On the Prediction of the Strain Rate Intensity Factor in Metal Forming Processes

The strain rate intensity factor is the coefficient of the principal singular term in a series expansion of the equivalent strain rate in the vicinity of maximum friction surfaces. Such singular behaviour occurs in the case of several rigid plastic models (rigid perfectly plastic solids, the double-shearing model, the double slip and rotation model, some of viscoplastic models). Since it is only possible to introduce the strain rate intensity factor for singular velocity fields, it is obvious that standard finite element codes cannot be used to calculate it. The currently available distributions of the strain rate intensity factor have been found from closed form solutions or with the use of simple approximate solutions (for instance upper bound solutions). Closed form solutions are available for boundary value problems with simple geometry (flow through infinite rough channels, compression of infinite layers between rough plates and so on) and, therefore, are mostly of academic interest. Simple approximate solutions can predict general tendencies in the distribution of the strain rate intensity factor but cannot predict its distribution with a sufficient accuracy for industrial applications. For, the strain rate intensity factor reflects a very local effect inherent in the velocity field whereas simple approximate methods, such as the upper bound method, estimate global parameters, such as the limit load. The purpose of the present research is to propose a special numerical technique for calculating the strain rate intensity factor in the case of plane strain deformation of rigid perfectly plastic materials and to verify it by means of comparison with an analytical solution. The technique is based on the method of Riemann.