13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- The simple linear superposition equation, as shown in Eq. (1), is preferentially considered to model the creep-fatigue crack growth rate[3]. fatigue creep d d d ( ) ( ) d d d a a a N N N = + (1) where (da/dN)fatigue denotes the fatigue crack growth rate, including the effect of environment (oxidation for example). It can be achieved by Eq. (2) according to the Paris law. (da/dN)creep represents the creep crack growth rate. Selecting K as the creep crack growth dominant parameter due to its practicability, (da/dN)creep is thereby expressed by Eq. (3). fatigue d ( ) (Δ ) d n a C K N = (2) creep max h d ( ) ( ) d m a A K t N = (3) where Kmax = ΔK / (1 - R), C, n, A and m are material related parameters. In order to take the creep-fatigue interaction into account, a three-term crack growth model was developed by adding a third-term to the traditional linear superposition equation, see Eq. (4). fatigue creep interaction d d d d ( ) ( ) ( ) d d d d a a a a N N N N = + + (4) where (da/dN)interaction denotes the influence of creep and fatigue interaction on the crack growth rate, and the expression should be discussed. As Grover and Saxena [5] indicated, at short th, the creep zone size is small relative to the cyclic plastic zone size during all the crack growth period since the creep zone grows very slowly, resulting in fatigue dominating cracking. At long th, the creep zone grows larger than cyclic plastic zone size, and the crack growth rate becomes time dependent. In between, the cracking will rely on both creep and cyclic plastic damage. The most significant interaction occurs when creep and cyclic plastic damage size are comparable. Also provided in their study is that the ratio of the creep and cyclic plastic zone sizes is dependent on the dwell time th, load ratio R and the material related parameters. This implies that the creep fatigue interaction should also depend on these parameters. Based on these, a factor, η, was proposed to characterize the intensity of the creep and fatigue interaction, as shown in Eq.(5). 2 1 2 3 exp( (ln ) ) p f p K p h= - + D + (5)
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