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The modelling of metal cutting has proved to be particularly complex due to the diversity of physical phenomena involved, including thermo-mechanical coupling, contact/friction and material failure. The present work outlines the wide range of complex physical phenomena involved in the chip formation in a descriptive manner. In order to improve and understand the process different numerical strategies have been used for simulation. Several of these numerical strategies are reviewed and a short discussion of their relative merits and drawbacks is presented. By means of several examples, where a combined experimental/numerical effort was undertaken, we try to illustrate what numerical techniques, models and pertinent parameters are needed for successful simulations.

One of the most widely employed models to evaluate ductile damage and fracture is due to Gurson. An inconvenience of the model is that several material parameters must be determined in order to represent adequately a given experimental behavior. Determination of such parameters is not trivial but can be performed by means of inverse analyses using optimization procedures. In this work, the material parameters are sought by fitting force vs. displacement curves computed using finite element simulation to experimental curves obtained from tensile tests. The resulting optimization problem is nonconvex and may present several local minima, thereby posing some difficulties to gradient-based optimization procedures due to the strong dependence on initial estimates of the design variables (the material parameters in this case). An approach based on a genetic algorithm is used in an attempt to avoid this problem. This strategy makes also possible to exploit the parallel nature of evolutionary algorithms as, at each generation, the evaluation of the fitness function of one individual is independent of the fitness of the rest of the population. In this particular implementation, each individual is represented by a gray encoding sequence of genes, the parental selection is performed by means of a tournament selection, the crossover probability is 0.8 and the probability of mutation is 0.05.

The plastic transforming industry has shown considerable growth in the last years. In this context, commercial simulators have been developed, some of which combine simplified mathematical models with rheological properties of commercial polymers. In spite of the successes, these approximations are not able to capture important details of the flow behavior. The present work addresses some aspects of the polymer melt flow in plane channels using a more elaborate mathematical formulation based on the full momentum and energy conservation laws. The physical equations are discretized using finite differences based on a collocated mesh and second-order spatial accuracy formulas. Solutions featuring the development of hydrodynamic and thermal boundary layers are presented for a commercial polymer.

SUMMARYThis work presents a fully implicit finite difference scheme aimed at simulation of polymer melt flow in channels and mould cavities. This class of problems is characterized by strong material non-linearity and coupling of momentum, heat and mass transfer. The computational approach is based on the generalized Newtonian model and utilizes central discretization for both diffusive and convective terms, collocated meshes and artificial dissipation control to handle spurious pressure modes. The formulation accounts for the full interaction between the thermal effects caused by viscous heating and the momentum diffusion effects dictated by a shear rate and temperature-dependent constitutive model. Solutions for plane channels and asymmetric sudden expansion illustrate application to polymer melt flow.

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