13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- behavior). These results support that uniaxial tension-compression straining is more detrimental than cyclic shear, by a factor of nominally two or greater on life. Fatigue crack nucleation rather than fatigue crack growth seems particularly influenced for Rε = 0 and Rε = 0.5, which suggests that crack nucleation assisted by stress concentration (e.g., notch, pore, or inclusion) might exhibit a reduced dependence on the strain ratio. Furthermore, tension-compression fatigue life results seem to show slightly less variability, and for both displacement conditions, the variability seems to increase with decreasing strain ratio. Figure 4 presents an example of the stress-strain evolution for one realization in tension after 20 straining cycles for three different strain ratios. As expected, higher strain ratios lead to higher tensile mean stresses. The mean stress evolves slowly and after 20 cycles the change is less 10%; therefore we may consider that the fatigue life estimations are performed at a relatively stable mean stress level for each strain ratio. Even when mean stress assessed may differ from a fully relaxed state, the fatigue model was calibrated under similar conditions [1], which reduces the inaccuracies. 3.3 Crack growth vs cycles for notched specimens Figure 5 presents the simulation results for three strain ratios using models with a notch root radius of 144 µm and a similar microstructure. Compared to the smooth specimens, the results from models with a notch show a reduction in fatigue life of about an order of magnitude. As expected, the lower the strain ratio, the larger the fatigue life, while tension-compression simulations resulted in lower lives than shear loading. However, the separation in life between tension-compression and shear cases increases with decreasing strain ratio, which was not clearly observed in simulations with smooth specimens. Note that the cracks for the shear case did not nucleate at the notch, but grew in the bulk of the specimen. The computed results for tension-compression, which nucleated the crack at the notch, lie within two orders of magnitude on life. In the case of shear loading, the life is longer and exhibits greater scatter as the cracks formed in the bulk of the specimen. Figure 3. Comparison of the results for strain ratios Rε = 0, Rε = 0.5 and Rε = -1 using simulations with unidirectional periodic conditions undergoing an equivalent nominal strain range of 0.8%.
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