Effect of Grain Size on Superplastic Deformation of Metallic Materials

*Allavikutty Raja, Rengaswamy Jayaganthan, Abhishek Tiwari and Ch. Srinivasa Rakesh*

### **Abstract**

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 and low strain rate of the order of 10<sup>−</sup><sup>4</sup> s<sup>−</sup><sup>1</sup> . Fine grain materials (1–20 μm) are generally considered as favorable for superplastic deformation. They possess highstrain-rate sensitivity "m" value, approximately, equal to 0.5 at the temperature of 0.5 times the melting point and at a strain rate of 10<sup>−</sup><sup>3</sup> to 10<sup>−</sup><sup>4</sup> s<sup>−</sup><sup>1</sup> . Ultrafine grains (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 scale grain size microstructures are discussed in this chapter.

**Keywords:** grain size, superplasticity, deformation mechanism, coarse-grained superplasticity, fine-grained superplasticity, ultrafine-grained superplasticity, nano-grained superplasticity, superplasticity of mixed grain sizes

#### **1. Introduction**

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

$$
\pi = \mu \,\frac{dw}{dy} \tag{1}
$$

The materials which exhibit Newtonian flow completely undergo shear by diffusion without the contribution of dislocations and cavities. If the relationship between shear stress and shear strain is nonlinear, it is called non-Newtonian flow. Superplastic deformation is such a flow in which shear stress does not follow linear relationship. Backofen and Avery [1] proposed a power-law relationship for superplastic deformation which is given in Eq. (2):

$$
\sigma = K \dot{e}^m \tag{2}
$$

where σ is the true stress, ε̇ is the strain rate, n is the strain-hardening exponent, *m* is the strain-rate sensitivity, and K is material parameter. For Newtonian fluids, *m* = 1. Superplasticity is exhibited by certain polycrystalline materials at the deformation temperature of above 0.5Tm, where Tm is the absolute melting point of the material and strain rate ranges from 10<sup>−</sup><sup>5</sup> to 10<sup>−</sup><sup>3</sup> s<sup>−</sup><sup>1</sup> [2]. For a material to exhibit superplasticity, it should have stable, equiaxed, fine grain microstructure. Materials deformed at lower temperatures resist necking by work hardening, while superplastic materials resist necking due to the sensitivity of flow stress to strain rate, called strain-rate sensitivity (*m*) [3].

The superplastic materials generally exhibit m value greater than 0.3. Observations through scratch offsets at grain boundaries established grain boundary sliding (GBS) as a primary deformation mechanism [4–6]. Other than diffusional creep, dislocation creep and grain boundary sliding (GBS) were the different mechanisms that govern high-temperature deformation. Mukerjee et al. proposed a semiempirical relationship correlating strain rate, grain size, temperature, activation energy, and stress to define the nature of superplastic deformation. The empirical relationship is given by Eq. (3):

$$\dot{\mathbf{c}} = \frac{AD\_0 Gb}{kT} \left(\frac{b}{d}\right)^p \left(\frac{\sigma}{G}\right)^n \exp\left(\frac{-Q}{RT}\right) \tag{3}$$

where D0 is the diffusion coefficient, G is the shear modulus, Q is the activation energy, T is the absolute temperature, R is the gas constant, b is the magnitude of the Burgers vector, d is the grain size, p is the grain size exponent, n is the stress

**99**

rearrangement [15, 16].

*Effect of Grain Size on Superplastic Deformation of Metallic Materials*

exponent (1/m), A is the constant dependent on microstructure and mechanism, and k is the Boltzmann constant. In general superplastic deformation was divided into three regions, as shown in **Figure 1**, based on the stress and strain rate range in which the deformation is taking place. The detailed discussion of these regions was discussed elsewhere [7]. The strain-rate dependence of stress, in turn, depends on the microstructure of the material and temperature range of the deformation. According to Eq. (3), the strain rate of superplastic deformation has an inverse relationship with grain size to the power "p." Moreover, with the advent of severe plastic deformation methods, fabrication of ultrafine grain (UFG) and nano-sized grains can be obtained using cryo forming [8, 9], multiaxial forging, equal-channel angular pressing (ECAP), friction stir processing (FSP), and high-pressure torsion (HPT). According to the Hall-Petch relationship, improvement in room-temperature mechanical properties in different alloys was studied extensively [10–13]. The advancement in superplastic deformation due to these UFG and nano-grain sizes is multifold. They are high-strain-rate, low-temperature, and room-temperature superplasticity due to grain refinement and uniform thinning during superplastic bulge forming by controlling the grain size at the apex and edge. Hence, in this chapter, the effect of grain size varying from microscale to nanoscale on the super-

