Issue34

K. Tanaka et alii, Frattura ed Integrità Strutturale, 34 (2015) 309-317; DOI: 10.3221/IGF-ESIS.34.33 312 crack path is coincident to the fiber angle, i.e. 90     (deg). There is no big difference between R = 0.1 and 0.5. The crack angle increases with decreasing fiber angle ， and takes a maximum at 22.5°. The crack angle for the cases of   22.5°, 45°, 67.5° is below the dotted line, because the macroscopic crack path consists of the matrix path with 0   and fiber path with 90     . Fatigue Crack Propagation under Mode I Loading The fatigue crack propagation rate for MD and TD specimens is plotted against the range of stress intensity factor,  K , in Fig. 4(a). Both for R =0.1 and 0.5, the crack propagation rate is lower in MD than in TD. The resistance to crack propagation is improved by fiber reinforcement, and fibers aligned perpendicular to the crack growth direction block more severely crack propagation. For each material, the crack propagation rate is higher under larger R ratio. In Fig. 4(b), the crack propagation rate is correlated to the range of energy release rate,  G I , which is defined by           2 2 2 I Imax Imin max min I I 1 1 G G G H K K H R R K          (4) It is interesting to see that the data of each material under R =0.1 and 0.5 tend to merge, and these is no big influence of R ratio. Still, there exists a slight difference among MD, TD and PPS. For isotropic materials, the stress intensity factor divided by Young’s modulus,  K/E , is often used to correlate the crack propagation data for different materials. This parameter can be interpreted to represent the range of crack-tip radius as shown in Fig. 5 [8]. The crack-tip radius in orthotropic materials is [9]   I I 4 H G    (5) so the range of crack-tip opening radius is given by   max min I I 4 H G          (6) Fig. 6 shows the relation between crack propagation rate and a parameter representing crack-tip opening radius, H I  G I . The data for MD, TD and PPS come closer, indicating this parameter plays a more role in crack propagation. Still in the figure, MD has a stronger resistance to crack propagation in comparison with TD and PPS. Fatigue Crack Propagation under Mixed Loading of Mode I and II Except for the cases of MD and TD, the direction of crack propagation is inclined to the loading axis and cracks propagate under mixed loading of mode I and II. The energy release rates for mode I and II were calculated by FEM for cracks propagating at the measured angle shown in Fig. 3. Fig. 7 shows the crack propagation rate as a function of the range of energy release rate for mode I,  G I , for R =0.1. When compared at the same  G I , the crack propagation rate is highest for PPS and gets slower with deceasing fiber angle. The data are bounded by the relation for MD and TD. To check the contribution of mode II, the crack propagation rate is plotted in Fig. 8 against the range of the total energy release rate,  G total , which is defined by total I II G G G      (7) The data for 22.5  45  67.5  move only slightly toward right, because the amount of  G II is small relative to  G I . Since crack propagation is mainly controlled by mode I loading and no equation is available for crack-tip opening for mixed mode loading, a parameter,  G total /E , is adapted as a rough estimate of the crack-tip opening radius for all cases including MD and TD, where E is Young’s modulus given in Tab. 2. Fig. 9 shows the crack propagation rate correlated to  G total /E for R =0.1 and 0.5. All data tend to merges into a single relation for R =0.1, while there is some scatter for R =0.5. This parameter would be useful to estimate the crack propagation law for various fiber orientation, though the physical meaning of this parameter needs to be explored in the future.