Characterization of Hot Deformation Behavior for Pure Aluminum Using 3D Processing Maps

Introduction

Processing map was used to evaluate hot deformation behavior of materials, and it was still a powerful method to establish and optimize material thermal processing parameters. It was viable to predict the characteristics and mechanism of deformation under different deformation conditions using the processing map, such as dynamic recovery and dynamic recrystallization (DRX), wedge cracking, cavitation and adiabatic shear band [1, 2, 3]. Classically, there were two kinds of processing map: the first one was based on the atomic model, just like Raj processing map; the other one was based on dynamic material model [4]. Prasad proposed dynamic material modeling (DMM) model on the base of physical system simulation, continuum mechanics and irreversible thermodynamics theory [5, 6], and this model was developed subsequently by Narayana [7], and this model has been successfully applied in more than 200 kinds of alloy materials.

It was generally believed that metal materials were divided into two types by stacking fault energy: dynamic recovery alloys (high-stacking fault energy) and DRX alloys (low-stacking fault energy). The stacking fault energy mainly represented the ability level of the dislocation sliding. When material stacking fault energy was high, the fault ribbon between two adjacent displacement was narrow, it was easy for sliding and climbing, and this kind of material was prone to occur dynamic recovery; When material stacking fault energy was low, it was difficult for sliding and climbing, DRX was preferred to occur because of dislocation pile-up. Recently, it was considered that DRX of aluminum only occur at high temperature and high strain rate, and the DRX in aluminum alloy was regarded to be divided into three processes [8, 9, 10, 11]: (1) discontinuous DRX, included grain nucleation and propagation; (2) continuous DRX, which the dislocation networks formed subgrain structures with low-angle boundaries. The misorientation increased along with plastic deformation, initially grain boundaries were immobilized because of pinning effect; (3) geometric DRX, where the initial grains were deformed and fragmented as high-angle boundaries created by subgrain formation were pinched-off and annihilated eventually [12].

Hot deformation of the specimen was considered to be kind of the nonlinear energy dissipation, as well as material processing can be regarded as a process of energy dissipation. At present, the actual applications of processing maps were mostly based on DMM. Liu [13] studied hot deformation behavior of Ti-6.0Al-7.0Nb biomedical alloy and optimized the hot deformation conditions using processing map method, and it is found that hot working had very short transient and it is essential of steady state type because of that the energy dissipation maps exhibited similar features at different strains. Xu [14] investigated the hot deformation behavior of as-cast AZ91D magnesium alloy using the processing map and the standard kinetic analysis. The result suggested that the thermally activated climb process associated with basal glide was considered to be the rate-controlling factor or deformation mechanism for the two regions. Lin [15] studied the high-temperature flow behavior of 7075 aluminum alloy, and processing maps were constructed by superimposing the instability map over the energy dissipation map. Metallographic photos showed that the high-angle boundaries and coarse precipitations distributed in the grain interior boundaries, which should be avoided in the final products. Rajamuthamilselvan [16] studied the hot deformation behavior of stir cast 7075 alloy using processing map, and the DRX zone, instable zones, interface crack and wedge cracking were confirmed. As mentioned above, after being superimposed on the energy dissipation map, the traditional processing map can be achieved to optimize the hot processing, and investigations have been conducted in different kinds of materials.

Nevertheless, the traditional processing map was independent of the strain. Liu [17] constructed the 3D processing maps with consideration of the effect of strain on the workability, and he investigated the metal workability of magnesium alloy ZA31B using 3D processing maps. Wang [18] determined the stable and instable processing conditions of whole deformation process combined traditional and 3D processing maps, and the optimized processing parameters for AA7050 aluminum alloy were determined. Quite few of researchers utilized the 3D processing map to investigate the deformation behavior of materials. It can be conceded that little research work was focused on the hot deformation characteristics and hot workability design for pure aluminum using 3D processing maps.

