Issue34

K. Tanaka et alii, Frattura ed Integrità Strutturale, 34 (2015) 309-317; DOI: 10.3221/IGF-ESIS.34.33 311 Fatigue Crack Propagation Tests Fatigue tests were performed with a tension-compression electro-servo-hydraulic testing machine. Fatigue testing was done in air at room temperature under load-controlled conditions with the load ratio R of 0.1 and 0.5. The waveform of the cyclic load was triangular and the frequency was between 2.5 and 8 Hz. The crack length was measured with a video microscope at the magnification of 100. Fig. 1 illustrates a fatigue crack formed from the notch. The angle of the macroscopic direction of crack propagation,  , and the crack length, c , were measured experimentally. The crack length projected on the plane perpendicular to the loading axis is denoted by a as shown in Fig. 1. The crack propagation rate is calculated from the crack length along crack propagation direction. Fracture Mechanics Parameters The macroscopic crack path was perpendicular to the loading axis for the cases of  = 0° (MD) and 90° (TD), while inclined for the other fiber angles. Using the macroscopic crack angle measured experimentally, the energy release rate of crack propagation was calculated by the method of a modified crack closure integral of the finite element method (FEM) [6]. The details of FEM are described in Appendix. The energy release rate of is expressed as     2 2 I I II II , G a Y a W G a Y a W         (1) where  is the applied gross stress, a is crack length, W is plate width, Y I ( a/W ) and Y II ( a/W ) are correction coefficients for mode I and II loading. For the case of collinear crack growth for MD and TD specimens, the energy release rate is converted to the stress intensity factor by using [7]       1 2 2 12 1 12 1 I I I I 1 2 2 1 2 1 1 , where 2 2 1 E G E G H K H E E E E             (2) The 1/ H I value for MD is 17.4 GPa, and 12.0 GPa for TD. For isotropic materials, we have 2 I I G K E  . For MD and TD, G I can be converted to the stress intensity factor, K I , by the above equation. The value of K I is expressed as   I I K a F a W     (3) where F I ( a/W ) is a correction factor. E XPERIMENTAL RESULTS AND DISCUSSION Fatigue Crack Propagation Path ptical micrographs of cracks for MD, 45°, and TD specimens fatigued under R = 0.1 are shown in Fig. 2, respectively, where the square region shown in (a), (c ),(e) are enlarged in (b), (d), (f). For MD and TD specimens, the crack path is microscopically zigzag shaped and macroscopically straight perpendicular to the loading direction. On the other hands, the crack path of 45° specimen is inclined, making the angle of   = 24.4° with respect to the plane perpendicular to the loading axis. The microscopic crack path is either in the matrix or along fibers. For MD specimens, the crack propagation is blocked by fibers and circumvents fibers along fiber surfaces, showing zigzag path. For TD specimens, the crack path is less tortuous following the fiber direction. For 45° specimens, the crack propagates nearly 45° along the fiber and turns to horizontal in the matrix. The macroscopic direction is a combination of these two paths and is less than the fiber angle of 45°. The macroscopic crack path for 22.5° and 67.5° specimens was not perpendicular to the loading axis. Fig. 3 shows the change of crack propagation angle  with the fiber angle  for R = 0.1 and 0.5. The dotted line in the figure indicates the O