Kinematic characteristics of deformed porous structures

Abstract

Experimental and computational methods of studying the stress state in the plastic region are characterized by various methods and accuracy of measurements, methods of mathematical processing of experimental information, and interpretation of results. The experimentally determined kinematics as a starting point is the most widely used method to study the stress-strain state in the plastic region. When studying the process of plastic deformation of porous blanks, the model of a rigid-plastic isotropic-strengthening porous body with a loading surface that has the shape of an ellipsoid with semi-axes. It depends on the amount of porosity and the ratio of the associated flow law as a mechanical model of the material. In the axisymmetric extrusion of porous blanks, the viscoplasticity method was used to determine the field of flow velocities based on the results of experimental studies. R-functions were applied to approximate experimentally obtained values. The problem of finding approximations was formulated in a variational statement. Cubic splines of one argument were used to interpolate functions. As a result, an approach was proposed, which consists of a particular sequence of calculating the derivatives of the coordinates of the nodes in time in combination with the R-functions approach. All the calculations were performed in Euler variables, eliminating the need to switch from Lagrangian variables and simplifying the solution. Additionally, this method allowed for working with an irregular and non-rectangular grid in areas with any shape of boundaries. This approach is more effective from the point of view of the approximation’s accuracy and the speed of calculations. Finally, the equation for calculating the porosity in the volume of the deformable workpiece based on the information about the distortion of the dividing grid elements was obtained. For stationary axisymmetric processes, a technique was developed that allowed for replacing the calculation of the accumulated deformation of the base material along the deformation trajectory by integration over the region. A technique was developed for determining the stress-strain state at unstable and stable stages of axisymmetric plastic deformation of porous blanks. The calculation results were compared based on the proposed experimental and calculation techniques and the finite element method.