Therefore, in this study, the hot deformation behavior of pure aluminum was investigated by isothermal compression tests under wide ranges of forming temperatures and strain rates. The effects of forming temperature, strain rate and strain on the flow behaviors were analyzed. 3D processing maps were employed to explore the deformation mechanisms during hot deformation so as to realize the process parameter optimization.

Materials and experiments

The nominal chemical composition of pure aluminum 1060 used in this experiment was shown in Table 1. Compression specimens were machined to a cylinder with diameter of 8 mm and height of 12 mm. The annealing was applied at 573 K for 2 h in order to remove residual stress with furnace cooling, and the microstructure after annealing was shown in Figure 1. It can be seen that the microstructure was mainly equiaxial grain which showed a uniform meshed distribution, and a little columnar crystals interspersed with the microstructure. Besides, in order to minimize the friction effect between specimen and fixture, two flat ends of the test specimen in the process were painted with a layer of nickel base lubricant.

Figure 1:

Microstructure of 1060 aluminum after annealing treatment.

Samples were protected by argon in the whole test process, and the experiment adopted self-resistance heating with heating rate of 10 K/s. The deformation temperature was measured by thermocouples welded to the center of the specimen end face. As shown in Figure 2, the specimens were heated to the deformation temperature and soaked for 3 min to ensure a homogenous temperature distribution before compression. The isothermal hot compression experiment was carried out at deformation temperature of 523, 573, 623, 673, 773, 823 K, and strain rates of 0.005, 0.01, 0.1, 1, 5 and 10 s⁻¹. All specimens were compressed to 60 % of their initial height, and compression samples were shown in Figure 3. Gleeble-1500 thermal simulator automatically controlled the deformation conditions, such as temperature, reduction and strain rate. The load versus displacement curves can be obtained from the compression tests, and the curves were finally converted into true stress–true strain curves. All data of true stress and true strain were collected using software. After compression of each sample, the argon was removed rapidly and the specimen was quenched with water to keep the deformed microstructure. Deformed specimens were split into two parts along the compression axis symmetrically, and then the cross-section was polished with sandpapers and electropolished with electrolyte (85 % alcohol, 15 % perchloric acid) at a Lectropol-5 Electrolytic polishing machine (polishing voltage of 22 V, time of 60 s). Finally, the cross-section was etched with an etching solution (5 ml HF, 50 ml H₂O) for microstructure observation at an KEYENCE WHX-100 digital microscope.

Figure 2:

Experimental procedure of hot compression tests.

Figure 3:

The original sample and isothermal compression samples.

Flow behavior of pure aluminum

The true stress–strain curves are illustrated in Figure 4. The deformation temperature and strain rate influenced the flow behavior obviously, the peak stress increased with the decreasing of deformation temperature and the increasing of strain rate. For each curve, the flow stress increased rapidly at the early stage of deformation due to the dislocation multiplication. After the stress peak, the curve appeared into two forms: (1) the flow stress decreased and then kept a steady state; (2) the flow stress remained fairly steady as the strain increased. As flow stress–strain curve of strain rate 0.005 s⁻¹, temperature 523 K showed the first form, part of the work hardening was gradually offset due to the effect of dynamic recovery, which made the slope of the stress–strain curve decrease and it tend to be stable. The second form was the result of equilibrium of work hardening and dynamic softening, such as flow stress–strain curve of strain rate 1 s⁻¹, temperature 523 K.

Figure 4:

Flow stress–strain curves of pure aluminum at strain rate of: (a) 0.005 s⁻¹; (b) 0.01 s⁻¹; (c) 0.1 s⁻¹; (d) 1 s⁻¹; (e) 5 s⁻¹ and (f) 10 s⁻¹.

The optical microstructure of pure aluminum under different deformation conditions are shown in Figure 5. It can be observed that grain boundary showed the sawtooth shape in Figure 5(a), which was attributed to dynamic recovery during deformation, and the grain elongated perpendicular to the direction of compression in Figure 5(b) and 5(c). In the compression process, screw dislocation gliding and edge dislocation climbing occurred and led to dislocation cancellation, as well as grain multilateral process [19]. Figure 5(d) presented the optical microstructure of the specimen compressed at 773 K and strain rate of 0.005 s⁻¹, the fine grains can be observed in the microstructure and the DRX can be deduced to occur and the fine grains can be achieved.

