PSI - Issue 5

G. Lesiuk et al. / Procedia Structural Integrity 5 (2017) 904–911 Lesiuk et al. / Structural Integrity Procedia 00 (2017) 000 – 000

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(2014), Szata (2002) the review of each approach is performed. In the study performed by Ostash et al. (2007) the usefulness of the several models is discussed on the background of the kinetic fatigue fracture diagrams building basis.

Fig.1. Potential influence of R-ratio on the kinetics of fatigue crack growth, crack length history, lifetime of structural components, Szata and Lesiuk (2009)

According to this review, we can underline the three main ways of the KFFD constructions based on: force factors (  - stress based,  K-based), deformation criterions (  - strain based or CTOD, CTOA - based) or energy approach. The force criterion is strongly dependent from the linear elastic fracture mechanics – therefore  K is not always appropriate quantity when process of fatigue crack growth leads to the reduction of the non-cracked ligament of structural components. In this case we can observe the plasticization of the material large under limited loading. In this case, the application of the parameter K or its range ΔK for the description of the results is meaningless because the limitations of linear-elastic fracture mechanics are exceeded (Rozumek 2014). On the other hand, the deformation criteria are widely used in order to overcome the troubles of the FCGR description in case when the plastic zone before a crack tip is of the same order as a body dimension. As an example of the strain, deformation approach formula is the model proposed by Manson (1966): = (∆ √ ) (7) where: B and n are experimentally determined constants,  pl represents plastic strain range, a means the crack length. In the authors’ opinion the most physical approach is energy approach mainly based on fracture mechanics parameter – cyclic J or its range  J or another strain energy density parameter based on the energy irrevocably dissipated during the fracture process. Some fatigue fracture models are rewritten from Paris (1963) formula, one of example is model proposed by Dowling and Begley (1976): = (∆ ) . (8) 2. Energy description of fatigue crack growth process

2.1. Strain energy density H model formulation

The process of fatigue crack growth is associated with the formation of new crack faces. For this purpose the accumulation process of energy is activated. Therefore, the dissipation of damage energy should be associated with the fatigue crack-growth rate. In several concepts based on model proposed by Noroozi et al. (2005, 2007) to model