Even though the laser forming process is not used at a large scale, it has a potential value for small product series. Its advantage is in its capacity to deform a sheet into arbitrary shapes by a contact-free laser irradiation, avoiding the need for costly tools in which materials need to be formed in arbitrary shapes. One of the reasons that the process has not become very popular is by the difficulty to predict and control the process and determine the right processing plan to obtain the shape needed. The simulation of the laser forming process is not easy to carry out, because the nature of the problem is three-dimensional and the process is transient. In addition, the description of the material behavior, which includes thermo-elastoplastic behavior, is complex and results in strongly nonlinear problems. Moreover, the temperature dependent material behavior, including the microstructural evolution of the material is often not known to a sufficient degree of precision, which leads to approximate descriptions. For that reason, in the current study a simple application, bending of a flat plate by irradiation over a straight line, is studied by a range of models with a varying degree of complexity. The models are compared in order to evaluate if a simplified model can be used to obtain adequate numerical results under particular conditions. Simplifications can be the reduction of the moving point heat source to a fixed but transient line heat source over the complete trajectory, or reducing the 3D model to a 2D model. From the analysis, it becomes clear that the effects of all three dimensions and the heat source movement are relevant for the ultimate precision of the simulation results, and to obtain the correct tendencies of the effect of changes of some of the parameters on the process results. Nevertheless, the results also demonstrate that some relevant thermal and stress data can be obtained using simplified models at a considerably lower computational cost. In particular, the thermal data are less affected by model simplifications, whereas the stress and deformation fields are more sensitive to the model approximations. An improved 2D model is proposed and evaluated, which is able to take into account the effect of the moving point heat source, while ignoring the longitudinal dimension.
In this study the elastoplastic behavior of cantilever beams under a combined compressive axial load and an imposed lateral bending deflection are analyzed. Eventhough the particular condition of elastoplastic buckling has been studied before, the developed theories are limited to the prediction of the initial failure of the beam. In the current study the elastoplastic behavior of cantilever beams under compressive load at levels below the critical buckling load are studied in order to determine the remaining load bearing capacity of the beam under combined bending and axial loads, including the behavior at progressive levels of plastic deformation. The elastoplastic bending process is analyzed using the finite element method. In particular, the analysis is focused on the evaluation of the limiting bending force necessary to increase or reduce the curvature of the beam in the plastic zone. The bending force depends on the compressive axial load, the geometrical dimensions of the beam, material coefficients, such as Young’s modulus and yield stress, and the hardening model. The large number of variables involved, is reduced by introducing two dimensionless load parameters. The results of the analysis are presented and discussed for a wide range of dimensionless loads. Also the influence of work hardening on the obtained bending force is analyzed, comparing between an ideal plastic behavior and a bilinear plasticity model with a linear hardening behavior.
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