Issue 37

N. Zuhair Faruq, Frattura ed Integrità Strutturale, 37 (2016) 382-394; DOI: 10.3221/IGF-ESIS.37.49 384             b c f a f f f N N G ' 2 ' 2          (2) In Eq. (2) the functions  ’ f (  ) ,  ’ f (  ) , b(  ) , c(  ) are fatigue constants that described above but need to be calibrated in terms of rho.  is the critical plane stress ratio and it is defined according to Eq. 3, [10]. n m n a n a a , , ,max          (3) In Eqs. (3) ߪ n,m and ߪ n,a are the mean value and amplitude of stress normal to the critical plane; τ a is shear stress amplitude relative to the same plane [10]. As to the MMCCM’s modus operandi , the modified Manson-Coffin diagram depicted in Fig. 2b shows how this multiaxial fatigue criterion estimates fatigue lifetime, with the modified Manson-Coffin curves, Eq. (2), moving the curve downwards as ratio  increases, resulting an increase in fatigue damage. To conclude, it is worth recalling here that, in the absence of stress concentration phenomena, critical plane stress ratio  equals unity under uniaxial fully-reversed loading, whereas it is equal to zero under pure torsional loading [11]. a. b. Figure 2 : a. Classic Manson-Coffin Curve. b. Modified Manson-Coffin Curve [11]. T HEORY OF C RITICAL D ISTANCE TO QUANTIFY THE EFFECTIVE LOCAL STRESS / STRAIN STATE s far as notched components are concerned in this study, a specific methodology is required in order to accurately take into account the presence of stress/strain concentration phenomena and determine the effective local stress/strain histories. The engineering aim of this section is to summarise a fundamental Theory of Critical distance and using the theory to estimate the effective local stress/strain states at the vicinity of notch apex different than notch tip, to predict fatigue lifetime of notched components. Generally, TCD is formalised in different forms that include a point, line, area, and volume method [4]. The point method is the simplest form that commonly used [6] and postulated that the elastoplastic stress/strain state to be used to assess the damaging effect of stress/strain concentrators and has to be determined at a distance (equal to L PM /2) from the notch apex (see Fig. 3b). The hypothesis is formed that the required critical distance is a material property, changed in different materials. However, its value remains constant in the same material regardless of notch geometry and notch sharpness [4]. According to the previous findings, that validity is fully supported by the experimental evidence and proved that the TCD is successful not only in predicting fatigue lifetime under constant amplitude loading but also under variable amplitude loading condition [6, 14]. From a practical point of view, to indicate the critical distance for a specific material, the best way is running an appropriate experimental investigation by testing specimens containing with known notched geometry under fully reversed constant amplitude axial force. A