Statistical Effects on Fatigue of Spring Materials

In this Chapter, we continue to study the stochastic influences on the fatigue life of springs. First, we evaluate the probabilistic effects that prevail at low amplitudes of cyclic stresses. The question is how to calculate the failure probability as a function of the stress amplitude. The answer to this question results from the study of experimental fatigue life data. The experimental data show different behavior in the regions of low and high stress amplitudes. To describe this phenomenon, we introduce the randomization of crack propagation, which is accompanied by the random deviation and branching of the crack. The randomization of crack propagation escalates with decreasing stress amplitude. The high inhomogeneity of the polycrystalline structure at the micro level hypothetically causes the random propagation. This hypothesis leads to the mathematical model of random crack propagation. The differential equation with stochastic coefficients describes the randomly propagating crack, which is analogous to the forced Brownian motion equation. Examples of solutions to the stochastic Brownian motion differential equation are presented. This Chapter is the final section of the last part of the book, which studies the life cycle of springs.