Quantification of Resistance of Grain Boundaries to Short-Fatigue Crack Growth in Three Dimensions in High-Strength Al A
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COMMONLY, grain boundaries (GBs) are considered to be one of the major barriers to short-fatigue crack growth[1–4] and account for the marked variation of the short-fatigue crack growth rate measured in most engineering alloys.[5–8] Several analytical models have been developed previously in attempts to take into account the effects of local GBs/phase boundaries and crystallographic orientation on short-fatigue crack growth behaviors. Hobson[9] accommodated the effect of GBs into two equations describing short crack growth via a statistical approach. However, his model yields good agreement only with experimental data within the first grain but fails beyond that.[10] Chan and Lankford[11] reconsidered the crack tip plastic strain range and modified the linear elastic fracture mechanics (LEFM) equation by introducing a crystallographic function KðUÞ with respect to the resolved shear stress in cracked grain and its neighboring grain in front of the crack tip. Their model cannot explain satisfactorily the marked scattering observed often in the growth rates of short cracks. For example, it predicts little or no deceleration in the growth rate when a crack is propagating through the boundary between two similarly orientated grains. Based on the constraint on the crack tip plastic zone size by a GB,[2] Navarro and colleagues[12–14] incorporated the Sachs factor averaged over the grains along the crack front into their two-dimensional (2-D) dislocation model, which took into account the effect of TONGGUANG ZHAI, Associate Professor, and WEI WEN, Graduate Student, are with the Department of Chemical and Materials Engineering, University of Kentucky, Lexington, KY 40506. Contact e-mail: [email protected] Manuscript submitted April 11, 2011. Article published online March 10, 2012 METALLURGICAL AND MATERIALS TRANSACTIONS A
slip band blocking by the GB in simulating short crack growth. Although it can predict the crack growth retardation at grain boundaries, this model cannot distinguish the difference in resistance between different types of GBs. Moreover, it cannot explain crack branching at GBs and crack deflection observed inside grains rather than at a GB where the resistance to crack growth is expected to be the largest. Recently, Bieler and colleagues[15,16] investigated the short-fatigue crack initiation and propagation in a duplex TiAl alloy and proposed a fracture initiation/ propagation parameter, incorporating the Schmid factor and crystal orientation of grains around a propagating crack, in an attempt to predict the crack initiation/ propagation. Although their model could predict the crack initiation site and crack path statistically, the resistance was not taken into consideration in calculating the crack growth rate in the alloy. The three-dimensional (3-D) effects of microstructures on short crack growth behaviors could hardly be accounted for using the existing 2-D models for short-fatigue crack propagation. With the aid of electron backscatter diffraction (EBSD), Zhai and colleagues[17–19] studied the effect of
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