Determination of flow curves by means of a compression test under sticking friction conditions using an iterative finite-element procedure

Abstract

A common method for the determination of flow curves is the application of a compression test. Using this method, friction in the interface between the die and the specimen leads to a bulging of the sample and thereby to an inhomogeneous stress and strain state. The calculation of the flow stress from experimentally determined force–displacement curves implies a uniaxial stress state, but this will produce an error because of the above-mentioned bulging, when friction occurs. One method of avoiding these sources of error is to minimize friction, e.g. by the use of lubricants together with useful geometries of the samples. Another strategy, described in this paper, applies sticking friction conditions during the testing, the calculation of the flow curve being done by the use of an iterative procedure, applying a corrective function. This corrective function can be calculated by a finite element (FE) analysis of the upsetting test. It will be shown that the first iteration gives adequate results, that the corrective function itself depends on the shape of the specimen and that the corrective function is not dependent on the hardening behaviour of the material, which means that if one sample geometry is used, the corrective function itself need not be calculated for every test.