Algorithm Research, Program Development And Experiment Validation Of GTN Model

Ductile fracture in metal usually experienced three stages, the gradual growth, slow nucleation and final coalescence of microvoids under certain conditions, these processes resulted in macroscopic crack initiation and fracture of materials. In 1975, based the micromechanically model proposed by Gurson and further modified by Tvergaard and Needleman, finally the GTN mesoscopic damage model was formed. But the effect of discontinuous was not considered in the original Gurson mesoscopic damage model, the necking of the intervoid matrix between the sites of the voids could not be predicted. Therefore, by adding the plastic limit load model into the GTN mesoscopic damage model, the numerical model was put forward to research the evolutionary and the fracture failure process of materials. In order to simulate the fracture process of materials under uniaxial tensile conditions, this paper took the following aspects into consideration:1. Based on the Gurson-Tvergaard-Needleman(GTN) mesoscopic damage constitutive theory, combining with the backward Euler fully implicit integration algorithm and elastic predictor-plastic correction method, the constitutive equations were discretized, the stress strain relations were updated, the corresponding consistent tangent operator was deduced detailedly, and the formulation of numerical algorithm was proposed. The critical void volume fraction for void coalescence cf was regarded as the bridge to combine the plastic limit load model and GTN mesoscopic damage model. The user material subroutine(UMAT) in the finite element software ABAQUS/STANDARD was studied here, and the modified GTN mesoscopic damage model was implemented in the finite element environment.2. In order to obtain the load-displacement response curves, the smooth and notched round bar specimens of OFHC were tested under uniaxial tensile loading. With the help of the true stress-true strain curve of the smooth round bar, Young’s modulus, initial yield strain, yield limit and strength limit were obtained. For the hardening after plastic yield, the Ramberg-Osgood hardening criterion was used here to fit curves and determine the hardening coefficient and hardening exponent.3. The axisymmetric finite element models of notched round bar specimens were created, and the eight node axisymmetric reduced integration element(CXA8R) was chosen, the simulation of the evolutionary and the fracture failure process was completed by the ABAQUS software with the interface of UMAT. According to the previous research experiences and methods, combining the comprehensive analysis of uniaxial tensile tests and the results of numerical predictions in this work to determine the damage parameters of the modified GTN mesoscopic damage model finally.4. According to the damage parameters and the UMAT, the modified GTN mesoscopic damage constitutive model in the finite element software ABAQUS was implemented. The fracture failure predictions of notched round bar specimens have a good agreement with the experimental observations, which verified the validity of the model, and the rationality and feasibility of the method.5. The crack initiation site and propagation path, the changes of stress triaxiality along the minimum cross section and the damage evolution law are analyzed here. Numerical results show that the crack initiates in the centre of the specimen and sharp load drop occurs shortly after the crack initiates, and the stress triaxiality is higher at the center of the notched round bar specimens than the free edge nearby. It mainly because the void volume fraction increases along with increasing plastic deformation, the void starts to coalesce when it reaches to the plastic critical load, and the void volume is from f to f*, and it increases rapidly, so the centre of notched specimens begin to initiation when f* increases to a certain degree. The crack initiation and growth will lead to the void grow up quickly, the load rapidly decline, and the load-carrying has a sharp drop, the fracture failure occur when the damage accumulation reaches to the limitation.