Figure 5:

Optical microstructure of pure aluminum at strain of 0.9: (a) 623 K, 5 s⁻¹; (b) 623 K, 1 s⁻¹; (c) 573 K, 1 s⁻¹ and (d) 773 K, 0.005 s⁻¹.

The TEM bright field images of pure aluminum under different deformation conditions are shown in Figure 6. Figure 6(a) showed the TEM bright field image result of the specimen at 623 K and strain rate of 5 s⁻¹, the grain boundary after the deformation process was the high-angle boundary which was at equilibrium, and this was forming because of the dynamic recovery in the deformation process. In Figure 6(b) and (c), the original grain boundary was bending after compression deformation, and a large number of dislocation was assembled at the grain boundary. Figure 6(d) represented the subgrain structure and the equiaxial grain structure was forming in this region, and the grain size was small because of the grain refinement that occurred under this condition; however, a few rough grain was still found in the same region.

Figure 6:

TEM bright field images of pure aluminum at strain of 0.9: (a) 623 K, 5 s⁻¹; (b) 623 K, 1 s⁻¹; (c) 573 K, 1 s⁻¹ and (d) 773 K, 0.005 s⁻¹.

Establishment of processing maps

Dynamic materials model

Based on the DMM [4], metal forging process was regarded as a closed thermodynamics system composed of equipment, die and workpiece. It was known that forging process was related to the internal energy dissipation of deformation material; therefore, the thermal deformation of metal material was a nonlinear energy dissipation process. As shown in Figure 7, the rectangular area was the input energy P of the external force to the deformation of material (power of unit volume material), it mainly contributed into two aspects: one is the plastic deformation, energy dissipation in plastic deformation was represented by G, which converted into plastic heat in the deformation process, most of the energy was converted into heat, while a small group stored in the form of lattice defects energy in the deformation material; and the other is microstructure evolution, such as dynamic recovery, DRX, internal crack, grain growth, dynamic spheroidizing of acicular structure and phase transition, and energy dissipation in microstructure evolution that was represented by J. Hence, the absorb energy P for thermal deformation material in the plastic deformation process can be expressed as [20]:

(1)P=σε˙=G+J=0ε˙σdε˙+0σε˙dσ,

Figure 7:

Schematic diagram of energy dissipation based on DMM: (a) nonlinear energy dissipation and (b) linear energy dissipation.

where σ was flow stress (MPa); ε˙ was strain rate (s⁻¹). The proportion of J and G in total energy was expressed as following [21]:

(2)dJdG=ε˙dσσdε˙=d(logσ)d(logε˙)=m.

As shown in eq. (2), strain rate sensitivity exponent m determines the allocation proportion of P between G and J, namely the total absorbed energy P was consumed in certain proportion in the plastic deformation G and microstructure evolution J, respectively.

Under certain deformation temperature and strain, the dynamic constitutive relation followed power law equation in hot deformation process [3]:

(3)σ=Kε˙m

J was defined as:

(4)J=mm+1σε˙

While for an ideal linear energy dissipation unit m=1, J reached the maximum [22].

(5)J=Jmax=P2=σε˙2

As the shaded part area shown in Figure 4(b), microstructure evolution J at ideal linear energy dissipation reaches the maximum, which was greater than J at the form of nonlinear energy dissipation. Then, divide nonlinear energy dissipation J by ideal linear energy dissipation J_max, and a dimensionless parameter of energy dissipation rates η can be obtained as follows [23]：

(6)η=JJmax=21−1σε˙0ε˙σdε˙

When m was approximately a constant value, it can be obtained [24]:

(7)η=2m1+m

Energy dissipation rates η reflected the ratio relationship between microstructure evolution J and total absorbed energy P under a certain deformation temperature and strain rate. In hot deformation process, η played an important role on selecting the optimum hot forming process parameters, and η also reflected microstructure evolution mechanism. As known, dynamic recovery, DRX and superplastic were security thermal deformation mechanism, while wedge cracks and voids were insecurity thermal deformation mechanism, which should be avoided in hot deformation process.

