In this paper, we present numerical computational methods for solving the fracture problem in brittle and ductile materials with no prior knowledge of the topology of crack path. Moreover, these methods are capable of modeling the crack initiation. We perform numerical simulations of pieces of brittle material based on global approach and taken into account the thermal effect in crack propagation. On the other hand, we propose also a numerical method for solving the fracture problem in a ductile material based on elements deletion method and also using thermo-mechanical behavior and damage laws. In order to achieve the last purpose, we simulate the orthogonal cutting process.
Fracture mechanics has been revisited by proposing different models of quasi static brittle fracture. In this work, the problem of the quasi static crack propagation is based on variational approach. It requires no prior knowledge of the crack path or of its topology. Moreover, it is capable of modeling crack initiation. In the numerical experiments, we use a standard linear (P1) Lagrange finite element method for discretization. We perform numerical simulations of a piece of brittle material without initial crack. An alternate minimizations algorithm is used. Based on these numerical results, we determine the influence of numerical parameters on the evolution of energies and crack propagation. We show also the necessity of considering the kinetic term and the crack propagation becomes dynamic.
Previous studies of the shearing process demonstrated that clearance and shear rate are the most influential parameters on the geometry of sheared billets. This paper illustrates a parametric numerical study of the impact of these parameters on the quality of the shear surface using the finite element simulation of shearing. In order to account for interactions between stress state evolution and the associated heating during shearing, a fully coupled thermo-mechanical simulation method was adopted. The influence of stress state, strain rate, and temperature on the material behavior were taken into account by using Johnson-Cook plasticity and ductile failure models. Many simulations were carried out involving diverse shear rates and shear clearances. The relationship between the parameters of shear surface geometry and the temperature was illustrated and proven. Contrary to the expectation of high-speed shearing performance, a burr free smooth shear surface was found using a low shear rate. This study illustrates a numerical strategy to determine the best shear clearance-rate set for aluminum alloy Al7075-T6 bars that minimizes the shear surface defects.
Fracture mechanisms in solids are governed by complex fracture phenomena such as crack initiation and multiple crack branching. Recently, the numerical modeling of dynamic fracture mechanisms has been based on the introduction of a crack phase field. Following our recent works on phase-field modeling of quasistatic brittle fracture, a numerical method is presented to investigate the dynamic failure mechanisms in brittle solids using the phase-field model and a staggered algorithm. For that, numerical experiments of a brittle piece under tensile loading are performed. Based on these numerical results, the importance of developing a numerical method to optimize the computation time is shown. The optimized method is presented in a linear (P1) finite elements case in elasticity. We then show the results of using the optimized method in the case of dynamic fracture mechanics in brittle materials, and we analyze when the dynamic solution converges to the quasistatic one. We also investigate the influence of the numerical parameters h (mesh size) and η (regularization parameter) on the evolution of energies, displacements and crack location. The influence of exerted loading δ and transverse wave speed C T is also elaborated.
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