Abstract
In ductile metals, plasticity-induced closure of fatigue cracks often retards significantly measured crack growth rates in the Paris regime and contributes strongly to the observed R-ratio effect in experimental data. This work describes a similarity scaling relationship based on the 3D small-scale yielding framework wherein the thickness, B, defines the only geometric length-scale of the model. Dimensional analysis suggests a scaling relationship for the crack opening loads relative to the maximum cyclic loads (Kop/Kmax) governed by the non-dimensional load parameter ) governed by the non-dimensional load parameter = Kmax/σ0 √B, i.e., a measure of the in-plane plastic zone size normalized by the thickness. Both Kop and Kmax refer to remotely applied values of the mode I stress-intensity factor. Large-scale, 3D finite element analyses described here demonstrate that Kop/Kmax values vary strongly across the crack front in thin sheets but remain unchanged when values vary strongly across the crack front in thin sheets but remain unchanged when Kmax, B, and σ0 vary to maintain = constant. The paper also includes results to demonstrate that the scaling relationship holds for non-zero values of the T-stress (which affect the Kop/Kmax values) and for an overload interspersed in the otherwise constant amplitude cycles. The present results focus on values) and for an overload interspersed in the otherwise constant amplitude cycles. The present results focus on R = Kmin/Kmax = 0 loading, although the scaling relationship has been demonstrated to hold for other = 0 loading, although the scaling relationship has been demonstrated to hold for other R > 0 loadings as well. The new similarity scaling relationship makes possible more realistic estimates of crack closure loads for a very wide range of practical conditions from just a few analyses of the type described here.
