**2. Recrystallization phenomenon during rolling**

Static recrystallization is likely favored phenomenon in steels during roughing passes and for plain carbon steels it continues between finishing passes as well. The static recrystallization is favored by low alloying levels and high temperatures, strains, and strain rates.

The recovery is suppressed during finish interpasses, but as dislocation density is increasing on account of work hardening at finish rolling, dynamic recrystallization (**Figure 3**) is initiated after surpassing a critical strain value εC. Dynamic recrystallization is markedly identified by necklace-type grain structure. After dynamic

*1.1.1 Reheating of slabs*

*Welding - Modern Topics*

*Typical setup of hot strip rolling mill.*

**Figure 1.**

*1.1.2 Rough rolling*

*1.1.3 Finish rolling*

*1.1.4 Accelerated cooling*

capacities.

**222**

**1.2 Types of hot rolling approaches**

The first step involves heating up of slabs to remove dendritic segregation and facilitate solutionizing of microalloying element which is intended to precipitate

Before inducing final reductions at finish rolling mill, slab is first introduced to be rolled in the roughing stands where thickness of slab is reduced from 200 to 300 mm to about 50 mm in several passes, usually four or five. In the roughing process, the width increases in each pass and is controlled by vertical edge rollers. Since the temperatures are high, recrystallization takes place during this process.

Finishing mill is generally a tandem rolling mill consisting of 5–7 rolling stands.

After finish rolling, the hot rolled coil is subjected to cooling on runout table where water is sprayed on the top and bottom of the steel at a steady flow rate to

The hot rolling process can be divided approaches based upon requirement of properties. They are chiefly identified as conventional controlled rolling (CCR) and recrystallization controlled rolling (RCR) (**Figure 2**). The recrystallization rolling requires rolling at high temperatures that leads to recrystallization and control of grain size. The process is designed to have mechanisms that inhibit grain growth after recrystallization. The conventional controlled rolling approach requires rolling in no-recrystallization zone, leading to unrecrystallized grains which ultimately lead

The conventional controlled rolling shall be presented in detail as RCR has been mainly used for higher gauge rolling, i.e., plate mills or mills with lower rolling load

induce phase and microstructure control leading to increased strengths.

The finishing temperature is dependent upon the rolling speed. The interpass

heating, or cooling is also controlled during rolling.

to finer sizes after phase transformation (**Figure 2**).

during hot rolling, contributing to the strength of the material.

*Welding - Modern Topics*

recrystallization during rolling pass, the recrystallized nuclei continue to grow after the deformation ends, leading to a phenomenon called metadynamic recrystallization.

In controlled rolling process CCR, the addition of microalloying elements is deliberate to prevent static recrystallization. However, at low rolling temperatures, increased strain rates and lower interpass times coupled with lower precipitation, dynamic recrystallization is favored. As shown in **Figure 3**, the strain accumulates to peak strain and then decreases which differs on basis of type of steel.

There has been an established relationship [1] between the maximum peak stress σ<sup>p</sup> and the limiting Zener-Hollomon parameter Z which is given by

$$\left[\sinh\left(\mathfrak{a}\,\mathfrak{o}\_{\mathbb{P}}\right)\right]^{\mathfrak{n}'} = \mathbf{A}\mathbf{Z} \tag{1}$$

method is to achieve this to calculate the dynamic mean flow stresses (MFS) at each rolling stand of roughing mill and more importantly at finish rolling mill. The MFS is chiefly dependent upon the alloying elements, rolling reduction, and temperature at each rolling pass and based upon these factors several models have been proposed [3]. A most widely used method, simplified rolling load versus inverse temperature, is plotted to determine the rolling conditions and has been depicted in **Figure 4**. When the mean flow stress, which is directly related to mill rolling load value, is plotted against the inverse absolute temperature, a slope kink signifying end of static recrystallization is observed. If rolling is accomplished below this temperature represented as TNR (temperature of no further recrystallization), there is a sudden jump in mean flow stress which is due to additive nature of work hardening induced in each pass [4]. The onset of recrystallization during finish rolling is controlled largely by rolling

*Grain Boundary Effects on Mechanical Properties: Design Approaches in Steel*

*DOI: http://dx.doi.org/10.5772/intechopen.88564*

interpass time. It has been reported [4] that for interpass intervals significantly longer than 1 second, static recrystallization takes place, whereas those involving interpass times of 15–100 ms, dynamic or metadynamic recrystallization is favored. Another important factor to include is consideration of strain-induced precipita-

When high strength low-alloyed steels are finish rolled, an additive buildup of strain causes an increase in MFS consecutively after each pass. When a critical strain value is surpassed, dynamic recrystallization is initiated, and a small drop in load caused by metadynamic recrystallization is observed during end of rolling. In carbon-manganese grades, this may be associated with the austenite to

**2.2 Modeling the mean flow stress to estimate the critical rolling parameters**

mean flow stress shall also depend upon these considerations also.

