Parameters of elementary cells for analytical determination of thermoelastic shrinkage stresses in filled thermoplastics
The introduction substantiates the relevance of research. The purpose of this work is to create a method and determine the parameters of elementary cells for analytical determination of thermoelastic shrinkage stresses in polymer composite materials with dispersed spherical and fibrous cylindrical fillers. It is considered elementary cells in the form of a thick-walled hollow microspheres from the matrix (for powder filler) and thick-walled hollow microcylinder (for fibrous filler), in the cavities which are located in connection with interference corresponding spherical or cylindrical particles. In this case, the internal radius of the cavities of the microsphere or microcylinder is equal to the radius of the filler particle. Calculation schemes have been developed that ensure equality of the volume content of the filler in the composite and its elementary cells. Analytical expressions are obtained for calculating the size of elementary cells depending on the size and volume content of the filler. Based on the relationship between the volume and mass content of components in the composite, variants for calculating the parameters of elementary cells depending on the size and mass content of the filler are proposed. As an example, the calculation of the parameters of elementary cells for a wide range of degrees of filling of a number of commercially produced thermoplastics (low and high-density polyethylene, polypropylene, polystyrene, polyethylene terephthalate, polyamides PA6, PA12-10, P12, polycarbonate, polyalkanamide, polysulfone) with powder (glass microspheres) and fiber (glass and carbon fiber) filler is made. The possibility of extending the proposed method to materials with polydisperse filler is shown. At the same time, for each particle size of the filler, its unit cell size is determined from the condition for fulfilling the requirement to preserve the volume and mass content of the filler for the entire cell dispersion, which is equal to the average value for the entire volume of the composite. Research results can be used in research and educational activities.