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Rheological-Dynamical Theory of Visco-Elasto-Plasticity and Fatigue: Part 1

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This paper is concerned with a new proposal regarding the analysis of visco-elasto-plasticity and fatigue and is based on rheological-dynamical theory. Due to the analogy between rheological model and dynamical model with viscous damping, it becomes obvious that inelastic response of members is essentially a dynamical problem. An analytical rheological-dynamical visco-elasto-plastic solution of one-dimensional longitudinal continuous vibration under loading and solution for the stress relaxation as unloading have been developed and used to obtain the fatigue limit of thin long bars. Rheologic behavior of the bar can be characterized by one parameter, i.e. dynamic time of retardation TKD=1/ω, like in a single-degree-of-freedom spring mass system. In all inelastic strains time rate effects are always present to some degree. Whether or not their exclusion has a significant influence on the prediction of the material fatigue behavior depends upon several factors like: maximum absolute stress in the cycle, coefficient of asymmetry of cycle, creep coefficient, slope of the strain hardening portion of the stress-strain curve, relative frequency and uniaxial yield stress. This paper provides description of dynamic magnification factor, relaxation of stress, stress concentration and the fatigue limit of thin long symmetrical bars.


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