A continual model of a damaged medium used for analyzing fatigue life of polycrystalline structural alloys under thermal–mechanical loading

  • Ivan A. Volkov
  • Leonid A. Igumnov
  • Francesco dell’Isola
  • Svetlana Yu. Litvinchuk
  • Victor A. EremeyevEmail author
Open Access
Original Article


The main physical laws of thermal–plastic deformation and fatigue damage accumulation processes in polycrystalline structural alloys under various regimes of cyclic thermal–mechanical loading are considered. Within the framework of mechanics of damaged media, a mathematical model is developed that describes thermal–plastic deformation and fatigue damage accumulation processes under low-cycle loading. The model consists of three interrelated parts: relations defining plastic behavior of the material, accounting for its dependence on the failure process; evolutionary equations describing damage accumulation kinetics; a strength criterion of the damaged material. The plasticity model based on the notion of yield surface and the principle of orthogonality of the plastic strain vector to the yield surface is used as defining relations. This version of defining equations of plasticity describes the main effects of the deformation process under monotone cyclic, proportional and nonproportional loading regimes. The version of kinetic equations of damage accumulation is based on introducing a scalar parameter of damage degree and energy principles, and account for the main effects of nucleation, growth and merging of microdefects under arbitrary regimes of low-cycle loading. The strength criterion of the damaged material is based on reaching a critical value of the damage degree. The results of numerically modeling cyclic thermal–plastic deformation and fatigue damage accumulation in heat-resistant alloys (Nimonic 80A, Haynes 188) under combined thermal–mechanical loading are presented. Special attention is paid to the issues of modeling the processes of cyclic thermal–plastic deformation and fatigue damage accumulation for complex deformation processes accompanied by the rotation of the main stress and strain tensor areas. It is shown that the present damaged medium model accurately enough for engineering purposes describes the processes of cyclic isothermal and nonisothermal deformation and fatigue damage accumulation under combined thermal–mechanical loading and makes it possible to evaluate low-cycle fatigue life of heat-resistant alloys under arbitrary deformation trajectories.


Modeling Thermal cyclic strength Complex deformation Damaged medium mechanics Fatigue life Strength Failure 



This work was supported by a grant from the Government of the Russian Federation (Contract No. 14.Y26.31.0031).


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Authors and Affiliations

  1. 1.Research Institute for MechanicsNational Research Lobachevsky State University of Nizhny NovgorodNizhny NovgorodRussian Federation
  2. 2.Dipartimento Ingegneria Strutturale e GeotecnicaUniversità di Roma “La Sapienza”RomeItaly
  3. 3.Faculty of Civil and Environmental EngineeringGdansk University of TechnologyGdańskPoland

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