Grain Size Hardening Effects in Mg-Gd Solid Solutions

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THE yield strength of a polycrystal, ry, can usually be related to the average grain diameter, d, by the Hall–Petch equation[1,2] ry ¼ r0 þ kd1=2 :

½1

In most face-centered and body-centered cubic metals this relation has been shown to hold over a wide range of grain sizes and it is well-accepted that the friction stress, r0, found by extrapolating the experimental data to infinite grain size has a sound physical interpretation. The same is not always true for hexagonal metals, including Mg and its alloys. Hauser et al.[3] and Armstrong,[4] for example, argue that the extrapolation is valid in pure Mg and suggest how r0 can be related to the critical resolved shear stresses, CRSS, for basal and prism slip. On the other hand, Eq. [1] with only one set of values for r0 and k has been shown not to hold for all grain sizes in several Mg-based alloys.[5–7] As a case in

DEVARAJAN NAGARAJAN, formerly Postgraduate Student, with the ARC Centre of Excellence for Design in Light Metals, Materials Engineering, School of Engineering, The University of Queensland, Brisbane, QLD 4072, Australia, is now Assistant Professor, with the Department of Metallurgical and Materials Engineering, National Institute of Technology, Rourkela - 769 008, Odisha, India. CARLOS H. CA´CERES, Reader in Casting Technology, is with the ARC-Centre of Excellence for Design in Light Metals, Materials Engineering, School of Engineering, The University of Queensland. Contact e-mail: [email protected] JOHN R. GRIFFITHS, Honorary Fellow, is with CSIRO Manufacturing, PO Box 883, Kenmore, QLD 4069, Australia. Manuscript submitted August 24, 2015. Article published online August 12, 2016 METALLURGICAL AND MATERIALS TRANSACTIONS A

point, for dilute concentrations in Mg-Zn alloys, the friction stress obtained by extrapolation is close to zero and, in some cases, negative.[7] At the same time, if a limited section of a dataset does have a linear relation between ry and d1/2 then the slope (i.e., k) can be interpreted in terms of the operative deformation modes[8,9] and this is the approach taken in the present paper. The term ‘‘notional friction stress’’ is, in the present work, used for the r0 derived from extrapolation to infinite grain size from data collected over a limited range of grain sizes: this is done to emphasize that its value is not necessarily physically meaningful. Following Kocks’ and Mecking’s descriptions for FCC metals,[10,11] k is the stress intensity factor required for the nucleation of multiple slip in grains adjacent to those ideally oriented for initial yield. In Mg and its alloys, the operative basal and prism slip systems are accompanied by twinning so as to satisfy the von Mises criterion[12] and all three deformation modes must, therefore, be included in any model for k. Likewise, Kocks pointed out[10] that r0, rather than being related to the CRSS for basal slip as previously assumed,[3,4] should be related to the CRSS at the end of the easy glide stage in single crystals, i.e., the stress at which multislip is activated. F

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