PSI - Issue 37

Jesús Toribio et al. / Procedia Structural Integrity 37 (2022) 1029–1036 Jesús Toribio / Procedia Structural Integrity 00 (2021) 000 – 000

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1. Introduction Round bars under tensile loading are very common in structural engineering. They are used in many forms such as wires, rods, strands, tendons, chords, shafts, etc., and frequently suffer fatigue (cyclic loading) due to the transient and oscillating nature of the external load, stress corrosion cracking in the case of harsh environments or corrosion-fatigue when the synergistic effect of both cyclic (fatigue) loading and corrosive environment takes place. In all these cases a surface crack usually appears and such a crack grows by any of the described mechanisms (Rolfe and Barsom, 1977; Toribio and Lancha, 1995). Therefore, when fatigue crack propagation appears and changes in the crack aspect ratio take place, stress intensity factor (SIF) solutions at different points of the crack front are necessary to account for the SIF variation over the line of the crack (Si, 1990; Carpinteri, 1993; Shih and Chen, 1997; Lin and Smith, 1997; Lin and Smith, 1998; Couroneau and Royer, 1998). Such part through cracks usually have a typical semi-elliptical shape (the straight-fronted and the semi-circular shapes being the limit cases) so that a detailed knowledge is required of the SIF K at the different points of the crack front. This value has been computed many times in the past by different authors, usually in its dimensionless version, under tension, torsion and bending and using different procedures such as compliance methods, finite element methods (FEM), boundary integral equation methods (BIEM), and so on. This paper offers a detailed and critical review of present numerical solutions with regard to the SIF in transversely cracked round bars under tension in order to compare different solutions and elucidate which of them is the best from the fracture mechanics point of view. The election of the best SIF solution for a part-through crack in a round bar under tension will help in the understanding of fatigue and fracture phenomena in longitudinal structural elements working in tension. 2. Review of SIF solutions A cylinder (round bar) under tension loading with a transverse semi-elliptical surface crack (Fig. 1) is a case of 3D fracture mechanics. In this framework, the dimensionless SIF Y ( Y = K / σ√πa ; σ = 4 F /  D 2 ) in mode I depends on the crack depth, the crack aspect ratio and the position of the considered point at the crack line.

D

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Fig. 1. Crack characterization.

Valiente (1980) obtained two solutions at the crack center on the basis of a geometrical model of crack with straight front. The expressions of the dimensionless SIF depend only on the relative crack depth a / D , i.e., they are one parameter K -solutions (and thus they are valid only for the specific geometry under consideration, i.e., for a definite crack aspect ratio: the straight-fronted edge crack as the specific case analyzed). The first of the solutions proposed was numerically obtained by the finite element method on the basis of the computation, firstly, of the sample compliance, and secondly, the energy release rate on the basis of the former. It is a global K -solution valid for the entire crack as a whole. The expression of the dimensionless SIF is the following: