A Methodology for Predicting Variability in Microstructurally Short Fatigue Crack Growth Rates

Abstract

A finite element model, which implements single crystal constitutive relationships, was used to simulate fatigue cracks growing at the microstructural level. Plastic deformation (slip) was allowed along two specified microscopic crystallographic planes. As the orientations of the slip systems were changed several crucial fatigue crack growth parameters, measured over all possible orientations, were found to vary: (1) crack tip forward slip band size, rp , 0.03 ≤ rp /(Kmax /λo )2 ≤ 0.31 where λo is the critical resolved shear stress on a slip system, (2) crack opening displacement, δ, 1.2 ≤ δ/(Kmax 2 /Em σo ) ≤ 7.8 where Em and σo are the elastic modulus and yield stress of a polycrystalline material with many randomly oriented double slip crystals, and(3) crack closure level, Sopen /Smax , 0.02 ≤ Sopen /Smax ≤ 0.35. Corresponding to these differences in crack growth parameters, crack growth laws were used to estimate the expected changes in crack growth rates when microstructurally short cracks grow through grains with different crystallographic orientations. The resulting predictions form approximate upper and lower bounds on crack growth rates for microstructurally short cracks. For several different materials, the crack growth rate variability predictions were in the range 7 ≤ (da/dN)(max)/(da/dN)(min) ≤ 37, which is consistent with experimentally measured variations.