Thermal destruction of polymeric fibers in the theory of temporary dependence of strength

Abstract

Objectives. This study mathematically describes the mutual influence of micro- and macrostages of the process of destruction of polymer materials and determines its main parameters and limiting characteristics. In addition, a relationship is established between molecular constants characterizing the structure of a material and those characterizing its macroscopic characteristics of strength. Finally, theoretical representations of the thermokinetics of the process of thermal destruction of polymer fibers from the standpoint of the kinetic thermofluctuation concept are developed, which makes it possible to predict the thermal durability of a sample under thermal loading.Methods. The structural–kinetic thermofluctuation theory was used to describe the initial stages of the fracture process and to derive a generalized formula for the rate of crack growth. The mathematical theory of cracks is used to describe the thermally stressed state of a material in the vicinity of an internal circular crack under mechanical and thermal loadings of the sample.Results. A theoretical formula for the full isotherm of durability in the range of mechanical stresses from safe to critical, as well as a theoretical relationship for the time dependence of the strength of polymer fibers under purely thermal loading in the full range of heat loads from safe to critical and at the stage of nonthermal crack growth, is given. The main parameters and limiting characteristics of durability under thermal loading are also indicated.Conclusions. A generalized structural–kinetic theory of the fracture of polymer fibers under purely thermal action on cracked specimens is presented. The developed theory combines three independent approaches: structural–kinetic (thermofluctuation theory), mechanical, and thermodynamic. The obtained theoretical relations are of practical interest for the development of methods for localization, intensification, and control of the crack growth kinetics.