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 ¯K=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 Kmax, B, and σ0 vary to maintain ¯K = 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 R = Kmin/Kmax = 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.