Energy Version of the Kinetic Equations of Isothermal Creep and Long-Term Strength
V. P. Radchenko, M. N. Saushkin, S. V. Gorbunov
Samara State Technical University, Samara, 443100 Russia
Keywords: kinetic equations, metal materials, plasticity, creep, softening, long-term strength, viscoelastic material, Lyapunov stability, third stage of creep, computational algorithm stability
Abstract
Energy-type kinetic equations of inelastic rheological deformation are proposed in which the elastic, plastic, and creep strains are the additive components of the total strain, and the damage parameter is taken into account. A model of viscoelastic material with a creep kernel of exponential type is considered. The Lyapunov stability of solutions under constant stress is studied. The stability range of the solutions of the differential equations of the mathematical model corresponding to asymptotically bounded creep is established. It is shown that the instability range of the solutions corresponds to the onset of the third stage of creep. The relationship is determined between the Lyapunov stability of the solutions and the stability of the computational algorithm for the numerical solution of the system of equations. The proposed model is experimentally verified. It is shown that the calculated and experimental data are in good agreement.
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