13th International Conference on Fracture June 16–21, 2013, Beijing, China Figure 8: da/dN =f( ΔK) curve in mode I for the R5 steel (R= –1), in air and under sea water flow at room temperature. To assess the duration of the crack propagation phase, a corrosion pit was modeled by a hemispherical surface defect with radius R. The existence of these hemispherical pits was observed by scanning electron microscopy on the surface of different specimens of R5 steel with precorrosion in salt fog chamber (Figure 3a) and with corrosion in A3 sea water flow (Figure 7). The longitudinal cross section of a pre-corroded specimen (after 4.37×108 cycles under a stress amplitude of 370 MPa) close to the fracture surface was observed as illustrated in Figure 9a. This shows a short crack initiated at a corrosion pit. Based on this observation, an initial fatigue crack of depth aint emanating from the surface of the hemispherical pit and perpendicular to the loading direction due to intercristalline corrosion cracking was assumed. The length of the initial short crack emanating from hemispherical defects was assumed to be aint =10 µm (close to the grain size). According to the asymptotic approximation proposed by Paris et al [16] the crack tip stress intensity factor in mode I is: KI =σY ( x,ν) √πa , where x = a/R, ν is the Poisson ratio, and a function Y(x,ν) for a penny shape crack emanating from hemispherical surface crack [16] : Y( x/ν)=1.015[ A(ν) +B( ν)( x 1+x)+C(ν)( x 1+x) 2 +D(ν)( x 1+x) 3]( 2) (2) with: A( ν)=1.683+ 3.336 7−5ν ,B(ν)=−1.025− 12.3 7−5ν ,C(ν)=−1.089+ 14.5 7−5ν ,D( ν)=1.068− 5.568 7−5ν . It was assumed that the propagation of the fatigue crack is divided in three stages: (i) a short crack propagation during Na int −a 0 cycles, from initiation aint to the crack size a0, then (ii) a small crack propagation period Na 0−a i cycles, from a0 to the crack size ai, and (iii) a long crack propagation Na i−a cycles, from ai to the final crack size a: NTotal =Na int−a 0 +Na 0−a i +Na i −a .With these three different regimes the very quick propagation of short crack and the quick propagation of small crack compared to long crack were considered.
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