**2. Description of softening flow behavior coupling with DRX**

Hot working behavior of alloys is generally reflected on flow curves which are a direct consequence of microstructural changes: the generation of dislocations, work hardening, WH, the rearrangement of dislocations, their self-annihilation, and their absorption by grain boundaries, DRV, the nucleation and growth of new grains, DRX. The latter is one of the most important softening mechanisms at high temperatures. This is a characteristic of low and medium stacking fault energy, SFE, materials e.g., *γ*-iron, the austenitic stainless steels, and copper. The most significant changes in the structure-sensitive properties occur during the primary recrystallization stage. In this stage the deformed lattice is completely replaced by a new unstrained one by means of a nucleation and growth process, in which practically stressfree grains grow from nuclei formed in the deformed matrix. The orientation of the new grains differs considerably from that of the crystals they consume, so that the growth process must be regarded as incoherent, i.e. it takes place by the advance of large-angle boundaries sepa‐ rating the new crystals from the strained matrix [1].

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. The process of recrystallization may be pictured as follows. After deformation, polygonization of the bent lattice regions on a fine scale occurs and this results in the formation of several regions in the lattice where the strain energy is lower than in the surrounding matrix; this is a necessary primary condition for nucleation. During this initial period when the angles between the sub-grains are small and less than one degree, the sub-grains form and grow quite rapidly. However, as the sub-grains grow to such a size that the angles between them become of the order of a few degrees, the growth of any given sub-grain at the expense of the others is very slow. Eventually one of the sub-grains will grow to such a size that the boundary mobility begins to increase with increasing angle. A large angle boundary, *θ* ≈ 30~40°, has a high mobility because of the large lattice irregularities or 'gaps' which exist in the boundary transition layer. The atoms on such a boundary can easily transfer their allegiance from one crystal to the other. This sub-grain is then able to grow at a much faster rate than the other sub-grains which surround it and so acts as the nucleus of a recrystallized grain. The further it grows, the greater will be the difference in orientation between the nucleus and the matrix it meets and consumes, until it finally becomes recogniz‐ able as a new strain-free crystal separated from its surroundings by a large-angle boundary [9].

the process. However, DRX is not a phenomenon restricted to fcc metals, it has been described on ice, some minerals, and even high purity α–Fe (bcc metal) [4-6]. In the deformed material DRX would affect the crystallographic texture and thus, material anisotropy. For example, DRX would eliminate some crystal defects, such as part of dislocations resulting from work hardening, which will improve hot plasticity, refine microstructure, and reduce the deforma‐ tion resistance [7]. High stacking fault energy (SFE) metals, such as aluminium alloys, alpha titanium alloys, and ferritic steels, undergo continuous dynamic recrystallization (CDRX) rather than discontinuous dynamic recrystallization (DDRX) during high temperature deformation. In particular, due to the high efficiency of dynamic recovery, new grains are not formed by a classical nucleation mechanism; the recrystallized microstructure develops instead by the progressive transformation of subgrains into new grains, within the deformed original grains. Dislocations produced by strain hardening accumulate progressively in lowangle (subgrain) boundaries (LABs), leading to the increase of their misorientation angle and the formation of high-angle (grain) boundaries (HABs), when a critical value of the misorien‐ tation angle is reached. The microstructure is thus intermediate between a subgrain and a grain structure: while grains and subgrains are entirely delimited by HABs and LABs, respectively, it will be referred to as an aggregate of crystallites, which are bounded partly by LABs and partly by HABs. On the contrary, low stacking fault energy (SFE) metals, such as magnesium alloys, austenitic steels, and beta titanium alloys, undergo discontinuous dynamic recrystal‐ lization (DDRX) rather than continuous dynamic recrystallization (CDRX) during high

**2. Description of softening flow behavior coupling with DRX**

rating the new crystals from the strained matrix [1].

