Coherent-light-shadow spot of a crack under mode I loading: Theory and experiment

The coherent-light-shadow field formed by crack-tip deformation under Mode 1 loading is studied theoretically and experimentally. First-order approximation of geometrical optics and higher order expansions are examined in the theoretical development. The wave-optical analysis shows that the interference fringe spacing around the caustic is approximately proportional toKsu−2/15 for the near-tip singular field, and, that the peak amplitude of the light-intensity distribution around the caustic is proportional toK ^4/15. The effects of diffraction on the measurement of the caustic diameter are examinediin detail. The analysis and accompanying experiments show that the diffraction effect alone could lead toK estimation errors of ±20 percent or more, if the edge of the shadow spot or it the peak-intensity point is used to determine the caustic diameter. An alternate measure of caustic diameter is therefore suggested for practical use. Effects of the size of the nominal initial curve and crack-tip bluntness onK measurements are included. Finally, possible applications of the coherent-light-shadow spot in fracture mechanics are outlined.