Three important deformation mechanisms at high-temperature deformation are diffusion creep, grain boundary sliding (GBS), and slip by dislocation movement. The mechanisms are common to both creep and superplasticity. Creep is the ability to resist deformation, while superplasticity is the ability to deform without necking. Diffusion creep is the vacancy movement. If the vacancy transfer occurs through grain boundaries, then the diffusion creep is called Coble creep. If the stress applied is parallel to grain boundaries, then the grain boundaries experience tension, while transverse grain boundaries experience compression (perpendicular to applied stress). As the vacancies occupy the transverse grain boundaries and get absorbed, a counter flux of atoms occurs toward the parallel-to-applied stress grain boundaries and causes grain elongation. If the vacancy transfers take place through the crystal lattice, then the diffusion creep is called Nabarro-Herring creep. Diffusion creep can be accommodated by another deformation mechanism GBS [4] and contains elongated grains [14]. The GBS that accommodates diffusion creep is called Lifshitz GBS. The other type of GBS called Rachinger GBS or simply GBS is a mechanism where adjacent grains are displaced at the grain boundaries between them but the grains remain equiaxed. GBS is impeded by obstacles like triple junctions or other types of stress concentration. Hence, GBS also required accommodation process. The accommodation process for GBS is delivered by slip activities like dislocation slip, grain rotation, grain boundary migration, and grain

Dynamic recrystallization (DRX) is one another important deformation mecha-

nism in many metals and alloys including Mg which produce fine grain microstructure. Fine grain microstructure is essential to improve material's mechanical properties, and it helps in improving the superplastic elongation of the material. The important factors that influence DRX are initial grain size, second-phase particles, stacking fault energy (SFE), thermomechanical processing, and severe plastic deformation conditions [17]. There are three types of DRX, namely, discontinuous DRX (DDRX), continuous DRX (CDRX), and geometric DRX (GDRX). Nucleation

*DOI: http://dx.doi.org/10.5772/intechopen.86017*

plastic deformation was studied and discussed.

**2. Superplastic deformation mechanisms**

**Figure 1.** *Schematic illustration of the strain-rate dependence of flow stress in a superplastic material.*

*Effect of Grain Size on Superplastic Deformation of Metallic Materials DOI: http://dx.doi.org/10.5772/intechopen.86017*

*Aluminium Alloys and Composites*

where σ is the true stress, ε̇

strain-rate sensitivity (*m*) [3].

cal relationship is given by Eq. (3):

ε̇<sup>=</sup> *AD*0*Gb* \_\_\_\_\_\_

material and strain rate ranges from 10<sup>−</sup><sup>5</sup>

plastic deformation which is given in Eq. (2):

σ = *K*ε̇

between shear stress and shear strain is nonlinear, it is called non-Newtonian flow. Superplastic deformation is such a flow in which shear stress does not follow linear relationship. Backofen and Avery [1] proposed a power-law relationship for super-

*m* is the strain-rate sensitivity, and K is material parameter. For Newtonian fluids, *m* = 1. Superplasticity is exhibited by certain polycrystalline materials at the deformation temperature of above 0.5Tm, where Tm is the absolute melting point of the

to 10<sup>−</sup><sup>3</sup>

superplasticity, it should have stable, equiaxed, fine grain microstructure. Materials deformed at lower temperatures resist necking by work hardening, while superplastic materials resist necking due to the sensitivity of flow stress to strain rate, called

The superplastic materials generally exhibit m value greater than 0.3. Observations through scratch offsets at grain boundaries established grain boundary sliding (GBS) as a primary deformation mechanism [4–6]. Other than diffusional creep, dislocation creep and grain boundary sliding (GBS) were the different mechanisms that govern high-temperature deformation. Mukerjee et al. proposed a semiempirical relationship correlating strain rate, grain size, temperature, activation energy, and stress to define the nature of superplastic deformation. The empiri-

> *kT* ( \_\_ *b d*) *p* ( \_\_σ *G*)

