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**94**

**97**

**1. Introduction**

ficient of viscosity. It is given by Eq. (1):

τ = *μ* \_\_\_

**Chapter 6**

**Abstract**

Effect of Grain Size on

Metallic Materials

*and Ch. Srinivasa Rakesh*

and low strain rate of the order of 10<sup>−</sup><sup>4</sup>

0.5 times the melting point and at a strain rate of 10<sup>−</sup><sup>3</sup>

scale grain size microstructures are discussed in this chapter.

nano-grained superplasticity, superplasticity of mixed grain sizes

Superplastic Deformation of

*Allavikutty Raja, Rengaswamy Jayaganthan, Abhishek Tiwari* 

The superplastic deformation exhibited by metals with different grain sizes and their corresponding deformation mechanism influences the industrial metalforming processes. The coarse-grained materials, which contain grain size greater than 20 μm, exhibited superplastic deformation at high homologous temperature

s<sup>−</sup><sup>1</sup>

(100 nm to less than 1 μm) exhibit superplasticity at high strain rate as well as at low temperature when compared to fine grain materials. It is attributed to the fact that both temperature and strain rates are inversely proportional to the grain size in Arrhenius-type superplastic constitute equation. The superplastic phenomenon with nano-sized grains (10 nm to less than 100 nm) is quite different from their higher-scale counterparts. It exhibits high ductility with high strength. Materials with mixed grain size distribution (bimodal or layered) are found to exhibit superior superplasticity when compared to the homogeneous grain-sized material. The deformation mechanisms governing these superplastic deformations with different

**Keywords:** grain size, superplasticity, deformation mechanism, coarse-grained superplasticity, fine-grained superplasticity, ultrafine-grained superplasticity,

Newtonian flow is the flow of a material in which the shear stress (*τ*) has linear relationship with the shear rate. The proportionality constant (*μ*) is called coef-

*dv*

The materials which exhibit Newtonian flow completely undergo shear by diffusion without the contribution of dislocations and cavities. If the relationship

generally considered as favorable for superplastic deformation. They possess highstrain-rate sensitivity "m" value, approximately, equal to 0.5 at the temperature of

. Fine grain materials (1–20 μm) are

s<sup>−</sup><sup>1</sup>

*dy* (1)

. Ultrafine grains

to 10<sup>−</sup><sup>4</sup>