Traditional processing maps of pure aluminum

Approach of processing maps

The traditional method of calculating strain rate sensitivity exponent m was adopting polynomial of 5 to fit the relationship of logσ and logε˙:

(12)logσ=a+b⋅logε˙+c⋅(logε˙)2+d⋅(logε˙)3+e⋅(logε˙)4+f⋅(logε˙)5

where a, b, c, d, e and f were all fitting coefficients.

The relation of m and logε˙can be obtained by the derivation of eq. (12):

(13)m=b+2c⋅logε˙+3d⋅(logε˙)2+4e⋅(logε˙)3+5f⋅(logε˙)4

And, the relation of mʹ and log ε˙ can be obtained by the derivation of eq. (13):

(14)m′=2c+6d⋅logε˙+12e⋅(logε˙)2+20f⋅(logε˙)3

When the strain and strain rate was the constant, flow stress was a function of deformation temperature as shown:

(15)σ(T)=C⋅fT=C⋅expmQRT

where C is a constant, which is independent of temperature. As defined of Malas stability criterion, s=(1/T)[∂(lnσ)/∂(1/T)]ε˙,ε. It was widely known: s=mQ/RT, where s and m were the functions of temperature. However, functional relationship between m and strain rate can be fitted by the m value at different strain rate. Therefore, eq. (15) can be converted into:

(16)σ(T)=C⋅exp(s)

Taking logarithm on both sides of eq. (16):

(17)ln σ(T)=lnC+s

s can be obtained by s=(1/T)[∂(lnσ)/∂(1/T)]ε˙,ε, then fitting s with logε˙ with polynomial of 5 at the same temperature, shown as follows:

(18)s=a+b⋅logε˙+c⋅(logε˙)2+d⋅(logε˙)3+e⋅(logε˙)4+f⋅(logε˙)5,

where a, b, c, d, e and f were all fitting coefficients.

The relation of s and logε˙can be obtained by the derivation of eq. (18):

(19)s′=b+2c⋅logε˙+3d⋅(logε˙)2+4e⋅(logε˙)3+5f⋅(logε˙)4

Establishment of traditional processing maps

The processing map method was very beneficial for optimizing hot workability and controlling microstructure in the material. The values of η at different temperatures and strain rates can be obtained based on eq. (7). Processing maps can be obtained through superimposing an instability maps on an energy dissipation maps [26]. Figure 8 showed the processing maps of pure aluminum processed under different strains based on Malas stability criterion. The contour numbers represented the efficiency of energy dissipation (η), and the shaded regions corresponded to flow instability: the red regions corresponded to instability regions of m; green regions corresponded to instability regions of mʹ; blue regions corresponded to instability regions of s; and sky blue regions corresponded to instability regions of sʹ. Analyzed by thermodynamic theory, forgings can be regarded as a closed system in the deformation process; the irreversible changes of microstructure evolution and heat transfer happened within the deformation. In addition, it still exchanged energy with surrounding environment, which was a nonlinear irreversible process and far-from equilibrium system.

Figure 8:

Processing maps of pure aluminum processed under different strains: (a) 0.1; (b) 0.2; (c) 0.3; (d) 0.4; (e) 0.5; (f) 0.6; (g) 0.7; (h) 0.8; and (i) 0.9.

As shown in Figure 8, it was far away from the equilibrium state of nonlinear irreversible process, the inside entropy was gradually decreasing in the whole deformation process. Malas instability regions affected by strain rate sensitivity exponent m were larger, mainly focused on high-strain rate region (strain rate of 1–10 s⁻¹), and low temperature (temperature of 523–750 K). Malas instability regions affected by temperature sensitivity exponent s mainly focused on low-temperature region (temperature of 523–578 K), and high-temperature region (temperature of 723–823 K). Generally, instability regions affected by strain rate sensitivity exponent m and temperature sensitivity exponent s were associated with the microstructure evolution. It was found that stability regions determined by Malas was mainly located at two domains: one located in the strain rate range of 0.1–0.3 s⁻¹ and temperature of 673–773 K with energy dissipation of 30 %, the other located in the strain rate range of 0.005–0.01 s⁻¹ and temperature range of 773–823 K with energy dissipation of 42 %. It was necessary to point out the variation of strain which plays significant role on the deformation behavior of materials; thus, the 3D instability map and 3D energy dissipation map of the pure aluminum were studied subsequently.

