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.
Highlights
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
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 obtained theoretical relations are of practical interest for the development of methods for localization, intensification, and control of the crack growth kinetics
Summary
Разработать теоретические представления термокинетики процесса теплового разрушения полимерных волокон с позиций кинетической термофлуктуационной концепции, позволяющей прогнозировать термическую долговечность образца при его тепловом нагружении. Использована структурно-кинетическая термофлуктуационная теория для описания элементарного акта процесса разрушения и вывода обобщенной формулы скорости роста трещины и математическая теория трещин для описания термонапряженного состояния материала в окрестности внутренней круговой трещины при механическом и тепловом нагружениях образца. Приводится теоретическая формула полной изотермы долговечности в интервале механических напряжений от безопасного до критического, а также теоретическое соотношение для временной зависимости прочности полимерных волокон при чисто тепловом нагружении в полном интервале тепловых нагрузок от безопасной до критической и на стадии атермического роста трещины. Представлена обобщенная структурно-кинетическая теория разрушения полимерных волокон при чисто тепловом воздействии на образцы с трещиной.
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