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Theoretical Modelling of the Effects of Grain Size on the Threshold for Fatigue Crack Growth

Ravichandran, KS and Dwarakadasa, ES (1991) Theoretical Modelling of the Effects of Grain Size on the Threshold for Fatigue Crack Growth. In: Acta Metallurgica et Materialia, 39 (6). pp. 1343-1357.

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Abstract

The dependence of the threshold for fatigue crack growth,$\Delta K_{th}$ on grain size has been modelled theoretically using fundamental micromechanistic processes of crack extension in polycrystalline materials.Near threshold, fatigue cracks generally propagate along slip bands piled up at the grain boundary. The effect of grain size on $\Delta K_{th}$ principally comes through the increase in the intrinsic fatigue threshold, $\Delta K_{eff,th}$due to larger degree of crack deflection in coarse grained structures and the accompanying high levels of crack closure as a consequence of zig-zag crack growth. Using Minakawa and McEvily's description of roughness induced crack closure, the magnitude of closure stress intensity at threshold, $K_{cl,th}$ is quantified.A strong pile-up is formed at the grain boundary before the crack attempts to propagate inside a grain.It is assumed that dislocations pile-up in the forward loading and are largely irreversible during unloading.By assuming a continuously distributed dislocation configuration, the number of dislocations which are in equilibrium with the resolved shear stress along the slip plane can be calculated. The grain boundary sustains the pile-up until the shear stress in the slip band reaches a critical value required for nucleating slip in the adjacent grain. Assuming complete slip irreversibility during unloading, the magnitude of crack flank disregistry due to the interference of asperities just behind the crack tip can be obtained in terms of the number of dislocations and the Burger's vector of the operative slip system. The magnitude of $\Delta K_{cl,th}$ can then be expressed in terms of slip length or grain size, macroscopic yield stress, critical resolved shear stress and the angle between slip plane and crack plane. Theoretically predicted closure levels as a function of grain size have been shown to be in good agreement with the experimentally obtained data. The magnitude of $\Delta K_{eff,th}$ as a function of grain size can be derived by considering the piled-up slip band as a kinked crack with the length of the kink being equal to the slip band length. The crack propagation is assumed to occur incrementally along the slip band. The intrinsic crack growth resistance is then formed by two contributions, one is the stress intensity necessary to maintan a critically stressed pile-up and the other is that required to incrementally cleave the slip band in each cycle. By summing $\Delta K_{cl,th}$ and $\Delta K_{eff,th}$ ,$\Delta K_{th}$ can be expressed as a function of grain size. A comparison of the theoretically predicted trend with the experimental data for a variety of alloy systems indicate good agreement. The factors responsible for the deviations are discussed.

Item Type: Journal Article
Additional Information: Copyright of this article belongs to Elsevier.
Department/Centre: Division of Mechanical Sciences > Materials Engineering (formerly Metallurgy)
Date Deposited: 06 Sep 2006
Last Modified: 19 Sep 2010 04:31
URI: http://eprints.iisc.ernet.in/id/eprint/8477

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