Sickle‐shaped surface crack in a notched round bar under cyclic tension and bending

Abstract

A B S T R A C T A sickle-shaped surface crack, also called crescent-moon (or crescent) crack, is assumed to exist at the root of a circular-arc circumferential notch in a round bar under tension and bending. For different notch sizes (i.e. different values of the stress concentration factor), the stress intensity factor along the crack front is computed through a three-dimensional finite-element analysis. The effect of the stress concentration factor on the stress intensity factor values is examined for several crack configurations. Finally, the surface crack growth under cyclic loading is analysed through a numerical procedure that employs the stress intensity factor values obtained. Some results of the present study are compared with those by other authors. a = crack depth for point A on the flaw front a el , b el = semi-axes of the ellipse c = notch depth D = bar diameter in the reduced cross-section S-S D 0 = bar diameter in an unnotched cross section F = tension loading K I,F , K * I,F = stress-intensity factor (SIF) and dimensionless SIF, respectively, for tension K I,MX , K * I,MX = stress-intensity factor (SIF) and dimensionless SIF, respectively, for bending M X K t,F , K t,MX = stress-concentration factor (SCF) for tension (F) and bending (M X ), respectively M X = bending loading about the X axis SCF = stress-concentration factor SIF = stress-intensity factor α = a el /b el = aspect ratio of the elliptical-arc crack front δ = c/D 0 = relative notch depth σ F = nominal tensile stress (referred to the reduced cross section) σ MX = nominal maximum bending stress (referred to the reduced cross section) ρ, ρ d = ρ/D 0 = notch radius and dimensionless notch radius ξ = a/D = relative crack depth for point A on the flaw front ζ , ζ * = ζ /h = coordinate and normalized coordinate, respectively, of the generic point P along the crack front Correspondence: A. Carpinteri.

Induced out‐of‐plane mode at the tip of blunt lateral notches and holes under in‐plane shear loading

“…The problem of such vertex singularities, also called corner point singularities, is well documented in a number of papers covering the last 30 years (see, among others, Bažant and Estenssoro, 11 Pook, 12–14 She and Guo, 15 Yu et al 16 ). The same problem has recently been analysed for fatigue strength problems by Carpinteri et al, 17,18 Doquet et al 19 and Hutar et al 20 Hutar considered the effect of free surfaces on fatigue crack behaviour for relatively thick specimens, where the solutions by Benthem and Bažant for a semi‐infinite body remains valid. Later, dealing with thin structures, a detailed numerical investigation demonstrated that the effect of 3D stress distributions on crack behaviour remains an open problem of major interest in Fracture Mechanics 20 …”

Surface cracks in fatigued structural components: a review

“…As far as surface cracks emanating from notches in particular structural components are concerned, Erjian 112 determined the SIF in the case of circumferential cracks in notched round bars by using approximate analyses; Lin and Smith 113 and Carpinteri et al [114][115][116][117][118] used the finite element (FE) analyses to determine the mode I SIF for various notched structural components such as plates, 113 circumferentially notched round bars, [114][115][116] notched pipes and shells. 117,118 Other complex structural components containing stress raisers, such as welded joints, round bars and railway axels, were examined by Carpinteri et al, 119 Fonseca et al 120 and Madia et al 121 (in the last paper mentioned, a wide collection of SIF solutions is reported for various crack sites in T-notched and V-notched components).…”

Stress intensity factors and fatigue growth of surface cracks in notched shells and round bars: two decades of research work

“…Therefore, during the last two decades, the present authors have extensively examined the following cracked notched solids: double‐curvature shells (i.e. shells with two distinct principal curvature radii), such as pressure vessels, pipe elbows and fuel tanks; and round bars, such as bolts, screws, pins, reinforcements, tendons for prestressed concrete structures and supports in suspension and stayed bridges …”

“…By employing the aforementioned SIF results, the fatigue behaviour is examined. In particular, crack paths, crack growth rate curves and crack front evolutions are determined by employing a theoretical model and compared with some data available in the literature.…”