Issue 48

L. Reis et alii, Frattura ed Integrità Strutturale, 48 (2019) 318-331; DOI: 10.3221/IGF-ESIS.48.31 321 the authors proposed a strain-based criterion [17], with two strain parameters, depending on the type of fatigue crack nucleation and growth, given in Eq. (7) and Eq. (8). For A type cracks: ቀ ∆ఊ ௚ ቁ ௝ ൅ ቀ ఌ ೙ ௛ ቁ ௜ ൌ 1 (7) For B type cracks: ∆ఊ ଶ ൌ . (8) where ∆γ is the shear strain range and g, h and j are material properties that must be determined experimentally. The same authors proposed a simplified formulation for A type cracks, which is given in Eq. (9). ∆ఊ ೘ೌೣ ଶ ൅ ∙ ∆ ௡ (9) where ∆γ max is the maximum shear strain range in a plane θ, ∆ε n is the normal strain, in the plane of maximum shear strain, and S is the normal strain effect coefficient and is a material parameter. Fatemi-Socie Fatemi and Socie [18] (F-S) prosed a critical plane criterion that, compared to Brown-Miller’s model, uses a normal strain parameter instead of the normal strain. The damage parameter is calculated using Eq. (10). ൤ ∆ఊ ೘ೌೣ ଶ ∙ ൬1 ൅ ∙ ఙ ೙,೘ೌೣ ఙ ೤ ൰൨ ୫ୟ୶ ഇ (10) where σ n,max is the maximum normal stress in the plane of maximum shear strain amplitude, σ y is the monotonic yield stress and k is a sensitivity parameter, that depends on the stress level. When a loading has mean stress, the damage parameter is calculated as shown in Eq. (11). max ఏ ൤ ∆ఊ ೘ೌೣ ଶ ∙ ൬1 ൅ ∙ ఙ ೙ೌ ାఙ ೙೘ ఙ ೤ ൰൨ (11) where ௡௔ is the normal stress amplitude and ௡௠ is the normal mean stress, both calculated in the plane with the maximum shear strain amplitude. Smith-Watson-Topper Smith et al. [19] developed a model, usually referred as the SWT model, to account the mean stress effect in uniaxial fatigue loading conditions. Later on, Socie [20] used a critical plane approach to extend the usage of this model in multiaxial loading conditions. In these conditions, the damage parameter is given by Eq. (12). max ఏ ሺ ௡ ሻ ∙ ∆ఌ భ ଶ (12) where ௡ is the normal stress on a plane θ and ∆ ଵ is the principal strain range in that plane.