**4. Observation for size and fraction of DRX grains**

**Volume fractions of dynamic recrystallization Exponents**

Based on the calculation results of this model, the effect of deformation temperature, strain and strain rate on the recrystallized volume fraction is shown in Fig. 12a~d. These figures show that as the strain' absolutevalue increases,theDRXvolume fractionincreases andreaches a constant value of 1 meaning the completion of DRX process. Comparing these curves with one anoth‐ er, itis found that,for a specific strain rate,the deformation strain required forthe same amount of DRX volume fraction increases with decreasing deformation temperature, which means that DRX is delayed to a longer time. In contrast, for a fixed temperature, the deformation strain required for the same amount of DRX volume fraction increases with increasing strain rate, which also means that DRX is delayed to a longer time. This effect can be attributed to de‐ creased mobility of grain boundaries (growth kinetics) with increasing strain rate and decreas‐ ing temperature. Thus, under higher strain rates and lower temperatures, the deformed metal

tends to incomplete DRX, that is to say, the DRX volume fraction tends to be less than 1.

0.2 0.4 0.6 0.8

1.0 -1 10s

0.2 0.4 0.6 0.8

*X*DRX

(a) (b)

*X*DRX

(c) (d)

Fig. 12 Predicted volume fractions of dynamic recrystallization obtained under different

The microstructures on the section plane of specimen deformed to the true strain of -0.9

were examined and analyzed under the optical microscope. Fig. 13 shows the as-received

microstructure of as-extruded 42CrMo high-strength steel specimen with a single-phase FCC

structure and a homogeneous aggregate of rough equiaxed polygonal grains, while with

negligible volume fraction of inclusions or second-phase precipitates. The grain boundaries

are straight to gently curved and often intersect at ~120° triple junctions. Fig. 14a~d show the

deformation temperatures with strain rates (a) 0.01 s-1, (b) 0.1 s-1, (c) 1 s-1, (d) 10 s-1.

6. Observation for Size and Fraction of DRX Grains

1.0 -1 0.1s

0.0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9 0.0

0.0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9 0.0

1348 K 1273 K 1198 K 1123 K

*ε*

*ε*

1348 K 1273 K 1198 K 1123 K

0.2 0.4 0.6 0.8 1.0

1.0 -1 1s

0.2 0.4 0.6 0.8

*X*DRX

*X*DRX


76 Recent Developments in the Study of Recrystallization

0.01s

**Table 3.** The kinetic model of DRX calculated from true compressive stress-strain curves.

*Z* =˙εexp (599.73210×10<sup>3</sup>

0.0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9 0.0

1348 K 1273 K 1198 K 1123 K

*ε*

0.0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9 0.0

1348 K 1273 K 1198 K 1123 K

*ε*

) / 8.31*T*

The microstructures on the section plane of specimen deformed to the true strain of -0.9 were examined and analyzed under the optical microscope. Fig. 13 shows the as-received micro‐ structure of as-extruded 42CrMo high-strength steel specimen with a single-phase FCC structure and a homogeneous aggregate of rough equiaxed polygonal grains, while with negligible volume fraction of inclusions or second-phase precipitates. The grain boundaries are straight to gently curved and often intersect at ~120° triple junctions. Fig. 14a~d show the typical microstructures of the specimens of as-extruded 42CrMo high-strength steel deformed to a strain of -0.9 at the temperature of 1123 K and at the strain rates of 0.01 s-1, 0.1 s-1, 1 s-1 and 10 s-1, respectively. Fig. 15a~d show the typical microstructures of the specimens of as-extruded 42CrMo high-strength steel deformed to a strain of -0.9 at the temperature of 1198 K and at the strain rates of 0.01 s-1, 0.1 s-1, 1 s-1 and 10 s-1, respectively. Fig. 16a~d show the typical micro‐ structures of the specimens of as-extruded 42CrMo high-strength steel deformed to a strain of -0.9 at the temperature of 1273 K and at the strain rates of 0.01 s-1, 0.1 s-1, 1 s-1 and 10 s-1, respectively. Fig. 17a~d show the typical microstructures of the specimens of as-extruded 42CrMo high-strength steel deformed to a strain of -0.9 at the temperature of 1348 K and at the strain rates of 0.01 s-1, 0.1 s-1, 1 s-1 and 10 s-1, respectively. At such deformation conditions the recrystallized grains with wavy or corrugated grain boundaries can be easily identified from subgrains by the misorientation between adjacent grains, i.e. subgrains are surrounded by low angle boundaries while recrystallized grains have high angle boundaries. The deformed metal completely or partially transforms to a microstructure of approximately equiaxed defect-free grains which are predominantly bounded by high angle boundaries (i.e. a recrystallized microstructure) by relatively localized boundary migration.