Hot working behavior of alloys is generally reflected on flow curves which are a direct consequence of microstructural changes: the generation of dislocations, work hardening, WH, the rearrangement of dislocations, their self-annihilation, and their absorption by grain boundaries, DRV, the nucleation and growth of new grains, DRX. The latter is one of the most important softening mechanisms at high temperatures. This is a characteristic of low and medium stacking fault energy, SFE, materials e.g., *γ*-iron, the austenitic stainless steels, and copper. The most significant changes in the structure-sensitive properties occur during the primary recrystallization stage. In this stage the deformed lattice is completely replaced by a new unstrained one by means of a nucleation and growth process, in which practically stressfree grains grow from nuclei formed in the deformed matrix. The orientation of the new grains differs considerably from that of the crystals they consume, so that the growth process must be regarded as incoherent, i.e. it takes place by the advance of large-angle boundaries sepa‐

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. The process of recrystallization may be pictured as follows. After deformation, polygonization of the bent lattice regions on a fine scale occurs and this results in the formation of several regions in the lattice where the strain energy is

temperature deformation [8].

62 Recent Developments in the Study of Recrystallization

Fig.1 shows typical flow curves during cold and hot deformation. During hot deformation, the shape of the flow curve can be 'restricted', or work hardening rates counterbalanced, by dynamic recovery or by dynamic recrystallization (i.e. discontinuous dynamic recrystalliza‐ tion). Dynamic recovery is typical of high-SFE metals (e.g. aluminium, low-carbon ferritic steel, etc.), where the flow stress saturates after an initial period of work hardening. This saturation value depends on temperature, strain rate and composition. On the other hand, as shown in Fig.1, a broad peak (or multiple peaks) typically accompany dynamic recrystallization. Fig.2 illustrates schematically the microstructure developments during dynamic recovery and dynamic recrystallization. During dynamic recovery, the original grains get increasingly strained, but the sub-boundaries remain more or less equiaxed. This implies that the substruc‐ ture is 'dynamic' and re-adapts continuously to the increasing strain. In low-SFE metals (e.g. austenitic stainless steel, copper, etc.), the process of recovery is slower and this, in turn, may allow sufficient stored energy build-up. At a critical strain, and correspondingly at a value/ variation in driving force, dynamically recrystallized grains appear at the original grain boundaries – resulting in the so-called 'necklace structure'. With further deformation, more and more potential nuclei are activated and new recrystallized grains appear. At the same time, the grains, which had already recrystallized in a previous stage, are deformed again. After a certain amount of strain, saturation/equilibrium sets in (see Fig.2b). Typically equili‐ brium is reached between the hardening due to dislocation accumulation and the softening due to dynamic recrystallization. At this stage, the flow curve reaches a plateau and the microstructure consist of a dynamic mixture of grains with various dislocation densities. It is important, at this stage, to bring out further the structural developments and structure– property correlation accompanying dynamic recovery and dynamic recrystallization respec‐ tively [10].

The true compressive stress-strain curves for as-extruded 7075 aluminum alloy under different temperatures and strain rates are illustrated in Fig. 3a~d. The flow stress as well as the shape of the flow curves is sensitively dependent on temperature and strain rate. Comparing these curves with one another, it is found that increasing strain rate or decreasing deformation temperature makes the flow stress level increase, in other words, it prevents the occurrence of

where work hardening (WH) predominates, flow stress exhibits a rapid increase to a critical value. At the second stage, flow stress exhibits a smaller and smaller increase until a peak value or an inflection of work-hardening rate, which shows that the thermal softening due to DRX and dynamic recovery (DRV) becomes more and more predominant, then it exceeds WH. At the third stage, two types of curve variation tendency can be generalized as following: decreasing gradually to a steady state with DRX softening (573~723 K & 0.01 s-1, 623~723 K & 0.1 s-1, 623~723 K & 1 s-1, 723 K & 10 s-1), decreasing continuously with significant DRX softening (573 K & 0.1 s-1, 573 K & 1 s-1, 573~623 K & 10 s-1). Thus, it can be concluded that the typical form of flow curve with DRX softening, including a single peak followed by a steady state flow as a plateau, is more recognizable at higher temperatures and lower strain rates. That is because 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

