Steady planar ideal flow of anisotropic materials

Abstract

This paper extends the ideal flow theory, which is well known for isotropic rigid perfectly plastic materials, to quite general orthotropic materials which comply with the principle of maximum plastic dissipation. The new theory is restricted to steady planar flow. The original ideal flow theory is widely used as the basis for inverse methods for the preliminary design of metal forming processes driven by minimum plastic work. The new theory extends this area of application to orthotropic materials. Moreover, another design criterion based on the Cockroft–Latham ductile fracture criterion is incorporated in the theory. To this end, the extended Bernoulli’s theorem relating pressure and velocity along any streamline during the steady planar flow of rigid perfectly plastic solids when the streamline is coincident everywhere with a principal stress trajectory is used. In particular, this theorem and the concept of ideal flow combine to evaluate the integral involved in the ductile fracture criterion. The final result is a simple relation between process parameters and the constitutive parameter involved in the ductile fracture criterion. The simplicity of this relation makes it suitable for quick design of metal forming processes.