Y-Y Ma et al/ Engineering Failure Analysis 47(2015)162-177 175 5303540 Fig. 12. Vertical section of Fe-Cr-Ni termary diagram based on Chromium-Equivalent LOP cycle load unbalance of cylindrical boc the whole shell Severe fractures soccurred on weakest fracture firstly occurred weld joints Fig. 13. Illustration of the fractures process on the CWP. It should be noted that Paris's law only represents the linear phase of crack growth curve. As the stress intensity factor range increases approaching its critical value of fracture toughness, K o, the fatigue cracks growth becomes much faster than that predicted by Paris, and Forman et al. 36 proposed the following relationship for describing the whole region of crack growth curve da/dN=C(△Km/(1-R)K-△K where R is the stress ratio, equal to Smin/Smax, K the critical stress intensity factor describes material toughness (a measure of resistance to crack propagation). Thus the number of cycles required to propagate a crack from an initial crack size ao. to a final crack a, can be calculated by using the following equation: (1-R)Kc-△K C(△K And an equation of Ak is usually assumed to relate the range of stress intensity factor as below: AK=a△dv rawhere da/dN means the cyclic rate of crack growth, C and m are material constants defined by experiment, DK donates the range of stress intensity factor. It should be noted that Paris’s law only represents the linear phase of crack growth curve. As the stress intensity factor range increases approaching its critical value of fracture toughness, Kc, the fatigue cracks growth becomes much faster than that predicted by Paris, and Forman et al. [36] proposed the following relationship for describing the whole region of crack growth curve da=dN ¼ CðDKÞ m=½ð1 RÞKc DK ð5Þ where R is the stress ratio, equal to Smin/Smax, Kc the critical stress intensity factor describes material toughness (a measure of resistance to crack propagation). Thus the number of cycles required to propagate a crack from an initial crack size a0, to a final crack af, can be calculated by using the following equation: Np ¼ Z af a0 ð1 RÞKc DK CðDKÞ m ð6Þ And an equation of DK is usually assumed to relate the range of stress intensity factor as below: DK ¼ aDr ffiffiffiffiffiffi pa p ð7Þ Fig. 12. Vertical section of Fe–Cr–Ni ternary diagram based on Chromium-Equivalent. Fig. 13. Illustration of the fractures process on the CWP. Y.-Y. Ma et al. / Engineering Failure Analysis 47 (2015) 162–177 175