An expression for fatigue life and probability distribution of fatigue strength under repeated torsion

Abstract

An expression for the fatigue life under repeated torsion (torsion fatigue) is developed and checked by using the test results of metals in the available literature. The shear fatigue strength coefficient, A′, and the theoretical shear fatigue limit, τ ac , in the expression mentioned above are the material constants. The statistical analysis of the data of A′ and τ ac obtained from the regression analysis of test results shows that A′ and τ ac follow the log-normal distribution and that τ ac also follows the normal distribution. Using the expression for the torsion fatigue life developed in this study and the distribution of A′ and τ ac , one can easily obtain the expressions for the torsion fatigue life with given survivability, which are in good agreement with test results. The probability distribution of the shear fatigue strength can also be obtained from the above-mentioned expression and the distribution of A′ and τ ac . It is shown that the shear fatigue strength follows a log-normal distribution in the medium and long-life region. Therefore, the log-normal distribution of the shear fatigue strength can be applied in the fatigue reliability assessment of elements subjected to repeated torsion.