Abstract
Present work applies the Upper-Bound Theorem (UBT) with Triangular Rigid Blocks (TRB) to metal forming compression processes like plane strain forge, offering an upper limit to required deformation energy. This analytical method, usually used by means of simplified models, is developed here incorporating different effects that impact in evolution of deformation process like shape factor and friction. By means of a new adaptive model, the shape and size of the rigid zones used for the UBT application are optimized according to the ratio of the width and the height of workpiece.
Highlights
Modern, exact solutions in metal forming processes are very difficult to obtain, due to their high degree of complexity on involved parameters
The Upper-Bound Theorem (UBT) is an analytical method that allows obtaining enough admissible solutions using a separation of a deformed workpiece in rigid zones, called Triangular Rigid Blocks (TRB) in plain strain problems [1]
An analysis of a new adaptive model is developed to improve the UBT application in forging processes. This procedure is based in a model with a flexible TRB configuration [5,6] and allows to improve the solutions obtained by classical UBT procedures by comparing the results obtained with different configurations, according to the “shape factor”, that is the ratio of the width and the height of the workpiece section to be analyzed
Summary
Exact solutions in metal forming processes are very difficult to obtain, due to their high degree of complexity on involved parameters. The Upper-Bound Theorem (UBT) is an analytical method that allows obtaining enough admissible solutions using a separation of a deformed workpiece in rigid zones, called Triangular Rigid Blocks (TRB) in plain strain problems [1] Modern trends in this field tried to extend the application of this analytical method to more general situations [2,3,4]. An analysis of a new adaptive model is developed to improve the UBT application in forging processes This procedure is based in a model with a flexible TRB configuration [5,6] and allows to improve the solutions obtained by classical UBT procedures by comparing the results obtained with different configurations, according to the “shape factor”, that is the ratio of the width and the height of the workpiece section to be analyzed
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