An analytical formulation as an alternative to FEM software giving strain and stress distributions for the three-dimensional solution of extrusion problems

作者：Karami Peyman^*; Abrinia Karen

来源：International Journal of Advanced Manufacturing Technology, 2014, 71(1-4): 653-665.

DOI：10.1007/s00170-013-5500-1

• Extrusion
• Analytical method
• FEM
• Strain and stress distribution
• Upper bound

A new improved analytical method based on the upper bound theorem is presented for the solution of extrusion problems. This method has been formulated in such a way as to eliminate the deficiencies in the previous works in order to enable it as a powerful analytical tool as an alternative to finite element software. The proposed formulation is a general method of solution, which could be used for the analysis of many bulk forming processes. However, in this paper, the forward extrusion of a square section from a round billet has been presented as an example. Kinematically admissible velocity fields were computed which gave a more physically realistic material flow patterns as compared to previous works. The distribution of strain and stress as well as the results for the effect of process parameters on the extrusion load and die geometry was also given. These results were compared with FEM data to observe the accuracy and effectiveness of the present method. For the extrusion of square sections from round billets, detailed analysis of strain distribution on the exit section was carried out using the components of the power due to internal deformation, interface friction, and velocity discontinuities at the entry and exit surfaces. Comparison with experimental data was made, and verification of the theoretical results was carried out. The improvement of the results computed using the present method was shown by comparison with the previous works.

• 出版日期2014-3