Characterization for Dynamic Recrystallization Kinetics Based on Stress-Strain Curves


True Stress (Mpa)

0.01s

723 K 673 K 623 K

(a) (b)

(c) (d)


True Stress (Mpa)

Fig.3 True stress-strain curves of as-extruded 7075 aluminum alloy at different strain rates

**Figure 3.** True stress-strain curves of as-extruded 7075 aluminum alloy at different strain rates and temperatures. (a)

and temperatures. (a) 0.01 s-1, 573~723 K, (b) 0.1 s-1, 573~723 K, (c) 1 s-1, 573~723 K, (d) 10

The similar flow behavior of as-cast AZ80 magnesium alloy with as-extruded 7075

aluminum alloy is illustrated in Fig. 4a~d. Both deformation temperature and strain rate have

considerable influence on the flow stress of AZ80 magnesium alloy. From the true

stress-strain curves in Fig. 4a~d, it also can be seen that the stress evolution with strain

exhibits three distinct stages. At the first stage where work hardening (WH) predominates and

cause dislocations to polygonize into stable subgrains, flow stress exhibits a rapid increase to

0 -50 -100 -150 -200 -250 -300

> 0 -50 -100 -150 -200 -250 -300

0.0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9 -1.0

True Strain

0.0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9 -1.0

723 K 673 K 623 K

573 K

True Strain



0.1s

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

65

573 K

723 K 673 K 623 K

573 K

shifted to lower strain levels [11].

0 -50 -100 -150 -200 -250 -300

0 -50 -100 -150 -200 -250 -300


True Stress (Mpa)

s

True Stress (Mpa)

0.0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9 -1.0

True Strain

0.0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9 -1.0

723 K 673 K 623 K

0.01 s-1, 573~723 K, (b) 0.1 s-1, 573~723 K, (c) 1 s-1, 573~723 K, (d) 10 s-1, 573~723 K.

573 K

True Strain

**Figure 1.** Typical flow curves during cold and hot deformation

**Figure 2.** Evolution of the microstructure during (a) hot deformation of a material showing recovery and (b) continu‐ ous dynamic recrystallization (CDRX).

softening due to DRX and dynamic recovery (DRV) and makes the deformed metals exhibit work hardening (WH). The cause lies in the fact that higher strain rate and lower temperature provide shorter time for the energy accumulation and lower mobilities at boundaries which result in the nucleation and growth of dynamically recrystallized grains and dislocation annihilation. For every curve, after a rapid increase in the stress to a peak value, the flow stress decreases monotonically towards a steady state regime with a varying softening rate which typically indicates the onset of DRX. In further, from all the true stress-strain curves, it can be summarized that the stress evolution with strain exhibits three distinct stages. At the first stage where work hardening (WH) predominates, flow stress exhibits a rapid increase to a critical value. At the second stage, flow stress exhibits a smaller and smaller increase until a peak value or an inflection of work-hardening rate, which shows that the thermal softening due to DRX and dynamic recovery (DRV) becomes more and more predominant, then it exceeds WH. At the third stage, two types of curve variation tendency can be generalized as following: decreasing gradually to a steady state with DRX softening (573~723 K & 0.01 s-1, 623~723 K & 0.1 s-1, 623~723 K & 1 s-1, 723 K & 10 s-1), decreasing continuously with significant DRX softening (573 K & 0.1 s-1, 573 K & 1 s-1, 573~623 K & 10 s-1). Thus, it can be concluded that the typical form of flow curve with DRX softening, including a single peak followed by a steady state flow as a plateau, is more recognizable at higher temperatures and lower strain rates. That is because 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 [11].

Fig.3 True stress-strain curves of as-extruded 7075 aluminum alloy at different strain rates and temperatures. (a) 0.01 s-1, 573~723 K, (b) 0.1 s-1, 573~723 K, (c) 1 s-1, 573~723 K, (d) 10 **Figure 3.** True stress-strain curves of as-extruded 7075 aluminum alloy at different strain rates and temperatures. (a) 0.01 s-1, 573~723 K, (b) 0.1 s-1, 573~723 K, (c) 1 s-1, 573~723 K, (d) 10 s-1, 573~723 K.

