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

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 Nf=A(Δε—Δε0)γ or Nf=A(Δε)Ψ(Δε—Δε0)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 Nf=NTR1/c exp δRα; at lower strainranges it is Nf=NTR1/b exp δRβ, where NT 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. Copyright © 1979, Wiley Blackwell. All rights reserved