Determination of flow stress by inverse solution using finite element method

Abstract

A newly developed method to determine flow stress of a material has been proposed. This method, named FC-method, is an application of inverse analysis. Since FC-method does not need uniformity of deformation which is the requirement for conventional methods such as uniaxial tensile or compression test, flow stress of a material expressed as a function of unknown material constants is obtained with good accuracy up to large strain range. FC-method employs, as the object function of inverse analysis, the balance of external and internal powers which are given to a material during a deformation process and spent for the deformation respectively. The external power is obtained from the load-displacement curve measured and the internal power is calculated through FEM analysis of the deformation. Then optimization of the balance through inverse analysis gives flow stress of the materia. Friction coefficient between the material and the tools for deformation is also one of the unknown constants and determined through FC-method simultaneously with flow stress. The object function of FC-method explicity contains unknown constants to be determined, therefore the cost of the analysis to obtain flow stress is reduced. Numerical study to verify FC-method was carried out using ring compression problem of type 304 stainless steel between two parallel plane dies, which clarified that FC-method was effective.