Volume formation of cylindrical product considering pressure

The widespread use of polymeric materials with different viscoelastic properties justifies the development of mathematical modeling of processes of products from these materials. Methods of investigation of the stress-strain state of polymer products with different geometries are developed in the solving of problems in various fields of engineering, electronics [1], construction [2], medicine [3], etc. In the papers [4-10] the mathematical models of polymer axisymmetric products formation are described in the implementation of the various polymerization reaction modes - volume, single-sided front, the front two-way front [11]. The volume mode is characterized by flowing of hardening reaction (temperature rise and deepening of polymerization degree) throughout the volume of the formed product. Front mode is noted for wave propagation (front) of hardening from one boundary surface of the product to another (single-sided frontal mode), or from the central region of the product to the boundary surface (bilateral front). Determining of the level of internal stresses is based on the use of the law of hereditary elasticity - Volterra integral equations written in tensor form. When considering the volume hardening mode [4] critical conversion depth of material was assumed to be zero. The critical conversion depth is the polymerized monomer concentration a = a(r,t), at which the determination of viscoelastic stresses and strains begins in a hardening material. In the analysis of the frontal regime [7-9], [11] there were considered the conditions of coexistence of solid and liquid regions of formed product. On the border of coexistence the complete stress tensor was set. Condition for the emergence of the solid part and its growth is to achieve a depth of polymerization of the critical value. A similar approach can be implemented in a volumetric reaction mode [10]. Determination of the dynamics of temperature and conversion fields is based on the heat equation and two kinetic equations for the degree of polymerization and crystallization. This paper presents a thermoviscoelasticity model of the polymeric cylindrical product formation in a volume mode of the hardening with nonzero critical conversion depth. The process of volume formation is characterized by the gradual deepening of the polymerization and the accompanying crystallization throughout the volume of the formed product. Borders of a solid layer and the moment of the hardening start are determined by the condition a(r,t) = a*, where a* - critical conversion depth. The stress-strain state of the formed product is determined by taking into account the pressure of the liquid layer to a formed solid part. The results of the numerical analysis of the formed product stress state and pressure of the liquid layer on the product solid part are presented and discussed.