**Figure 13.** Optical microstructures and average grain size of as-extruded 42CrMo high-strength steel undeformed (starting material)

(a)

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(b)

(c)

(d)

**Figure 15.** Optical microstructures of 42CrMo high-strength steel at a fix true strain of 0.9, a fix temperature of 1198 K

and different strain rates: (a) 0.01 s-1, (b) 0.1 s-1, (c) 1 s-1, (d) 10 s-1.

**Figure 14.** Optical microstructures of 42CrMo high-strength steel at a fix true strain of 0.9, a fix temperature of 1123 K and different strain rates: (a) 0.01 s-1, (b) 0.1 s-1, (c) 1 s-1, (d) 10 s-1.

(a)

(b)

(c)

(d)

**Figure 14.** Optical microstructures of 42CrMo high-strength steel at a fix true strain of 0.9, a fix temperature of 1123 K

and different strain rates: (a) 0.01 s-1, (b) 0.1 s-1, (c) 1 s-1, (d) 10 s-1.

78 Recent Developments in the Study of Recrystallization

**Figure 15.** Optical microstructures of 42CrMo high-strength steel at a fix true strain of 0.9, a fix temperature of 1198 K and different strain rates: (a) 0.01 s-1, (b) 0.1 s-1, (c) 1 s-1, (d) 10 s-1.

(a)

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(b)

(c)

(d)

**Figure 17.** Optical microstructures of 42CrMo high-strength steel at a fix true strain of 0.9, a fix temperature of 1348 K

and different strain rates: (a) 0.01 s-1, (b) 0.1 s-1, (c) 1 s-1, (d) 10 s-1.

**Figure 16.** Optical microstructures of 42CrMo high-strength steel at a fix true strain of 0.9, a fix temperature of 1273 K and different strain rates: (a) 0.01 s-1, (b) 0.1 s-1, (c) 1 s-1, (d) 10 s-1.

(d)

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(a)

(b)

(c)

(d)

**Figure 16.** Optical microstructures of 42CrMo high-strength steel at a fix true strain of 0.9, a fix temperature of 1273 K

and different strain rates: (a) 0.01 s-1, (b) 0.1 s-1, (c) 1 s-1, (d) 10 s-1.

80 Recent Developments in the Study of Recrystallization

**Figure 17.** Optical microstructures of 42CrMo high-strength steel at a fix true strain of 0.9, a fix temperature of 1348 K and different strain rates: (a) 0.01 s-1, (b) 0.1 s-1, (c) 1 s-1, (d) 10 s-1.

