Power Required in the Plastic Deformation of Metallic Powder Materials

A method is proposed for setting upper and lower bounds on the power required in plastic deformation, taking account of the plastic dilation of metallic powder materials (typical dilating materials such as steel or nonferrous alloys). For the upper bound, the basic relations of plasticity theory for rigid–plastic isotropic dilating materials are employed. A functional corresponding to the upper bound on the power required in the plastic deformation of a dilating material within a volume with a finite number of discontinuity surfaces (assumed constant) is derived. For the lower bound, a statically permissible approximate stress distribution is specified, and the lower bound on the power of the surface forces at particular speeds is determined. On the basis of the plastic potential, solutions are constructed for the upper and lower bounds of the plastic-deformation power. As an example, the steady plastic flow when strip is forced through a plane matrix is calculated. On the basis of the results, a system of equations is derived for the limits of the plastic zones, the stress, and the lower bounds on the force and power required in plastic deformation. © 2018, Allerton Press, Inc.