In the present Chapter, we continue to study the stochastic influences on fatigue life of springs. At first, we evaluate the probabilistic effects prevailing at low amplitudes of cyclic stresses. The question is the calculation of failure probability as the function of stress amplitude. The answer to this question results from the examination of the experimental fatigue life data. The experimental data demonstrate different behaviors in the regions of low and high amplitudes of stress. To describe this phenomenon, we introduce the randomization to the crack propagation, which accompanies by the accidental deviation and branching of crack. The randomization of crack propagation escalates with the reducing stress amplitude. The high inhomogeneity of the polycrystalline structure on the micro level cause hypothetically the random propagation. This hypothesis leads to the mathematical model for the randomly propagating crack. The differential equation with stochastic coefficients describes the randomly travelling crack. This equation is analogous to the equation of the enforced Brownian motion. The examples of the solutions for the Brownian stochastic differential equation are presented. This Chapter is the final section of the last part of the book, which studies the lifecycle of springs.
Statistical Effects on Fatigue of Spring Materials
Durability of Springs ; Kapitel : 12 ; 373-417
2021-02-25
45 pages
Aufsatz/Kapitel (Buch)
Elektronische Ressource
Englisch
Springer Verlag | 2021
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