INVERSION OF THE STRAIN‐LIFE AND STRAIN‐STRESS RELATIONSHIPS FOR USE IN METAL FATIGUE ANALYSIS

Abstract

Abstract— Two methods are described for inverting the strainrange/life and strainrange/stressrange equations commonly used in fatigue analysis in order to obtain closed‐form expressions for life and stressrange in terms of strainrange. In the Collocation approach the form used is N f = A (Δε—Δε 0 )γ or N f = A (Δε)Ψ(Δε—Δε 0 )γ. In the Spline‐Function approach the curve is divided into two regions. At strainranges above where the elastic and plastic lines intersect the equation is N f = N T R 1/c exp δ R α; at lower strainranges it is N f = N T R 1/b exp δ R β, where N T is transition life, R is strainrange normalised to transition strainrange, and b, c , α, β, δ are constants determinable from the constants of the equation to be inverted. Similar expressions are derived for the cyclic stress/strain curve in terms of the same constants. The methods are illustrated by an example, and found to have close conformity to the basic equations to be inverted.