As thermomechanical processing involves microstructural evolution in terms of static and dynamic recrystallization that takes place during the rolling process, the

A model equation for mean flow stress prediction for carbon-manganese grades

T

(5)

MFSMISAKA <sup>¼</sup> <sup>e</sup> <sup>0</sup>*:*126�1*:*75 C½ �þ0*:*594 C½ �2þ2851þ2698 C½ ��1120 C½ �<sup>2</sup>

tion, which inhibits recrystallization phenomenon.

by Misaka [5] has been proposed as below:

*Plot of mean flow stress versus inverse of absolute temperature.*

ferrite transformation.

**Figure 4.**

**225**

typical values of n<sup>0</sup> = 4.5 and A = 0.12.

$$\mathbf{Z} = \dot{\mathbf{e}} \cdot \exp\left(\frac{3000000}{\text{RT}}\right) \tag{2}$$

while Sun and Hawbolt [2] have reported peak Z dependent on initial grain size d0

$$\mathbf{Z\_{LIM}} = \mathbf{5} \ge \mathbf{10}^5 \cdot \exp\left(-\mathbf{0.0155 d\_0}\right) \tag{3}$$

The maximum peak strain ε<sup>p</sup> [2] that can be reached for given temperature T, strain rate ε\_, and strain ε has been established as

$$\mathbf{e}\_{\mathbf{p}} = \mathbf{1}.32 \ge \mathbf{10}^{-2} \mathbf{d}\_0 \,^{0.174} \mathbf{e}^{0.165} \exp\left(\frac{2930}{\mathbf{T}}\right) \tag{4}$$

The dynamic recrystallization threshold strain ε<sup>c</sup> will initiate when strain reaches 0.7 times the value of εp.

## **2.1 Determining rolling parameters for hot rolling**

In order to obtain good dimensional tolerance and optimum mechanical properties after rolling, optimum rolling parameters need to be established. The usual

**Figure 3.** *Stress-strain distribution with onset of recrystallization during rolling pass.*

#### *Grain Boundary Effects on Mechanical Properties: Design Approaches in Steel DOI: http://dx.doi.org/10.5772/intechopen.88564*

method is to achieve this to calculate the dynamic mean flow stresses (MFS) at each rolling stand of roughing mill and more importantly at finish rolling mill. The MFS is chiefly dependent upon the alloying elements, rolling reduction, and temperature at each rolling pass and based upon these factors several models have been proposed [3].

A most widely used method, simplified rolling load versus inverse temperature, is plotted to determine the rolling conditions and has been depicted in **Figure 4**. When the mean flow stress, which is directly related to mill rolling load value, is plotted against the inverse absolute temperature, a slope kink signifying end of static recrystallization is observed. If rolling is accomplished below this temperature represented as TNR (temperature of no further recrystallization), there is a sudden jump in mean flow stress which is due to additive nature of work hardening induced in each pass [4].

The onset of recrystallization during finish rolling is controlled largely by rolling interpass time. It has been reported [4] that for interpass intervals significantly longer than 1 second, static recrystallization takes place, whereas those involving interpass times of 15–100 ms, dynamic or metadynamic recrystallization is favored. Another important factor to include is consideration of strain-induced precipitation, which inhibits recrystallization phenomenon.

When high strength low-alloyed steels are finish rolled, an additive buildup of strain causes an increase in MFS consecutively after each pass. When a critical strain value is surpassed, dynamic recrystallization is initiated, and a small drop in load caused by metadynamic recrystallization is observed during end of rolling. In carbon-manganese grades, this may be associated with the austenite to ferrite transformation.

### **2.2 Modeling the mean flow stress to estimate the critical rolling parameters**

As thermomechanical processing involves microstructural evolution in terms of static and dynamic recrystallization that takes place during the rolling process, the mean flow stress shall also depend upon these considerations also.

