Superplasticity in Nanostructured Materials
Superplasticity is largely enhanced by decreasing the grain size to UFG and NC regimes. The constitutive equations describing the dependence of the different mechanisms acting during deformation as a function of grain size are described in this chapter. T
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Superplasticity in Nanostructured Materials
7.1
Introduction
Superplasticity is the property of materials exhibiting very high ductility up to hundreds or thousands of elongation during tension (Padmanabhan et al. 2018a). This is exhibited by microcrystalline materials once grain size is below 10 μm at temperatures 0.5–0.6 Tm and strain rates in the range of 103 to 104 s1 (Padmanabhan et al. 2018b). The constitutive equation describing the superplastic flow in microcrystalline materials is described by ε_ ¼ A
p DGb b σ n kT d E
which is the strain rate, D is the coefficient of grain boundary diffusion, G is the shear modulus, b is the Burgers vector, k is the Boltzmann constant, T is the temperature of testing, d is the grain size, p is the grain size exponent (usually equal to 2), σ is the flow stress, and n is the stress exponent. A decrease in grain size leads to increase in superplasticity at a given temperature and strain rate (Chuvil’deev et al. 2010). Basing on these considerations, the development of SPD techniques allowed to produce bulk materials optimized for superplastic forming (Valiev 2000). The equation suggests that low-temperature superplasticity can also be achieved by enhancing grain boundary diffusion (Padmanabhan et al. 2018c). The diffusion coefficient increases exponentially with increasing deformation temperature and such a strong relationship between the diffusion and temperature is the main reason for the occurrence of superplasticity at high homologous temperatures. The enhancement of diffusion at the grain boundaries can be realized without increasing the temperature by engineering the grain boundary composition and segregation (Edalati et al. 2017).
© Springer Nature Switzerland AG 2021 P. Cavaliere, Fatigue and Fracture of Nanostructured Materials, https://doi.org/10.1007/978-3-030-58088-9_7
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7.1.1
7 Superplasticity in Nanostructured Materials
Grain Boundary Sliding
During superplasticity, grain boundary sliding is the dominant deformation mechanism (Padmanabhan 2009). Given that grain boundary sliding during superplastic deformation is a thermally activated process, the macroscopic shear strain rate is given by γ_ ¼ N v ABv exp
h
ΔGτe kT
i
where Nv is the number of places per unit volume where thermally activated shear can occur, A is the area swept out per successful thermal fluctuation, m is the frequency of vibration, and ΔG is the Gibbs free activation energy, which is a decreasing function of the effective shear stress τe ¼ τ τ0, where τ is the applied stress and τ0 a back stress or threshold stress. Nv is given by Nv ¼
δ db2
where δ is the grain boundary width; given that ΔG ¼ ΔF Vτe with ΔF Helmholtz free energy and V ¼ d3, the shear strain rate is given by γ_ ¼
7.1.2
6δvD Vτe ΔF sinh exp kT d kT
Diffusion
For NC materials, owning to their fine grain size, large grain boundary area, and high self-diffusivity, superplasticity is expected at lower temperatures and/or higher strain rates (Dong et al. 2007). Before describing the dep
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