The similar flow behavior of as-cast AZ80 magnesium alloy with as-extruded 7075

aluminum alloy is illustrated in Fig. 4a~d. Both deformation temperature and strain rate have

considerable influence on the flow stress of AZ80 magnesium alloy. From the true

stress-strain curves in Fig. 4a~d, it also can be seen that the stress evolution with strain

exhibits three distinct stages. At the first stage where work hardening (WH) predominates and

cause dislocations to polygonize into stable subgrains, flow stress exhibits a rapid increase to

s


softening due to DRX and dynamic recovery (DRV) and makes the deformed metals exhibit work hardening (WH). The cause lies in the fact that higher strain rate and lower temperature provide shorter time for the energy accumulation and lower mobilities at boundaries which result in the nucleation and growth of dynamically recrystallized grains and dislocation annihilation. For every curve, after a rapid increase in the stress to a peak value, the flow stress decreases monotonically towards a steady state regime with a varying softening rate which typically indicates the onset of DRX. In further, from all the true stress-strain curves, it can be summarized that the stress evolution with strain exhibits three distinct stages. At the first stage

**Figure 2.** Evolution of the microstructure during (a) hot deformation of a material showing recovery and (b) continu‐

(a) (b)

**Figure 1.** Typical flow curves during cold and hot deformation

64 Recent Developments in the Study of Recrystallization

ous dynamic recrystallization (CDRX).

The similar flow behavior of as-cast AZ80 magnesium alloy with as-extruded 7075 aluminum alloy is illustrated in Fig. 4a~d. Both deformation temperature and strain rate have considerable influence on the flow stress of AZ80 magnesium alloy. From the true stress-strain curves in Fig. 4a~d, it also can be seen that the stress evolution with strain exhibits three distinct stages. At the first stage where work hardening (WH) predominates and cause dislocations to polygonize into stable subgrains, flow stress exhibits a rapid increase to a critical value with increasing strain, meanwhile the stored energy in the grain boundaries originates from a large difference in dislocation density within subgrains or grains and grows rapidly to DRX activation energy. When the critical driving force is attained, new grains are nucleated along the grain boundaries, deformation bands and dislocations, resulting in equiaxed DRX grains. At the second stage, flow stress exhibits a smaller and smaller increase until a peak value or an inflection of work-hardening rate, which shows that the thermal softening due to DRX and dynamic recovery (DRV) becomes more and more predominant, then it exceeds WH. At the third stage, two types of curve variation tendency can be generalized as following: decreasing gradually to a steady state with DRX softening (573~673 K & 0.01 s-1, 623~673 K & 0.1 s-1, 573 K & 1 s-1,, 673 K & 1 s-1), and decreasing continuously with significant DRX softening (523 K & 0.01 s-1, 523~573 K & 0.1 s-1, 523 K & 1 s-1,, 623 K & 1 s-1, 523~673 K & 10 s-1) [12-14].

A little different flow behavior of as-cast 42CrMo high-strength steel from as-extruded 7075 aluminum alloy and as-cast AZ80 magnesium alloy is illustrated in Fig. 5a~d. From the true stress-strain curves in Fig. 5a~d, it also can be seen that the stress evolution with strain exhibits three distinct stages. But the difference is as follows: at the third stage, three types of curve variation tendency can be generalized as following: decreasing gradually to a steady state with DRX softening (1123~1348 K & 0.01 s-1, 1198~1348 K & 0.1 s-1, 1273~1348 K & 1 s-1), maintaining higher stress level without significant softening and work-hardening (1123~1198 K & 1 s-1, 1123~1348 K & 10 s-1), and increasing continuously with significant work-hardening (1123 K

Fig. 5 True stress-strain curves of as-extruded 42CrMo high-strength steel obtained by

**Figure 5.** True stress-strain curves of as-extruded 42CrMo high-strength steel obtained by Gleeble 1500 under the dif‐

Gleeble 1500 under the different deformation temperatures with strain rates. (a) 0.01 s-1, (b)