A model equation for mean flow stress prediction for carbon-manganese grades by Misaka [5] has been proposed as below:

$$\mathbf{MFS\_{MISAKA}} = \mathbf{e} \begin{pmatrix} 0.126 - 1.75 \ \text{[C]} + 0.594 \ \text{[C]} 2 + \frac{2481 + 2696[C] - 1120[C]^2}{7} \end{pmatrix} \tag{5}$$

**Figure 4.** *Plot of mean flow stress versus inverse of absolute temperature.*

recrystallization during rolling pass, the recrystallized nuclei continue to grow after the deformation ends, leading to a phenomenon called metadynamic

to peak strain and then decreases which differs on basis of type of steel.

Z ¼ ε\_ � exp

½ � sinh ð Þ α σ<sup>P</sup> <sup>n</sup><sup>0</sup>

while Sun and Hawbolt [2] have reported peak Z dependent on initial grain

The maximum peak strain ε<sup>p</sup> [2] that can be reached for given temperature T,

<sup>0</sup>*:*<sup>174</sup>ε<sup>0</sup>*:*<sup>165</sup> exp

d0

The dynamic recrystallization threshold strain ε<sup>c</sup> will initiate when strain

In order to obtain good dimensional tolerance and optimum mechanical proper-

ties after rolling, optimum rolling parameters need to be established. The usual

σ<sup>p</sup> and the limiting Zener-Hollomon parameter Z which is given by

typical values of n<sup>0</sup> = 4.5 and A = 0.12.

strain rate ε\_, and strain ε has been established as

reaches 0.7 times the value of εp.

<sup>ε</sup><sup>p</sup> <sup>¼</sup> <sup>1</sup>*:*32 x 10�<sup>2</sup>

**2.1 Determining rolling parameters for hot rolling**

*Stress-strain distribution with onset of recrystallization during rolling pass.*

In controlled rolling process CCR, the addition of microalloying elements is deliberate to prevent static recrystallization. However, at low rolling temperatures, increased strain rates and lower interpass times coupled with lower precipitation, dynamic recrystallization is favored. As shown in **Figure 3**, the strain accumulates

There has been an established relationship [1] between the maximum peak stress

300000 RT 

ZLIM <sup>¼</sup> 5 x 10<sup>5</sup> � exp ð Þ �0*:*0155 d0 (3)

2930 T 

¼ AZ (1)

(2)

(4)

recrystallization.

*Welding - Modern Topics*

size d0

**Figure 3.**

**224**

Various researchers (Siciliano et al. [3], Sun and Hawbolt [2]) have worked upon refinement of the equation to include effect of recrystallization that would affect the value of MFS.

Recrystallization criteria are a function of initial grain size d0, strain ε\_, strain rate ε\_, and temperature T during rolling and are initiated when the strain at a pass exceeds critical strain ε<sup>C</sup> favored by appropriate temperature.

## *2.2.1 Critical strain evaluation for static recrystallization*

If d0 is the initial grain size, the critical strain to initiate dynamic crystallization is given by

$$\mathbf{e}\_{\rm C} = \mathbf{5.6} \ge \mathbf{10}^{-4} \mathbf{d}\_0 \, ^{0.3} \mathbf{Z}^{0.17} \, \tag{6}$$

Grain growth during interpass time tip is governed by

*Grain Boundary Effects on Mechanical Properties: Design Approaches in Steel*

*2.2.4 Evaluation for work hardening and fractional softening*

where fractional softening X is governed by recrystallization:

The value of q shall depend upon the type of recrystallization.

*2.2.5 Evaluation for predicting mean flow stress (MFS) in each rolling pass*

The modified mean flow stress modeling equation incorporating effect of man-

MFS ¼ ð Þ 0*:*78 þ 0*:*137 Mn ½ � X MFSMISAKAX 9*:*8X 1ð Þþ � XDYN KσSSXDYN (16)

XDYN <sup>¼</sup> <sup>1</sup> � exp 0*:*<sup>693</sup> <sup>ε</sup> � <sup>ε</sup><sup>c</sup>

ε\_ <sup>0</sup>*:*05d0

and where σSS is defined as steady state of stress after peak stress is achieved:

High-strength steel requires tensile properties as main requirement, whereas the requirements such as weldability and ductility are also of chief importance. Therefore, carbon which is the chief source of strength should not exceed very high values, and hence high-strength steel requires addition of alloying elements.

The addition of microalloying elements can be divided into two categories [6]:

1.Microalloying elements: niobium, vanadium, titanium, aluminum, and boron.

2. Substitutional elements: silicon, manganese, molybdenum, copper, nickel, and

For static recrystallization (SRX), q = 1.0.

ganese addition shall be

where XDYN is

chromium.

**227**

where

For metadynamic recrystallization (MDRX), q = 1.5.