*Schematic illustration of the strain-rate dependence of flow stress in a superplastic material.*

s<sup>−</sup><sup>1</sup>

*<sup>n</sup>* exp(

where D0 is the diffusion coefficient, G is the shear modulus, Q is the activation energy, T is the absolute temperature, R is the gas constant, b is the magnitude of the Burgers vector, d is the grain size, p is the grain size exponent, n is the stress

\_\_\_ −*Q*

*<sup>m</sup>* (2)

[2]. For a material to exhibit

*RT*) (3)

is the strain rate, n is the strain-hardening exponent,

**98**

**Figure 1.**

exponent (1/m), A is the constant dependent on microstructure and mechanism, and k is the Boltzmann constant. In general superplastic deformation was divided into three regions, as shown in **Figure 1**, based on the stress and strain rate range in which the deformation is taking place. The detailed discussion of these regions was discussed elsewhere [7]. The strain-rate dependence of stress, in turn, depends on the microstructure of the material and temperature range of the deformation. According to Eq. (3), the strain rate of superplastic deformation has an inverse relationship with grain size to the power "p." Moreover, with the advent of severe plastic deformation methods, fabrication of ultrafine grain (UFG) and nano-sized grains can be obtained using cryo forming [8, 9], multiaxial forging, equal-channel angular pressing (ECAP), friction stir processing (FSP), and high-pressure torsion (HPT). According to the Hall-Petch relationship, improvement in room-temperature mechanical properties in different alloys was studied extensively [10–13]. The advancement in superplastic deformation due to these UFG and nano-grain sizes is multifold. They are high-strain-rate, low-temperature, and room-temperature superplasticity due to grain refinement and uniform thinning during superplastic bulge forming by controlling the grain size at the apex and edge. Hence, in this chapter, the effect of grain size varying from microscale to nanoscale on the superplastic deformation was studied and discussed.

### **2. Superplastic deformation mechanisms**

Three important deformation mechanisms at high-temperature deformation are diffusion creep, grain boundary sliding (GBS), and slip by dislocation movement. The mechanisms are common to both creep and superplasticity. Creep is the ability to resist deformation, while superplasticity is the ability to deform without necking. Diffusion creep is the vacancy movement. If the vacancy transfer occurs through grain boundaries, then the diffusion creep is called Coble creep. If the stress applied is parallel to grain boundaries, then the grain boundaries experience tension, while transverse grain boundaries experience compression (perpendicular to applied stress). As the vacancies occupy the transverse grain boundaries and get absorbed, a counter flux of atoms occurs toward the parallel-to-applied stress grain boundaries and causes grain elongation. If the vacancy transfers take place through the crystal lattice, then the diffusion creep is called Nabarro-Herring creep. Diffusion creep can be accommodated by another deformation mechanism GBS [4] and contains elongated grains [14]. The GBS that accommodates diffusion creep is called Lifshitz GBS. The other type of GBS called Rachinger GBS or simply GBS is a mechanism where adjacent grains are displaced at the grain boundaries between them but the grains remain equiaxed. GBS is impeded by obstacles like triple junctions or other types of stress concentration. Hence, GBS also required accommodation process. The accommodation process for GBS is delivered by slip activities like dislocation slip, grain rotation, grain boundary migration, and grain rearrangement [15, 16].

Dynamic recrystallization (DRX) is one another important deformation mechanism in many metals and alloys including Mg which produce fine grain microstructure. Fine grain microstructure is essential to improve material's mechanical properties, and it helps in improving the superplastic elongation of the material. The important factors that influence DRX are initial grain size, second-phase particles, stacking fault energy (SFE), thermomechanical processing, and severe plastic deformation conditions [17]. There are three types of DRX, namely, discontinuous DRX (DDRX), continuous DRX (CDRX), and geometric DRX (GDRX). Nucleation

of new grains and grain growth at the expense of regions full of dislocations are called DDRX [18] which is mostly observed during hot deformation of materials with low to medium SFE. In materials with high SFE, the subgrains or cell structure with low-angle grain boundaries (LAGBs) formed during deformation is gradually evolved into high-angle grain boundaries (HAGBs) due to efficient dynamic recovery, which is known as CDRX [19]. In material like aluminum, the grains elongate with local serrations at high temperatures and large strain. On further increase in strain, these serrations pinch off and form high-angle grain boundaries which are called GDRX [20].