Fig. 18 shows the grain size distribution of as-extruded 42CrMo high-strength steel unde‐ formed (starting material). Fig. 19 shows the grain size distribution of 42CrMo high-strength steel at a fix true strain of 0.9, a fix temperature of 1123 K and different strain rates: (a) 0.01 s-1, (b) 0.1 s-1, (c) 1 s-1, (d) 10 s-1. Fig. 20 shows the grain size distribution of 42CrMo high-strength steel at a fix true strain of 0.9, a fix temperature of 1198 K and different strain rates: (a) 0.01 s-1, (b) 0.1 s-1, (c) 1 s-1, (d) 10 s-1. Fig. 21 shows the grain size distribution of 42CrMo high-strength steel at a fix true strain of 0.9, a fix temperature of 1273 K and different strain rates: (a) 0.01 s-1, (b) 0.1 s-1, (c) 1 s-1, (d) 10 s-1. Fig. 22 shows the grain size distribution of 42CrMo high-strength steel at a fix true strain of 0.9, a fix temperature of 1348 K and different strain rates: (a) 0.01 s-1, (b) 0.1 s-1, (c) 1 s-1, (d) 10 s-1. As depicted, under a fix temperature of 1123 K the microstructure of the as-cast billet with grain size of 53.1 µm became refined up to about 30.1 µm after upsetting under strain rate 0.01 s-1, to about 25.4 µm under strain rate 0.1 s-1, to about 20.4 µm under strain rate 1 s-1, to about 15.6 µm under strain rate 10 s-1. Under a fix temperature of 1198 K the microstructure of the as-cast billet with grain size of 53.1 µm became refined up to about 33.5 µm after upsetting under strain rate 0.01 s-1, to about 26.9 µm under strain rate 0.1 s-1, to about 21.0 µm under strain rate 1 s-1, to about 18.5 µm under strain rate 10 s-1. Under a fix temperature of 1273 K the microstructure of the as-cast billet with grain size of 53.1 µm became refined up to about 33.5 µm after upsetting under strain rate 0.01 s-1, to about 27.3 µm under strain rate 0.1 s-1, to about 19.7 µm under strain rate 1 s-1, to about 15.7 µm under strain rate 10 s-1. Under a fix temperature of 1348 K the microstructure of the as-cast billet with grain size of 53.1 µm became refined up to about 49.8 µm after upsetting under strain rate 0.01 s-1, to about 38.2 µm under strain rate 0.1 s-1, to about 32.2 µm under strain rate 1 s-1, to about 24.4 µm under strain rate 10 s-1. It can be summarized that under a fix temperature, as deformation strain rate increases, the microstructure of the as-received billet becomes more and more refined due to increasing migration energy stored in grain boundaries and decreasing grain growth time.

Area Fraction (%)

Area Fraction (%)

and different strain rates: (a) 0.01 s-1, (b) 0.1 s-1, (c) 1 s-1, (d) 10 s-1.

Area Fraction (%)

Area Fraction (%)

0 20 40 60 80 100 120 140 <sup>0</sup>

Grain Size (μm)

0 20 40 60 80 100 120 140 <sup>0</sup>

Grain Size (μm)

Under temperature 1198 K Under strain rate 0.01 s-1 Average grain size 33.5 μm

0 20 40 60 80 100 120 140

Grain Size (μm)

Under temperature 1198 K Under strain rate 1 s-1 Average grain size 21.0 μm

0 20 40 60 80 100 120 140

Grain Size (μm)

Under temperature 1123 K Under strain rate 0.01 s-1 Average grain size 30.1 μm

Area Fraction (%)

(c) (d)

Fig.19 Grain size distribution of 42CrMo high-strength steel at a fix true strain of 0.9, a fix

Area Fraction (%)

(c) (d) Fig.20 Grain size distribution of 42CrMo high-strength steel at a fix true strain of 0.9, a fix temperature of 1198 K and different strain rates: (a) 0.01 s-1, (b) 0.1 s-1, (c) 1 s-1, (d) 10 s-1.

Area Fraction (%)

(a) (b)

temperature of 1123 K and different strain rates: (a) 0.01 s-1, (b) 0.1 s-1, (c) 1 s-1, (d) 10 s-1. **Figure 19.** Grain size distribution of 42CrMo high-strength steel at a fix true strain of 0.9, a fix temperature of 1123 K

Area Fraction (%)

(a) (b)

Under temperature 1123 K Under strain rate 1 s-1 Average grain size 20.4 μm 0 20 40 60 80 100 120 140

Characterization for Dynamic Recrystallization Kinetics Based on Stress-Strain Curves

Grain Size (μm)

0 20 40 60 80 100 120 140

Grain Size (μm)

Under temperature 1198 K Under strain rate 0.1 s-1 Average grain size 26.9 μm

Under temperature 1198 K Under strain rate 10 s-1 Average grain size 18.5 μm

0 20 40 60 80 100 120 140

Grain Size (μm)

0 20 40 60 80 100 120 140

Grain Size (μm)

Under temperature 1123 K Under strain rate 0.1 s-1 Average grain size 25.4 μm

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Under temperature 1123 K Under strain rate 10 s-1 Average grain size 15.6 μm

