13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- where Gcf(a) is the fatigue delamination resistance, defined as the critical energy release rate during fatigue crack growth. The normalized Paris Law was thus reformed as: max d ( ( )) d r a a C g a N (3) where C’ and r are the new fatigue constants. A normalized fatigue threshold parameter could also be proposed based on the fatigue delamination resistance, shown as: th th cf ( ) ( ) G a g G a (4) 2.2. Calculation of fatigue delamination resistance The “compliance approach” [35] to obtain the fatigue delamination resistance, Gcf, is briefly introduced here. The approach is developed for fiber bridging cases and based on the following hypothesis: the delamination resistance of fatigue specimen is equal to the value of corresponding static specimen which exhibits the same force–displacement behavior. According to ‘‘compliance approach’’, the fatigue delamination resistance at certain crack length, a1, could be determined by comparing the normalized compliance of fatigue and static specimens. The procedure was summarized in the following equation: s f 1 f 1 0 s 1 cf 1 c ( ) ( ) cf 1 c 1 ( ) if 1 ( ) ( ) ( ) else ( ) ( ) C a C a C a C a G a G a G a G a (5) where C is the normalized compliance of specimen, calculated by Eq. (6). ε0 is the critical tolerance to consider experimental scatters of the compliance. The subscript “f” and “s” indicate the fatigue and static specimens, respectively. 3 1 C bh m (6) where m is the slope of force-displacement curve of the specimen, b and h the width and half thickness, respectively. 2.3. Fiber bridging zone model The mode I fiber bridging zone model is discussed here, as illustrated in Fig. 1. The SERR for double cantilever beam (DCB) specimen could be calculated using the equation below [37]: I 3 2 ( ) Pd F G b a h N (7) where F and N’ are correction factor for large displacements and load-block effect, respectively. χ is a correction for crack tip displacement and rotation, which allows for the beam not being perfectly built in. Generally, χh value can be obtained experimentally by plotting the cubic root of compliance as a function of crack length and determining the intercept on the x-axies [38]. For fiber
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