Issue 31

J.A.F.O. Correia et alii, Frattura ed Integrità Strutturale, 31 (2015) 80-96; DOI: 10.3221/IGF-ESIS.31.07 82 - The fatigue crack growth results from a process of successive crack increments due to crack re-initializations over the distance ρ* . Thus, the fatigue crack growth rate can be established according the following relation: f N ρ dN da *  (1) where N f is the number of cycles required to fail the material representative element, which can be computed using a fatigue damage relation such as the so-called strain-life relations. (a) (b) Figure 1: Crack configuration according to the UniGrow model: a) crack and the discrete elementary material blocks; b) crack geometry at the tensile maximum and compressive minimum loads [1]. Noroozi et al. [1] suggested the use of a strain-life relation based on Smith, Watson and Topper fatigue damage parameter [8]:       c b f f f b f f N ε σE N σ SWT ε σ         2 ' ' 2 ' 2Δ 2 2 max (2) Alternatively, Peeker and Niemi [12] in a similar approach for the fatigue crack propagation suggested the use of the Morrow’s equation [7] to compute the failure of the material representative element:     ' 2 ' 2 2 b c f m f f f N N E           (3) The Morrow’s equation was derived from the Coffin-Manson relation [6, 7] of the material, and allows mean stress effects to be accounted for:     c f f b f f N ε N E σ ε 2 ' 2 ' 2 Δ     (4) SWT-life equation, Eq. (2), was originally derived by the multiplication of the Coffin-Manson Eq. (4) by the Basquin relation [21] available for a stress R -ratio equal to −1:   b f f N σ σ σ 2 ' 2 Δ max    (5) In the previous two equations, f σ ' and b represents, respectively, the fatigue strength coefficient and exponent; f ε ' and c represents, respectively, the fatigue ductility coefficient and exponent and E is the Young modulus. The maximum stress, σ max , mean stress, σ m , and the strain range,  ε have to be evaluated as the average values at the elementary material block size, ρ* , taking into account an elastoplastic analysis. To compute the elastoplastic stresses and strains at the elementary material blocks ahead of the crack tip, Noroozi et al. [1,10] proposed the following analytical procedure: - The elastic stresses are computed ahead of the crack tip, using the Creager-Paris solution [22] for a crack with a tip radius ρ* , using the applied stress intensity factors.