown that excessive averaging at large deformations occurs if the non-local integral is evaluated on the reference configuration, i.e., without updating the element interaction matrix resulting from the discretization of the non-local integral.

From an engineering point of view, it is beneficial to reduce the number of mechanical tests required to calibrate the plasticity and fracture models of a structural material. In this study, the ductile fracture model for three high-strength steels is identified based on unit cell simulations, metal and porous plasticity modelling, and strain localization analysis combined with a single uniaxial tensile test per material. Finite element simulations of a unit cell model with a spherical void are performed with the matrix material described by metal plasticity and used to calibrate the parameters of the porous plasticity model. Strain localization analyses are conducted using the imperfection band approach with metal plasticity outside and porous plasticity inside the imperfection band. These simulations are first used to determine the nucleation rate in the porous plasticity model giving the experimentally obtained fracture strain in uniaxial tension, and then to compute the fracture locus under proportional loading in generalized axisymmetric tension. By combining the fracture locus with a simple damage accumulation rule and metal plasticity, finite element simulations of ductile fracture in tensile tests on smooth and notched specimens of the three steels are performed. Comparison of the predicted results with existing experimental data shows that the fracture model gives satisfactory estimates of ductility for a wide range of stress triaxiality ratios in steels of different strengths. This study shows the potential of micromechanical analyses in the calibration of fracture models for engineering applications.

In this paper, we investigate the possibility of predicting ductile fracture of pipeline steel by using the Gurson–Tvergaard–Needleman (GTN) model where the onset of void coalescence is determined based on in situ bifurcation analyses. To this end, three variants of the GTN model, one of which includes in situ bifurcation, are calibrated for a pipeline steel grade X65 using uniaxial and notch tension tests. Then plane-strain tension tests and Kahn tear tests of the same material are used for assessment of the credibility of the three models. Explicit finite element simulations are carried out for all tests using the three variants of the GTN model, and the results are compared to the experimental data. The capability of the simulation models to capture onset of fracture and crack propagation in the pipeline steel is evaluated. It is found that the use of in situ bifurcation as a criterion for onset of void coalescence in each element makes the GTN model easier to calibrate with less free parameters, all the while obtaining similar or even better predictions as other widely used formulations of the GTN model over a wide range of different stress states.