Abstract
The article presents a mathematical model for the phenomenon of fatigue accumulation in the slender bar subjected to lateral bending. The model is based on the Euler-Bernoulli type bar, a bi-linear elastic-plastic model and, for simulation of fatigue, a system of equations describing the decrease resistance parameters of the material: the ultimate strain and stress. In the article is exposes the bar response to two types of dynamic loads, as well as a fatigue test simulating process using the proposed model, which results in the Wöhler diagram of the material for the bending vibrations. The conclusions outline the outlook of the model as well as its shortcomings. The author expounds the advantages of the model, but the reader is also challenged to reflect on the opportunity of using mathematical models of great complexity.
Highlights
Mathematical modelling in the field of material fatigue occupies a central place in the literature dedicated to this problem
Starting from the elementary mathematical model of the S-N curve, known as Wöhler curve, [1], up to contemporary mathematical models based on differential equations and partial and even more complicated derivatives, [2,3,4,5], [8,9,10,11], the purpose of mathematical modelling in this area was to predict the ceding of materials or to specify a period of time during which the material will not yield under certain conditions, or will yield with a very low probability
The mathematical model of the accumulation of fatigue in the material of the bars subject to the bending vibrations appears as a natural development of the models published by the author, [6], [7]
Summary
Mathematical modelling in the field of material fatigue occupies a central place in the literature dedicated to this problem. The model presented in these article attempts, with simple means, to adapt to the problem of materials fatigue, mathematical models developed to simulate the memory of materials or mathematical models of materials that change their qualities during operation, [6,7]. The results presented in this article represent a stage of development towards models that consider two-dimensional and three-dimensional structures. It is the application of the model in structural analysis programs that work through different numerical methods
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