PSI - Issue 5

G. Lesiuk et al. / Procedia Structural Integrity 5 (2017) 904–911

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Lesiuk et al./ Structural Integrity Procedia 00 (2017) 000 – 000

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fatigue crack propagation proposed by Correia et al. (2013), based on the local strain approach to fatigue, aiming the determination of the fatigue crack propagation life for a structural detail. This model is well known in literature as a UniGrow model. It based on the following assumptions (according to Noroozi et al., 2007):  The material is composed of simple particles of a finite dimension  that represents the elementary material block size, below which material cannot be regarded as a continuum (see Fig. 2),  The fatigue crack tip is supposed to be equivalent to a notch with radius    The fatigue crack growth process is considered as representing successive crack increments (after N f cycles) due to crack re-initiations over the distance  .

(a)

(b)

Fig. 2. Crack configuration according to the UniGrow model: (a) crack and discrete elementary material blocks; (b) crack shape at the tensile maximum and compressive minimum loads (Noroozi et al. 2005, 2007). According to above - the fatigue crack growth rate can be determined as = ∗ . (9) From the energy point of view, this assumption is well described by the critical surface energy parameter  . The energy description incorporated to the Noroozi concept is clearly to understand when the damage energy  necessary for elementary act of fatigue crack growth on the material block  * can be divided into two components (in case of fatigue loading) Γ = + , (10) where the W c represents a part of energy stored in cyclic loading (corresponds to the cyclic load alternations) and W s is a static component of the energy corresponded with the maximal value of loading. In this case, the crack will grow if the critical value of energy is reached Γ = Γ . (11) From the energy point of view, the proper kinetic fatigue fracture energy model introduction must always satisfy the first principle of thermodynamics + = + + Γ, (12) where: A – the work of external stresses, Q – the heat input to the body during the loading, W – a deformation energy after N cycles of loading, T – a kinetic energy of the body,  – a damage energy during the chang e of a crack surface after one “quantum” – elementary “bricks” in Norozii discrete model. After differentiating (12) over the number of cycles, assuming that a slow growth of a crack length does not go together with heat processes, and neglecting the small changes of a kinetic energy (for low frequencies of a cyclic loading) we obtain generalized formula of fatigue crack growth   =   +   . (13)