13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- 3. Results and discussion 3.1. Fatigue crack growth modeling The stress intensity factor for the studied specimen implemented in AFGROW code depends on several parameters and is given by Eq. 1. ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ Δ = r a a K β π σ . . (1) where β is the geometry correction factor is expressed below (Eq. 2): 4 3 2 1 0.15 3.46 4.47 3.52 λ λ λ λ β + − ⎟ = − + ⎠ ⎞ ⎜ ⎝ ⎛ r a (2) where: ( ( )) a r/ 1/ 1 = + λ The interest model is NASGRO model when totality of fatigue crack growth curves is considered. Nasgro model are expressed bellow (Eq. 3): q crit p th n K K K K K R f C dN da ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ − ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ Δ Δ − ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎟Δ ⎠ ⎞ ⎜ ⎝ ⎛ − − = max 1 1 1 1 (3) f present the contribution of crack closure and the parameters C, n, p, q were determined experimentally and ΔKth is the crack propagation threshold value of the stress–intensity factor range. For constant amplitude loading, the function f was determined by Newman [28] (see Eq. 4). ( ) { 0≥ = MaxR,A +AR+AR +AR R K K f = 3 3 2 2 1 0 max op (4) Crack growth parameters of Nasgro model for both materials are presented in Table 3. Table 3. Parameters of Nasgro model for Al-alloys Al-Alloy ΔKtho MPa m KIC MPa m KC MPa m n p q C 2024 T351 2.857 37.36 74.72 3 0.5 1 1.707×10-10 6061 T6 3.846 28.57 50.0 2.3 0.5 0.5 0.840×10-10 3.2. Residual stress effect on fatigue crack growth The variation of the fatigue crack growth rate (FCGR) as a function of the amplitude of the stress intensity factor ΔK through residual stresses fields obtained for different preload levels for 2024 T351 Al-alloy is shown in Figure 11. The result shows that FCGR depends on the magnitude of the compressive residual stresses developed at edge of hole.
RkJQdWJsaXNoZXIy MjM0NDE=