(c) (d)

exhibits three distinct stages. But the difference is as follows: at the third stage, three types of

curve variation tendency can be generalized as following: decreasing gradually to a steady

state with DRX softening (1123~1348 K & 0.01 s-1, 1198~1348 K & 0.1 s-1, 1273~1348 K &

1 s-1), maintaining higher stress level without significant softening and work-hardening

(1123~1198 K & 1 s-1, 1123~1348 K & 10 s-1), and increasing continuously with significant

True Stress MPa)

(a) (b)

True Stress MPa)

1s

0 -26 -52 -78 -104 -130 -156

0 -38 -76 -114 -152 -190 -228

0.0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9 -1.0

True Strain


1198K 1123K

1273K 1348K

0.0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9 -1.0

True Strain


Characterization for Dynamic Recrystallization Kinetics Based on Stress-Strain Curves

1198K

1273K 1348K

1123K

0.1s

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

67

10s

0.01s

work-hardening (1123 K & 0.1 s-1) [15-17].


0.0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9 -1.0

True Strain


1198K 1123K

1273K 1348K

0.0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9 -1.0

True Strain

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

1198K

1273K

1348K

1123K

0 -20 -40 -60 -80 -100 -120

0 -30 -60 -90 -120 -150 -180

0.1 s-1, (c) 1 s-1, (d) 10 s-1.

True Stress (MPa)

True Stress (MPa)

From the true compressive stress-strain data of as-extruded 42CrMo high-strength steel shown in Fig. 5a~d, the values of the strain hardening rate ( *θ* =d*σ* / d*ε* ) were calculated. The critical

& 0.1 s-1) [15-17].

**3.1. The initiation of DRX**

**3. DRX critical strain and DRX kinetic model**

**Figure 4.** True stress-strain curves of as-cast AZ80 magnesium alloy obtained by Gleeble 1500 under different defor‐ mation temperatures with strain rates (a) 0.01 s-1, (b) 0.1 s-1, (c) 1 s-1, (d) 10 s-1.

(1123~1198 K & 1 s-1, 1123~1348 K & 10 s-1), and increasing continuously with significant Characterization for Dynamic Recrystallization Kinetics Based on Stress-Strain Curves http://dx.doi.org/10.5772/54285 67

exhibits three distinct stages. But the difference is as follows: at the third stage, three types of

curve variation tendency can be generalized as following: decreasing gradually to a steady

state with DRX softening (1123~1348 K & 0.01 s-1, 1198~1348 K & 0.1 s-1, 1273~1348 K &

1 s-1), maintaining higher stress level without significant softening and work-hardening

work-hardening (1123 K & 0.1 s-1) [15-17].

Fig. 5 True stress-strain curves of as-extruded 42CrMo high-strength steel obtained by **Figure 5.** True stress-strain curves of as-extruded 42CrMo high-strength steel obtained by Gleeble 1500 under the dif‐ ferent deformation temperatures with strain rates. (a) 0.01 s-1, (b) 0.1 s-1, (c) 1 s-1, (d) 10 s-1.

Gleeble 1500 under the different deformation temperatures with strain rates. (a) 0.01 s-1, (b)

A little different flow behavior of as-cast 42CrMo high-strength steel from as-extruded 7075 aluminum alloy and as-cast AZ80 magnesium alloy is illustrated in Fig. 5a~d. From the true stress-strain curves in Fig. 5a~d, it also can be seen that the stress evolution with strain exhibits three distinct stages. But the difference is as follows: at the third stage, three types of curve variation tendency can be generalized as following: decreasing gradually to a steady state with DRX softening (1123~1348 K & 0.01 s-1, 1198~1348 K & 0.1 s-1, 1273~1348 K & 1 s-1), maintaining higher stress level without significant softening and work-hardening (1123~1198 K & 1 s-1, 1123~1348 K & 10 s-1), and increasing continuously with significant work-hardening (1123 K & 0.1 s-1) [15-17]. 0.1 s-1, (c) 1 s-1, (d) 10 s-1.
