Micromechanics of shear ligament toughening
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INTRODUCTION
F R A C T U R E toughness in materials exhibiting planar slip behavior, e.g., titanium alloys, has generally been related to the ability of the microstructure to cause crack deflection and the tendency of the crack to meander as it "zip-zaps" between grains following planar slipbands. ]1'2'31 As a result, the toughness in Ti-alloys is frequently attributed to the tortuosity of the crack path or the roughness of the fracture surface. In several recent studies, t4-Sj titanium aluminide alloys based on either the alpha-two or ~ phases have been found to exhibit planar slip, crack deflection, and in many instances, tortuous crack paths and rough fracture surfaces. Because of these observations, toughness in both types of titanium aluminide alloys has been considered to arise, at least partly, from crack deflection and crack-path tortuosity} 4-8] with the other possible toughening mechanisms being cracktip blunting and crack bridging. The beneficial effects of a tortuous crack path and fracture surface asperities in retarding fatigue crack growth through roughness-induced crack closure have been reported extensively in the literature. [9,10,11]In contrast, the mechanisms by which a rough fracture surface or a tortuous crack path enhance fracture toughness during quasistatic crack growth are less forthcoming. One of the possible toughening mechanisms is the reduction in the crack-tip stress intensity factor and the change in the mode of cracking associated with a deflected crack. ]12] While this mechanism offers a possible explanation for deflected cracks manifesting a relatively large angle of deflection (>60 deg), it does not appear to be a plausible explanation for deflected crack with smaller angles of crack deflection because of no or low reduction in the local stress intensity factor. A complete understanding of the relationship between fracture toughness and surface roughness is further complicated by a recent study by Davidson} 13] who reported the lack of a correlation between the Klc and a particular roughness parameter for a number of SiCp-reinforced aluminum alloy composites. In other studies, fractal geometry has been used to KWAI S. CHAN, Principal Engineer, is with Southwest Research Institute, San Antonio, TX 78228-0510. Manuscript submitted December 10, 1990. METALLURGICAL TRANSACTIONS A
characterize the irregularities of fracture s u r f a c e s , ]14,15,16] with the stipulation that fracture toughness and surface roughness might be related in terms of a fractal dimension. ]141 In a recent overview article of this subject, Dauskardt et al. ]171identified no unique fractal signatures for the fracture surfaces of several well-characterized microstructures and fracture modes in steels. Consequently, they concluded that universal correlations between fracture toughness and a fractal dimension are deemed unlikely. These findings underscore the fact that there is still a lack of a complete understanding of the relationships between crack deflection, surface roughness, and fracture toughness
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