13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- Figure 12. Short crack emanating from a surface defect in the form of void created by a previous inclusion in cold drawn steel. Fatigue crack propagation from left (surface defect) to right The dimensionless SIF Y employed is that calculated by Astiz [21], for the central point of the crack front by using the finite element method, which depends on the relative crack depth a/D and the aspect ratio a/b through the coefficients Cij (Table 2), i j 4 3 ij 0 0 1 = = ≠ = ∑∑ i j i a a Y C D b (4) Table 2. Coefficients Cij of Eq. (4) taken from ref. [21] i j=0 j=1 j=2 j=3 0 1.118 -0.171 -0.339 0.130 2 1.405 5.902 -9.057 3.032 3 3.891 -20.370 23.217 -7.555 4 8.328 21.895 -36.992 12.676 Solution of equation (3) was obtained in incremental form, the convergence being guaranteed by the adequate choice of the crack increment Δa (sufficiently low). The number of cycles associated with crack initiation Ni can also be estimated as follows [17, 18], i f p = − N N N (5) where the common definition of initiation in reality pertains to both nucleation and propagation of microcracks [22]. Table 3 shows the fatigue life Nf experimentally obtained for a stress range about half of the yield strength of each material. In both the hot rolled bar and the cold drawn wire the life is around 300000 cycles, which indicates that the cold drawing process improves the fatigue performance in a similar way that the increase of material strength. In addition, the main part of the fatigue life (measured as number of cycles) is associated with the propagation phase in the hot rolled bar and with the initiation phase in the cold drawn wire. Table 3. Fatigue life Nf (experimental, average of five tests), number of cycles for propagation Np (obtained by simulations) and number of cycles for initiation Ni (Ni = Nf – Np) Steel Δσ (MPa) Nf (cycles) Np (cycles) Ni (cycles) Hot rolled bar 347 308200 253700 54500 Prestressing steel wire 790 312910 57655 255255
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