A Mathematical Model Describing the Variation in Material Properties

Abstract

A mathematical model that describes the variation in material properties with time under a load is proposed. The material properties are considered at thermodynamic and structural levels. At the thermodynamical level, the free energy function is additively decomposed in the time parameter into terms that describe the history of loading of the body and its current parameters. At the structural level, damage as a scalar internal variable is used. The relations derived are analyzed for modeling and practical applications Keywords: mathematical model, damage, variation in material properties Introduction.To analyze the behavior of highly stressed structural members after failure, it is necessary to use fracture mechanics [10,11,16] or damage mechanics [2,12,18].Currently, the service life of engineering objects is estimated taking into account the evolution of the internal structure of the material. This structure changes its parameters under the action of external mechanical, thermal, and chemical factors [2]. This circumstance is one of the physical factors restricting the application of engineering models of delayed fracture (fatigue) in which the kinetics of fracture is determined by the variation of external factors with time.The accumulation of structural changes in a material under external loads is a multiscale and multistage kinetic process. It develops at different scales: atomic, dislocation, substructural, and structural. This necessitates combining micro-, meso-, and macroscopical model descriptions of the process, taking into account wave effects that may occur during dynamic changes of the structure [2,15,20]. The process is multistage in the sense that as structural changes occur, the material goes through sequential states, each characterized by its individual regularities and nonlinearly depending on the history of service of the object.All these phenomena cause variation of the rheology of the materials of parts and assemblies with time, i.e., change of the effective properties of the materials. Therefore, reliable prediction of the service life of parts and assemblies, assessment of the remaining service life, and revealing of the cause of failure of structural members are impossible without adequate mathematical models that describe the dominating structural processes occurring in individual service conditions of the object. Analysis of Alternative Descriptions of the Change of the Service Properties of an Object.External loads change the internal structure and the behavior of the material in service conditions, i.e., the response of the object. It is of importance to allow for the time-dependent rheological parameters of the materials (chronorheological properties) of parts and assemblies.There are three lines of study into the kinetics of structural changes and their effect on the chronorheological properties of metal systems: (i) study of the physical aspects of the structural changes in materials under external loads [2]; (ii) experimental study and description of metal systems in the context...

Assessment of elliptical defect dimensions influence on the metal structure contact strength properties

“…, in which the force load is applied. A mathematical model of a spatially nonlocal continuum body is provided in [6]. As a result of force loads, a stress state is formed in a body, which is characterized by tensor 𝜎 �(𝑥), x ϵ X.…”