13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- As discussed in the results section, the cyclic crack growth behavior of the Ti foils could be described by the Paris relation between cyclic fatigue crack growth rate (da/dN) and applied stress intensity, �K : m da C K dN = ∆ (1) C and m are obtained from a linear curve fit to the experimental data. For a single-edge-notched specimen, the applied stress intensity range, ΔK, is related to the far field stress amplitude, �� and the crack length, a, by K Y a σ π ∆ = ∆ (2) Y is a geometry correction factor defined in terms of the ratio of the crack length a to the specimen width w. The determination of the geometry correction factor depends on the specimen’s geometry and the applied loading type. For a single-edge-notched specimen, Y is given by 2 3 4 1.12 0.231 10.55 21.72 30.39 a a a a Y w w w w = − + − + (3) Figure 3. FEM models of the foil specimen. (a) FEM model of unloaded foil specimen. (b) Foil specimen under a uniform stress, which represents the condition used for the intensity factor given by Eq. 3. (c) Foil specimen loaded through the face-loaded grips with a uniform displacement u2 boundary condition is applied along the right grip. Correction of the effective stress intensity factor Eq.3 is limited to loading configurations which can provide a uniform stress throughout the specimen cross section. In the present investigation, the foil specimen is constrained to move parallel to the applied tensile load by the linear bearing; this most closely represents a fixed-displacement end condition. The application of Eq. 3 to a fixed-end displacement loading configuration can overestimate the applied stress intensity factor [15]. The center line of the specimen shift can cause a bending moment which increases the applied Mode I stress intensity factor. This overestimation is of particular importance as a crack grows and the
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