**Figure 18.** Grain size distribution of as-extruded 42CrMo high-strength steel undeformed (starting material).

Characterization for Dynamic Recrystallization Kinetics Based on Stress-Strain Curves http://dx.doi.org/10.5772/54285 83

Fig. 18 shows the grain size distribution of as-extruded 42CrMo high-strength steel unde‐ formed (starting material). Fig. 19 shows the grain size distribution of 42CrMo high-strength steel at a fix true strain of 0.9, a fix temperature of 1123 K and different strain rates: (a) 0.01 s-1, (b) 0.1 s-1, (c) 1 s-1, (d) 10 s-1. Fig. 20 shows the grain size distribution of 42CrMo high-strength steel at a fix true strain of 0.9, a fix temperature of 1198 K and different strain rates: (a) 0.01 s-1, (b) 0.1 s-1, (c) 1 s-1, (d) 10 s-1. Fig. 21 shows the grain size distribution of 42CrMo high-strength steel at a fix true strain of 0.9, a fix temperature of 1273 K and different strain rates: (a) 0.01 s-1, (b) 0.1 s-1, (c) 1 s-1, (d) 10 s-1. Fig. 22 shows the grain size distribution of 42CrMo high-strength steel at a fix true strain of 0.9, a fix temperature of 1348 K and different strain rates: (a) 0.01 s-1, (b) 0.1 s-1, (c) 1 s-1, (d) 10 s-1. As depicted, under a fix temperature of 1123 K the microstructure of the as-cast billet with grain size of 53.1 µm became refined up to about 30.1 µm after upsetting under strain rate 0.01 s-1, to about 25.4 µm under strain rate 0.1 s-1, to about 20.4 µm under strain rate 1 s-1, to about 15.6 µm under strain rate 10 s-1. Under a fix temperature of 1198 K the microstructure of the as-cast billet with grain size of 53.1 µm became refined up to about 33.5 µm after upsetting under strain rate 0.01 s-1, to about 26.9 µm under strain rate 0.1 s-1, to about 21.0 µm under strain rate 1 s-1, to about 18.5 µm under strain rate 10 s-1. Under a fix temperature of 1273 K the microstructure of the as-cast billet with grain size of 53.1 µm became refined up to about 33.5 µm after upsetting under strain rate 0.01 s-1, to about 27.3 µm under strain rate 0.1 s-1, to about 19.7 µm under strain rate 1 s-1, to about 15.7 µm under strain rate 10 s-1. Under a fix temperature of 1348 K the microstructure of the as-cast billet with grain size of 53.1 µm became refined up to about 49.8 µm after upsetting under strain rate 0.01 s-1, to about 38.2 µm under strain rate 0.1 s-1, to about 32.2 µm under strain rate 1 s-1, to about 24.4 µm under strain rate 10 s-1. It can be summarized that under a fix temperature, as deformation strain rate increases, the microstructure of the as-received billet becomes more and more refined due to increasing migration energy stored in grain boundaries and decreasing grain growth time.

82 Recent Developments in the Study of Recrystallization

0 20 40 60 80 100 120 140

Grain Size (μm)

**Figure 18.** Grain size distribution of as-extruded 42CrMo high-strength steel undeformed (starting material).

As-received 42CrMo high-strength steel Average grain size 53.1 μm

Area Fraction (%)

Fig.19 Grain size distribution of 42CrMo high-strength steel at a fix true strain of 0.9, a fix temperature of 1123 K and different strain rates: (a) 0.01 s-1, (b) 0.1 s-1, (c) 1 s-1, (d) 10 s-1. **Figure 19.** Grain size distribution of 42CrMo high-strength steel at a fix true strain of 0.9, a fix temperature of 1123 K and different strain rates: (a) 0.01 s-1, (b) 0.1 s-1, (c) 1 s-1, (d) 10 s-1.

Fig.20 Grain size distribution of 42CrMo high-strength steel at a fix true strain of 0.9, a fix temperature of 1198 K and different strain rates: (a) 0.01 s-1, (b) 0.1 s-1, (c) 1 s-1, (d) 10 s-1.