<sup>ε</sup>0*:*<sup>5</sup> <sup>¼</sup> <sup>1</sup>*:*44 x 10�<sup>3</sup>

**3. Effect of chemical composition**

σSS ¼ 7*:*2 ε\_ exp

<sup>2</sup> <sup>þ</sup> <sup>1</sup>*:*2 X 10<sup>7</sup> tip � <sup>2</sup>*:*65 t0*:*<sup>5</sup>

Accumulated strain ε<sup>a</sup> at each pass is governed by the following equation:

<sup>X</sup> <sup>¼</sup> <sup>1</sup> � exp 0*:*<sup>693</sup> <sup>t</sup>

� � exp �<sup>113000</sup>

ε<sup>a</sup> ¼ ε<sup>n</sup> þ ð Þ 1 � X εn�<sup>1</sup> (14)

t0*:*<sup>5</sup> � � � �<sup>q</sup>

ε0*:*<sup>5</sup>

<sup>0</sup>*:*<sup>25</sup> exp

300000 RT � �<sup>0</sup>*:*<sup>09</sup>

� �<sup>2</sup> !*,* (17)

� �*,* (18)

6420 T

RT � � (13)

(15)

(19)

<sup>d</sup><sup>2</sup> <sup>¼</sup> dMDRX

*DOI: http://dx.doi.org/10.5772/intechopen.88564*

where Z is Zener-Holloman parameter defined by

$$\mathbf{Z} = \dot{\mathbf{e}} \cdot \exp\left(\frac{3000000}{\text{RT}}\right) \tag{7}$$

To calculate type of crystallization that occurs at a particular pass, the strain values need to be compared against critical strain value.

#### *2.2.2 Grain size evaluation for static recrystallization*

If ε<sup>a</sup> (strain at a pass) is less than the critical strain εc, static recrystallization is favored, leading to grain size governed by the equation:

$$\mathbf{d}\_{\rm SRX} = \mathbf{343} \,\mathrm{e}^{-0.5} \mathbf{d}\_0^{0.4} \,\exp\left(\frac{-45000}{\mathrm{RT}}\right) \tag{8}$$

Time for 50% completion of recrystallization (static) is

$$\mathbf{t}\_{0.5}^{\text{SRX}} = 2.3 \ge 10^{-15} \mathbf{e}^{-2.5} \mathbf{d}\_0^{-2} \exp\left(\frac{230000}{\text{RT}}\right) \tag{9}$$

Grain growth during interpass time tip is governed by

$$\mathbf{d}^2 = \mathbf{d}\_{\rm SRX}^2 + 4 \,\mathbf{X} \,\mathbf{10}^\7 \left( \mathbf{t}\_{\rm lp} - 4.32 \,\mathbf{t}\_{0.5} \right) \exp\left( \frac{-113000}{\mathbf{RT}} \right) \tag{10}$$

#### *2.2.3 Grain size evaluation for dynamic recrystallization*

If ε<sup>a</sup> (strain at a pass) is greater than the critical strain εc, dynamic recrystallization is favored, leading to grain size governed by equation:

$$\mathbf{d}\_{\text{MDRX}} = 2.6 \,\mathrm{x} \,\mathrm{10}^4 \mathbf{Z}^{-0.23} \tag{11}$$

Time for 50% completion of recrystallization (dynamic) is

$$\mathbf{t}\_{0.5}^{\text{MDRX}} = \mathbf{1.1} \ge \mathbf{Z}^{-0.8} \exp\left(\frac{230000}{\text{RT}}\right) \tag{12}$$

*Grain Boundary Effects on Mechanical Properties: Design Approaches in Steel DOI: http://dx.doi.org/10.5772/intechopen.88564*

Grain growth during interpass time tip is governed by

$$\mathbf{d}^2 = \mathbf{d}\_{\text{MDRX}}\mathbf{1}^2 + \mathbf{1.2 X 10}^\top (\mathbf{t}\_{\text{lp}} - \mathbf{2.65 t\_{0.5}}) \exp\left(\frac{-113000}{\text{RT}}\right) \tag{13}$$

*2.2.4 Evaluation for work hardening and fractional softening*

Accumulated strain ε<sup>a</sup> at each pass is governed by the following equation:

$$
\varepsilon\_{\mathbf{a}} = \varepsilon\_{\mathbf{n}} + (\mathbf{1} - \mathbf{X})\varepsilon\_{\mathbf{n}-1} \tag{14}
$$

where fractional softening X is governed by recrystallization:

$$\mathbf{X} = \mathbf{1} - \exp\left(\mathbf{0.693} \left[\frac{\mathbf{t}}{\mathbf{t}\_{0.5}}\right]^{\mathrm{q}}\right) \tag{15}$$

The value of q shall depend upon the type of recrystallization. For static recrystallization (SRX), q = 1.0. For metadynamic recrystallization (MDRX), q = 1.5.

