A New Approach for Determining the Friction Law in Metal Forming

The most popular friction law in metal forming applications is Tresca’s law which postulates that the friction stress is equal to a portion of the local shear yield stress. The friction factor involved in this law should be found from experiment. A typical test for this purpose is the ring compression test. The test must be supplemented with a theoretical analysis. The latter is often based on upper bound solutions. There are several difficulties with the interpretation of test results. The distribution of the friction factor over the surface is not uniform, though it is assumed to be uniform in the theoretical analyses. It is very difficult (or even impossible) to minimize this non-uniformity to a reasonable level in experiment. It is rather necessary to develop theoretical techniques to account for it in inverse problems where the frictional boundary condition should be obtained as a result of the theoretical analysis and experimental data. Another difficulty is that sticking can occur on a part of the friction surface. This actually happens in ring compression tests, and usually is not accounted for in theoretical analyses. This difficulty is specific to the ring compression test (and other similar tests) and can be overcome by selecting an appropriate test. Such a test is proposed in the present paper. Dies have the form of a cone. The specimen is a pre-shaped hollow cylinder such that the die exactly fits the cavity made at each cylinder face. The new test reduces to the ring compression test in a limit. The cone angle should be chosen such that no sticking occurs. In the paper, an upper bound solution is proposed to supplement experimental data. Using this solution, conclusions are drawn on the applicability of the test for determining the friction factor.