**Figure 20.** Grain size distribution of 42CrMo high-strength steel at a fix true strain of 0.9, a fix temperature of 1198 K and different strain rates: (a) 0.01 s-1, (b) 0.1 s-1, (c) 1 s-1, (d) 10 s-1.

0 20 40 60 80 100 120 140

Grain Size (μm)

Under temperature 1348 K Under strain rate 1 s-1 Average grain size 32.2 μm

0 20 40 60 80 100 120 140 <sup>0</sup>

Grain Size (μm)

Area Fraction (%)

(c) (d) Fig.22 Grain size distribution of 42CrMo high-strength steel at a fix true strain of 0.9, a fix temperature of 1348 K and different strain rates: (a) 0.01 s-1, (b) 0.1 s-1, (c) 1 s-1, (d) 10 s-1.

**Figure 22.** Grain size distribution of 42CrMo high-strength steel at a fix true strain of 0.9, a fix temperature of 1348 K

In the deformed material DRX is one of the most important softening mechanisms at high temperatures. DRX occurs during straining of metals at high temperature, characterized by a nucleation rate of low dislocation density grains and a posterior growth rate that can produce a homogeneous grain size when equilibrium is reached. This is a characteristic of low and medium stacking fault energy, SFE, materials e.g., *γ*-iron, the austenitic stainless steels, and

In the deformed material DRX is one of the most important softening mechanisms at high temperatures. DRX occurs during straining of metals at high temperature, characterized by a nucleation rate of low dislocation density grains and a posterior growth rate that can produce a homogeneous grain size when equilibrium is reached. This is a characteristic of low and medium stacking fault energy, SFE, materials e.g., *γ*-iron, the austenitic stainless steels, and copper. Hot working behavior of alloys is generally reflected on flow curves which are a direct consequence of microstructural changes: the nucleation and growth of new grains, DRX, the generation of dislocations, work hardening, WH, the rearrangement of dislocations, their selfannihilation, and their absorption by grain boundaries, DRV. By the in-depth analysis of the coupling effect in DRX behavior and flow behavior the prediction of DRX evolution can be

The characteristics of softening flow behavior coupling with DRX for as-extruded 42CrMo high-strength steel, as-cast AZ80 magnesium alloy and as-extruded 7075 aluminum alloy have been discussed and summarized as follows: (1) increasing strain rate or decreasing deformation temperature makes the flow stress level increase, in other words, it prevents the occurrence of softening due to DRX and dynamic recovery (DRV) and makes the deformed metals exhibit work hardening (WH); (2) for every curve, after a rapid increase in the stress to a peak value, the flow stress decreases monotonically towards a steady state regime (a

Area Fraction (%)

(a) (b)

0 20 40 60 80 100 120 140

Characterization for Dynamic Recrystallization Kinetics Based on Stress-Strain Curves

Grain Size (μm)

0 20 40 60 80 100 120 140

Grain Size (μm)

Under temperature 1348 K Under strain rate 0.1 s-1 Average grain size 38.2 μm

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Under temperature 1348 K Under strain rate 10 s-1 Average grain size 24.4 μm

Under temperature 1348 K Under strain rate 0.01 s-1 Average grain size 49.8 μm

Area Fraction (%)

7. Conclusions

**5. Conclusions**

performed.

and different strain rates: (a) 0.01 s-1, (b) 0.1 s-1, (c) 1 s-1, (d) 10 s-1.

Area Fraction (%)

Fig.21 Grain size distribution of 42CrMo high-strength steel at a fix true strain of 0.9, a fix temperature of 1273 K and different strain rates: (a) 0.01 s-1, (b) 0.1 s-1, (c) 1 s-1, (d) 10 s-1. **Figure 21.** Grain size distribution of 42CrMo high-strength steel at a fix true strain of 0.9, a fix temperature of 1273 K and different strain rates: (a) 0.01 s-1, (b) 0.1 s-1, (c) 1 s-1, (d) 10 s-1.

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Fig.22 Grain size distribution of 42CrMo high-strength steel at a fix true strain of 0.9, a fix temperature of 1348 K and different strain rates: (a) 0.01 s-1, (b) 0.1 s-1, (c) 1 s-1, (d) 10 s-1. **Figure 22.** Grain size distribution of 42CrMo high-strength steel at a fix true strain of 0.9, a fix temperature of 1348 K and different strain rates: (a) 0.01 s-1, (b) 0.1 s-1, (c) 1 s-1, (d) 10 s-1.

