13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- Fatigue life Nf was experimentally obtained by means of Whöler tests. The experimental results corresponding to prestressing steel are similar as those previously obtained by Beretta and co-workers [3, 4]. In addition, a numerical estimation was made of the number of cycles needed for crack propagation Np, on the basis of a simple model previously used by other authors in the scientific literature [17, 18], considering that it follows the Paris law [19], m d d = ∆ a C K N (1) and the stress intensity range ∆K is given by, π σ ∆ = ∆ K Y a (2) where Y is the dimensionless stress intensity factor (SIF). The number of cycles for propagation was calculated by following expression derived from the Paris law, C 0 p m m/2 m m/2 1 a a da N C Y a σ π = ∆ ∫ (3) where a0 and aC are respectively the initial and the final crack sizes, the first associated with the fatigue threshold [2] and the latter with the critical instant of failure (KImax=KIC, according to the local fracture criterion) and the path followed by the crack during propagation is that plotted in Fig. 11. During its growth, the fatigue crack exhibits an elliptical shape in the Paris regime. 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.0 0.2 0.4 0.6 0.8 1.0 a/b a/D Hot rolled bar Prestressing steel wire Figure 11. Geometrical changes in the crack front during fatigue crack propagation The crack front was characterized as an ellipse with semiaxes a (crack depth) and b, its centre been at the wire surface. On the basis of the experimental tests [11] and extrapolating for small crack sizes where the crack front exhibits a quasi-circular appearance (Fig. 12), a relationship was obtained between the relative crack depth (crack depth divided by the diameter, a/D) and the aspect ratio (ratio between the semiaxes of the ellipse, a/b), Fig. 11. The size effect appearing in the steel samples was taken into account during the propagation phase because it changes the geometric evolution during fatigue. In a previous research work, Shin and Cai [20] observed how when the sample diameter decreases, the fatigue crack growth rate (FCGR) changes at the crack surface when compared with the same value at the crack centre, whereas for higher diameters the FCGR (represented by the Paris law) is the same at the centre and the surface. The aforesaid size effect affects how the crack front evolves (and thus the crack aspect ratio).
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