Mathematical modeling of single action pressing of powder materials under dry friction conditions

The paper presents a theoretical analysis of the single action pressing of powder materials featuring plasticity and compressibility. It takes into account dry external friction between the die material and side walls, which determines the strong nonlinearity of the problem considered. This problem has a number of features that complicate its numerical solution: the presence of external friction, the elastic-plastic law of material behavior description, as well as the calculation of large displacements and, as a consequence, strong geometric nonlinearity. To consider these features, a combination of Fleck–Kuhn–McMeeking and Gurson– Tvergaard–Needleman models was used to consider a wide range of changes in the porosity of materials. The numerical solution of the problem was carried out using finite element analysis with isoparametric elements. The increment of plastic deformations at each step was determined from nonlinear equations of plastic flow. Stresses at the Gaussian points were updated according to the specified increments of deformations to calculate the material behavior during deformation. Unknown density and strain values as functions of coordinate and time were calculated. The influence of the different height-to-diameter ratio of the blank and the value of external friction of the material stress-strain state and compaction kinetics were considered. The distribution of equivalent stresses and the value of volumetric plastic deformations in the material, as well as the nonuniformity of relative density at the end of the pressing period were studied. The theoretical analysis made it possible to study the basic compaction kinetics laws for powder materials with nonuniform density under conditions of dry friction on side walls. The results obtained are relevant for predicting possible negative changes in the blank geometry when implementing the single action pressing scheme for powder materials.