#### 7. Conclusions **5. Conclusions**

**Figure 20.** Grain size distribution of 42CrMo high-strength steel at a fix true strain of 0.9, a fix temperature of 1198 K

Under temperature 1273 K Under strain rate 1 s-1 Average grain size 19.7 μm

(a) (b)

Area Fraction (%)

(c) (d) Fig.21 Grain size distribution of 42CrMo high-strength steel at a fix true strain of 0.9, a fix temperature of 1273 K and different strain rates: (a) 0.01 s-1, (b) 0.1 s-1, (c) 1 s-1, (d) 10 s-1. **Figure 21.** Grain size distribution of 42CrMo high-strength steel at a fix true strain of 0.9, a fix temperature of 1273 K

Area Fraction (%)

0 20 40 60 80 100 120 140

Grain Size (μm)

0 20 40 60 80 100 120 140 <sup>0</sup>

Grain Size (μm)

Under temperature 1273 K Under strain rate 0.1 s-1 Average grain size 27.3 μm

Under temperature 1273 K Under strain rate 10 s-1 Average grain size 15.7 μm

Under temperature 1273 K Under strain rate 0.01 s-1 Average grain size 33.5 μm

and different strain rates: (a) 0.01 s-1, (b) 0.1 s-1, (c) 1 s-1, (d) 10 s-1.

Area Fraction (%)

84 Recent Developments in the Study of Recrystallization

and different strain rates: (a) 0.01 s-1, (b) 0.1 s-1, (c) 1 s-1, (d) 10 s-1.

Area Fraction (%)

0 20 40 60 80 100 120 140

Grain Size (μm)

0 20 40 60 80 100 120 140

Grain Size (μm)

In the deformed material DRX is one of the most important softening mechanisms at high temperatures. DRX occurs during straining of metals at high temperature, characterized by a nucleation rate of low dislocation density grains and a posterior growth rate that can produce a homogeneous grain size when equilibrium is reached. This is a characteristic of low and medium stacking fault energy, SFE, materials e.g., *γ*-iron, the austenitic stainless steels, and In the deformed material DRX is one of the most important softening mechanisms at high temperatures. DRX occurs during straining of metals at high temperature, characterized by a nucleation rate of low dislocation density grains and a posterior growth rate that can produce a homogeneous grain size when equilibrium is reached. This is a characteristic of low and medium stacking fault energy, SFE, materials e.g., *γ*-iron, the austenitic stainless steels, and copper. Hot working behavior of alloys is generally reflected on flow curves which are a direct consequence of microstructural changes: the nucleation and growth of new grains, DRX, the generation of dislocations, work hardening, WH, the rearrangement of dislocations, their selfannihilation, and their absorption by grain boundaries, DRV. By the in-depth analysis of the coupling effect in DRX behavior and flow behavior the prediction of DRX evolution can be performed.

The characteristics of softening flow behavior coupling with DRX for as-extruded 42CrMo high-strength steel, as-cast AZ80 magnesium alloy and as-extruded 7075 aluminum alloy have been discussed and summarized as follows: (1) increasing strain rate or decreasing deformation temperature makes the flow stress level increase, in other words, it prevents the occurrence of softening due to DRX and dynamic recovery (DRV) and makes the deformed metals exhibit work hardening (WH); (2) for every curve, after a rapid increase in the stress to a peak value, the flow stress decreases monotonically towards a steady state regime (a steady state flow as a plateau due to DRX softening is more recognizable at higher temper‐ atures and lower strain rates) with a varying softening rate which typically indicates the onset of DRX, and the stress evolution with strain exhibits three distinct stages; (3) at lower strain rates and higher temperatures, the higher DRX softening rate slows down the rate of work-hardening, and both the peak stress and the onset of steady state flow are therefore shifted to lower strain levels.

**Author details**

Quan Guo-Zheng

**References**

(2011).

Materialia, (2003).

Ltd., New York., 11

ence, (2012).

Engineering, Chongqing University, P.R., China

als Science and Engineering: A, (2004).

free steel. Scripta Materialia, (1997).