#### *2.2.5 Evaluation for predicting mean flow stress (MFS) in each rolling pass*

The modified mean flow stress modeling equation incorporating effect of manganese addition shall be

$$\text{MFS} = (\mathbf{0.78} + \mathbf{0.137}[\mathbf{Mn}]) \mathbf{X} \,\text{MFS}\_{\text{MISAKA}} \mathbf{X} \,\mathbf{9.8} \,\mathbf{X} \,(\mathbf{1} - \mathbf{X}\_{\text{DYN}}) + \mathbf{K} \sigma\_{\text{SS}} \mathbf{X}\_{\text{DYN}} \tag{16}$$

where XDYN is

$$\mathbf{X\_{DYN}} = \mathbf{1} - \exp\left(\mathbf{0.693} \left[\frac{\mathbf{e} - \mathbf{e\_c}}{\mathbf{e\_{0.5}}}\right]^2\right),\tag{17}$$

where

Various researchers (Siciliano et al. [3], Sun and Hawbolt [2]) have worked upon refinement of the equation to include effect of recrystallization that would affect

Recrystallization criteria are a function of initial grain size d0, strain ε\_, strain rate

If d0 is the initial grain size, the critical strain to initiate dynamic crystallization

0*:*3

300000 RT 

<sup>0</sup>*:*<sup>4</sup> exp �<sup>45000</sup>

exp �<sup>113000</sup>

dMDRX <sup>¼</sup> <sup>2</sup>*:*6 x 104Z�0*:*<sup>23</sup> (11)

230000 RT 

RT 

> 230000 RT

> > RT

Z0*:*<sup>17</sup> (6)

(7)

(8)

(9)

(10)

(12)

ε\_, and temperature T during rolling and are initiated when the strain at a pass

<sup>ε</sup><sup>C</sup> <sup>¼</sup> <sup>5</sup>*:*6 x 10�4d0

Z ¼ ε\_ � exp

To calculate type of crystallization that occurs at a particular pass, the strain

If ε<sup>a</sup> (strain at a pass) is less than the critical strain εc, static recrystallization is

d0 <sup>2</sup> exp

If ε<sup>a</sup> (strain at a pass) is greater than the critical strain εc, dynamic recrystalliza-

d0

exceeds critical strain ε<sup>C</sup> favored by appropriate temperature.

*2.2.1 Critical strain evaluation for static recrystallization*

where Z is Zener-Holloman parameter defined by

values need to be compared against critical strain value.

favored, leading to grain size governed by the equation:

dSRX <sup>¼</sup> <sup>343</sup> <sup>ε</sup>�0*:*<sup>5</sup>

Time for 50% completion of recrystallization (static) is

Grain growth during interpass time tip is governed by

*2.2.3 Grain size evaluation for dynamic recrystallization*

t MDRX

**226**

tion is favored, leading to grain size governed by equation:

Time for 50% completion of recrystallization (dynamic) is

<sup>0</sup>*:*<sup>5</sup> <sup>¼</sup> <sup>1</sup>*:*1xZ�0*:*<sup>8</sup> exp

<sup>0</sup>*:*<sup>5</sup> <sup>¼</sup> <sup>2</sup>*:*3 x 10�<sup>15</sup>ε�2*:*<sup>5</sup>

<sup>2</sup> <sup>þ</sup> 4 X 10<sup>7</sup> tip � <sup>4</sup>*:*32 t0*:*<sup>5</sup>

*2.2.2 Grain size evaluation for static recrystallization*

t SRX

<sup>d</sup><sup>2</sup> <sup>¼</sup> dSRX

the value of MFS.

*Welding - Modern Topics*

is given by

$$
\varepsilon\_{0.5} = 1.44 \ge 10^{-3} \text{\AA}^{0.05} \text{d}\_0^{0.25} \exp\left(\frac{6420}{\text{T}}\right), \tag{18}
$$

and where σSS is defined as steady state of stress after peak stress is achieved:

$$
\sigma\_{\rm SS} = 7.2 \text{ è } \exp\left(\frac{3000000}{\text{RT}}\right)^{0.09} \text{.} \tag{19}
$$
