A consideration on stable growth of a ductile crack in a center cracked plate of 70/30 brass

Abstract

The deformation of a ductile crack and the strain distribution in the vicinity of the crack tip were investigated in order to study the stable growth process of a crack in a center-cracked plate of 70/30 brass. Specimens which have a short fatigue crack in its center were prepared so that the outer boundaries of the specimens did not disturb the substantial characteristics of the strain distribution near the crack tip. The distribution of strain, ϵ y , in the tensile direction near the crack tip is approximately expressed by the following equation regardless of the crack length, a. ϵ y ≅ C 1 ϵ f ( a/ r) b ( C 1 = 0.10 ~ 0.13, b = 0.4 ~ 0.5, 0.01 < r/ a < 0.5) where ϵ f is the fracture ductility in the tensile test of a round bar and r is the distance from the crack tip. The crack opening displacement, δ( x), near the crack tip has a unique correlation with the distance, x, from the crack tip, that is, δ( x) ∝ x/ a. These two equations imply that the following equation holds between the rate of crack growth, d a, due to the increase in external loading and the crack length, a, i.e. d a/d ϵ 0 ∝ a, where ϵ 0 indicates the external average strain defined by a gauge length of 20 mm.