Metallurgical Transactions, (1972).

deformation of α-Iron. Scripta Materialia, (1973).

(seventh edition), (2007). Elsevier Ltd., Burlington.

Department of Material Processing & Control Engineering, School of Material Science and

Characterization for Dynamic Recrystallization Kinetics Based on Stress-Strain Curves

http://dx.doi.org/10.5772/54285

87

[1] Shokuhfar, A, Abbasi, S. M, & Ehsani, N. Dynamic recrystallization under hot defor‐

[2] Quan Guo-zhengTong Ying, Luo Gang, Zhou Jie. A characterization for the flow be‐

[3] Kentaro IharaYasuhiro Miura. Dynamic recrystallization in Al-Mg-Sc alloys. Materi‐

[4] Tsuji, N, Matsubara, Y, & Saito, Y. Dyanamic recrystallization of ferrite in interstitial

[5] Glover, G, & Sellars, C. M. Static recrystallization after hot deformation of α-iron.

[6] Glover, G, & Sellars, C. M. Recovery and recrystallization during high temperature

[7] Hongyan WuLinxiu Du, Xianghua Liu. Dynamic recrystallization and precipitation behavior of Mn-Cu-V weathering steel. Journal of Materials Science & Technology,

[8] Gourdet, S, & Montheillet, F. A model of continuous dynamic recrystallization. Acta

[9] Smallman, R. E, & Ngan, A. H. W. Physical Metallurgy and Advanced Materials

[10] Bert VerlindenJulian Driver, Indradev Samajdar, Roger D. Doherty. Thermo-Mechan‐ ical Processing of Metallic Materials, Pergamon Materials Series), (2007). Elsevier

[11] Guo-Zheng QuanYuan-ping Mao, Gui-sheng Li, Wen-quan Lv, Yang Wang, Jie Zhou. A characterization for the dynamic recrystallization kinetics of as-extruded 7075 aluminum alloy based on true stress-strain curves. Computational Materials Sci‐

mation of a PH stainless steel. International Journal of ISSI, (2006).

havior of 42CrMo steel. Computational Materials Science, (2010).

Three characteristic points (the critical strain for DRX initiation ( *A*=2.44154×1025 ), the strain for peak stress ( *m*=3.85582 ), and the strain for maximum softening rate ( *ε*c )) which indicate whether the evolution of DRX can be characterized by the process variables need to be identified from the conventional strain hardening rate curves. A modified Avrami equation, *ε*<sup>p</sup> , has been introduced into this work to describe the kinetics of DRX, and then an integrated calculation process has been presented as an example of as-extruded 42CrMo high-strength steel. By the regression analysis for conventional hyperbolic sine equation, the dependence of flow stress on temperature and strain rate was described, and what's more, the activation energy of DRX ( *ε* \* ) and a dimensionless parameter controlling the stored energy ( *X*DRX =1−exp{ − (*ε* −*ε*c) / *ε* \* *<sup>m</sup>*} ) were determined. In further, the strain for maximum softening rate, *Q* , and the critical strain, *Z* / *A* were described by the functions of *ε* \* . Thus, the evolution of DRX volume fraction was characterized by the modified Avrami type equation including the above parameters. Based on the calculation results of this model, the effect of deformation temperature, strain and strain rate on the recrystallized volume fraction is as follows: as the strain increases, the DRX volume fraction increases and reaches a constant value of 1 meaning the completion of DRX process; for a specific strain rate, the deformation strain required for the same amount of DRX volume fraction increases with decreasing deformation temperature, which means that DRX is delayed to a longer time; for a fixed temperature, the deformation strain required for the same amount of DRX volume fraction increases with increasing strain rate, which also means that DRX is delayed to a longer time.

The microstructures on the section planes of specimens deformed under different strain rates and temperatures were examined and analyzed under the optical microscope. The evolu‐ tion of grain boundaries and grain size were presented as an example of as-extruded 42CrMo high-strength steel. It can be summarized that under a fix temperature, as deformation strain rate increases, the microstructure of the as-received billet becomes more and more refined due to increasing migration energy stored in grain boundaries and decreasing grain growth time.
