Influence of Temperature and Grain Size on Threshold Stress for Superplastic Flow in a Fine-Grained Magnesium Alloy
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INTRODUCTION
TYPICAL fine-grained superplastic materials show a sigmoidal variation in a logarithmic plot of the dependence of flow stress on strain rate at elevated temperatures.[1] The strain-rate sensitivity m, which is determined from the slope of the plot, passes through a maximum. A value of m > 0.3 delineates the superplastic regime, region II, and the material deforms superplastically, with grain-boundary sliding (GBS) being a major feature of the flow process. Both the high- and low-strain-rate ranges exhibit values of m in the range 0.1 to 0.3. At high strain rates, i.e., region III, deformation is generally believed to correspond to conventional recovery-controlled dislocation creep. It has been suggested that the decrease in the m value with a decreasing strain rate at low strain rates (region I) results from a threshold stress for deformation, from the effects of microstructural instability (grain-growth hardening), or from an independent flow mechanism.[2] In many cases, the existence of region I can be rationalized by the notion of the threshold stress. The constitutive equation for flow in regions I and II, taking the threshold stress into consideration, is generally expressed as p Gb b r r0 n D ½1 e_ ¼ A kT d G where e_ is the strain rate; A is a constant; k is the Boltzmann’s constant; T is the absolute temperature; G is the dynamic, unrelaxed shear modulus; b is the H. WATANABE, Researcher, is with the Osaka Municipal Technical Research Institute, Joto-ku, Osaka 536-8553, Japan. Contact e-mail: [email protected] T. MUKAI, Group Leader, is with the Structural Metals Center, National Institute for Materials Science, Tsukuba 305-0047, Japan. K. HIGASHI, Professor, is with the Department of Materials Science, Osaka Prefecture University, Naka-ku, Sakai 599-8531, Japan. Manuscript submitted January 8, 2008. Article published online July 11, 2008 METALLURGICAL AND MATERIALS TRANSACTIONS A
Burgers vector; d is the grain size; p is the grain size exponent; r is the flow stress; r0 is the threshold stress; n is the stress exponent (=1/m); D (=D0 exp (-Q/RT)) is the diffusion coefficient; D0 is the pre-exponential factor for diffusion; R is the gas constant; and Q is the activation energy. Despite the fact that the existence of threshold stress is very well proved experimentally, the origin and nature of the threshold stress are still unexplained; the threshold stress for superplastic flow has been the source of great debate and has remained mainly as an adjusting factor for obtaining a stress exponent of 2.[3] Existing models of the threshold stress developed for dislocation creep in coarse-grained materials may be applicable to the threshold stress for superplastic flow.[3] The grain size, temperature, and melting or solidus temperatures are sometimes recognized to be variables for threshold stress for creep.[4–7] The chemical composition of the alloy, or solute concentration, in a narrow sense may also affect the magnitude of the threshold stress.[3] Very limited data are available for the grai
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