The nominal variation of the fatigue crack growth rate, da/dN, as a function of the nominal stress intensity factor range, AK, for a hypothetical, fine-grained alloy is the same as that shown by the solid line in Fig. 14.12. This crack growth response was obtained at room temperature at a load ratio of zero. Optical microscopy of the crack profiles reveals a highly planar (straight) fracture path normal to the tension fatigue loading direction. Measurements of changes in compliance during loading and unloading do not show any crack closure over the entire range of ?K. This material was given a proprietary heat treatment which results in a drastic change in the fracture mode, without altering the overall stress-strain characteristics of the alloy or the grain size. The heat-treated alloy exhibited a highly tortuous crack path, with periodic deflections of 45° from the nominal mode I growth plane and a deflected segment ratio (D/{D + S}) of 0.5. For R = 0,
(a) Predict the variation of da/dN with ?K for the heat-treated alloy, by accounting for the combined effects of
(i) changes in crack-tip stress intensity factor due to crack deflection,
(ii) changes in apparent crack growth rate due to crack deflection, and
(iii) no mismatch between fracture surface asperities.
(b) Repeat the calculations in (a) by considering crack closure due to fracture surface mismatch with the mismatch factor, x - 0.1 and 0.25
Assume small-scale yielding and that crack deflection and the associated contact between the crack faces are the primary source of the change in crack propagation behavior.
