PSI - Issue 39

J.M. Alegre et al. / Procedia Structural Integrity 39 (2022) 148–156 Author name / Structural Integrity Procedia 00 (2021) 000–000

151

4

σ ∆ , the stress-intensity factor ranges at the vertices of the elliptical

For a fatigue load defined by the stress range

crack are obtained as:

1 (3) Using these SIF values, and assuming a Paris type fatigue crack growth, da/dN = C· ( ∆ K ) m , the crack advance of the vertices of the ellipse can be obtained after a defined block of cycles as: ( ) ( ) ( ) 1 1 2 2 ; ; m m m a a c a N C K a N C K c N C K ∆ = ∆ ⋅ ⋅ ∆ ∆ = ∆ ⋅ ⋅ ∆ ∆ = ∆ ⋅ ⋅ ∆ (4) where C and m are the Paris law coefficients, ∆ N is the desired number of cycles per block (e.g., ∆ N = 1000 cycles) defined by the user. Finally, the new crack size and crack position are updated by means of: ( ) 1 2 2 2 new a a a a 1 2 2 ; ; a a a a c c K F ∆ = ⋅ ∆ ⋅ a K F ∆ = ⋅ ∆ ⋅ a K F ∆ = ⋅ ∆ ⋅ a σ π σ π σ π

2 2 = + ∆ + ∆ = + ∆ = − ∆ c c

(5)

2

c

new

new h h a

1

The whole procedure is repeated, updating the crack shape for each block of cycles, until the failure condition is reached, or the desired number of cycles is completed. An example of the application of the sequential methodology, using the present SIF solutions, is presented Figure 3.

Fig. 3 Experimental and predicted fish-eye fatigue crack growth initiated from an internal defect on a round bar subjected to uniaxial tensile load.

4. Prediction of the fatigue crack shape An interesting fact observed for this geometry is the preferential trend of the crack to propagate toward a circular shape pattern, known as fish-eye , independently of the aspect ratio of the initial defect. This fact is also observed experimentally, as presented in Figure 4, where the irregular initial crack shape quickly develops to a circular crack. The analysis presented in this paragraph corresponds to a specimen of radius 3 R mm = , subjected to a uniaxial stress load of 0 200 MPa σ = , and with an initial flaw in the position 0 0 ( 2 / 3 ) 2 a h R mm + = = . The fatigue crack growth law is defined using a Paris equation with material parameters, C = 2.99 ·10 -8 and m = 3 (units in mm/cycle and MPa·m 1/2 ), typical for a Ti6Al4V alloy fabricated by Selective Laser Melting (Jiao et al., 2017). Figure 5 shows this preferred trend for various initial elliptical cracks with different aspect ratios, from a circular shape ( 0 0 / 1 a c = ) to a very elongated shape ( 0 0 / 0.2 a c = ) and assuming an initial crack size of 0 0.05 a mm = . A quick trend to a circular crack shape is observed, regardless of the shape of the initial crack. This trend is faster the smaller the initial flaw and the more centered on the specimen.