Transformation superplasticity of zirconium
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I.
INTRODUCTION
Superplastic deformation is characterized phenomenologically by tensile failure strains above 100 pct and can be classified into two mechanism types: fine-structure superplasticity and internal-stress superplasticity.[1] The former type of superplasticity relies on grain-boundary sliding and is operative in metals with grains smaller than 10 mm, which must be stable at the temperature of deformation. This can be achieved through duplex microstructures or through grain-boundary pinning by fine second-phase particles.[1] Since pure metals display neither duplex structures nor grain-boundary pinning, they exhibit rapid grain growth at elevated temperatures and are, thus, typically incapable of fine-structure superplasticity. However, certain pure metals can deform superplastically by the second mechanism (internal-stress superplasticity), where internal mismatch stresses are biased by an external stress, resulting in a strain increment. These mismatch stresses and the resulting strain increments can be repeatedly produced by thermal cycling of pure metals exhibiting coefficients of thermal expansion anisotropy[1,2] (e.g., Zn,[3,4,5] and U[3,4,6]) and/or an allotropic phase transformation[1,7] (e.g., Fe,[8,9,10] Co,[8,11] Ti,[8,12] Zr,[8,13] and U[8]). Since the only requirement for internal-stress superplasticity is the repeated creation of internal mismatch stresses, these pure metals can be deformed superplastically by this alternate mechanism independently of their grain size. In transformation superplasticity, internal mismatch stresses are produced by the volumetric difference between the two allotropic phases |DV/V| (referred to as DV/V in this article). A net plastic strain increment is produced in the direction of the applied stress after each phase transformation as a result of the accommodation of these internal PETER ZWIGL, formerly Research Assistant, Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, is Senior Process Engineer, Intel Corp., Santa Clara, CA 95052. DAVID C. DUNAND, Associate Professor, is with the Department of Materials Science and Engineering, Northwestern University, Evanston, IL 60208. Manuscript submitted December 12, 1997. METALLURGICAL AND MATERIALS TRANSACTIONS A
mismatch stresses by the weaker allotropic phase, which can deform either by time-independent plastic yield or by a time-dependent creep mechanism such as dislocation creep or diffusional creep. Transformation superplasticity was systematically investigated first by Greenwood and Johnson,[8] who developed a model predicting a linear relationship between the applied stress (s) and the plastic strain increment per transformation (Dε), D« '
2 DV s 5zn z z z 3 V s0 (4 z n 1 1)
[1]
where s0 is the average internal stress (averaged over both transformation time and spatial orientation of the phase transformation) of the plastically deforming weaker phase, and n is the stress exponent of the creep law describing the plastic accommodation. Greenwood and
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