3D dynamic processing maps of pure aluminum

The 3D processing maps were based on the 2D processing maps proposed by Prasad model, which consisted two parts: one 3D energy dissipation map and one 3D instability map. The 3D processing maps can be described by the distribution of the efficiency of energy dissipation and flow instability regions under various processing conditions [27].

Determination of material parameters

The stress values were obtained at strain of 2 %, 4 %，6 %，8 %，10 %，20 %，30 %，40 %, 50 %，60 %，70 %，80 %，90 %, strain rate of 0.005, 0.01, 0.1, 1, 5, 10 s⁻¹, and temperature of 523, 573, 623, 673, 773, 823 K, respectively. Thus σ(εi,ε˙i,Ti) represented the stress at certain strain, strain rate and temperature. Taking ε−(ε˙i,Ti) for example, and assuming that there were three levels for each factor as described in Table 2, the mean stress value of σ(ε,ε˙) and σ(ε,T) at different levels could be acquired as follows:

(20)σ(ε,ε˙)=∑Tσ(ε,ε˙,T)/3,

(21)σ(ε,T)=∑ε˙σ(ε,ε˙,T)/3,

Table 2:

The table ε−σ(ε˙i,Ti) of three test factors with three levels.

ε	σ(έ,T)
	σ(εi,ε˙1,T1)	σ(εi,ε˙1,T2)	σ(εi,ε˙1,T3)	σ(ε˙1)	…	σ(ε˙2)	…	σ(ε˙3)	σ(ε)
ε1				σ(ε1,ε˙1)		σ(ε1,ε˙2)		σ(ε1,ε˙3)	σ(ε1)
ε2		σ(εi,ε˙1,Ti)		σ(ε2,ε˙1)		σ(ε2,ε˙2)		σ(ε2,ε˙3)	σ(ε2)
ε3				σ(ε3,ε˙1)		σ(ε3,ε˙2)		σ(ε3,ε˙3)	σ(ε3)

where σ(ε,ε˙) was the mean value of all temperatures, σ(ε,T) was the mean value of all strain rates and σ(ε,ε˙,T) was the flow stress corresponding to the processing parameters.

The mean stress value of σ(ε) at different levels could be acquired as follows:

(22)σ(ε)=∑T−ε˙σ(ε,ε˙,T)/9=∑ε˙σ(ε,ε˙)/3=∑Tσ(ε,T)/3,

where σ(ε) was the mean value of all temperatures and strain rates.

The table of ε˙−σ(εi,Ti) can be obtained in the same way, then the mean stress value of σ(ε˙,ε), σ(ε˙,T), σ(ε˙) at different levels could be acquired. Then, the mean stress value of σ(T,ε), σ(T,ε˙), σ(T) at different levels could be acquired by establishing the table of T−(εi,ε˙i). Based on the physical theory of plastic deformation, the relation of σ and ε˙ was shown as follows [3, 28]:

(23)σ=Nεn

(24)σ=Mε˙m

(25)σ=SexpmQRT=Sexps′T=Sexp(s)

Eqs. (23), (24), and (25) can be transformed into another form by taking logarithm of both sides.

(26)lnσ=lnN+nlnε

(27)lnσ=lnM+mlnε˙

(28)lnσ=lnS+mQRT=lnS+s′T=lnS+s

The values of n and m can be obtained from the slope of lines in ln σ−lnε plot according to eqs. (26) and (27). We define s′=mQ/R, then s′ can be acquired from the slope of lines in lnσ−1/T plot according to eq. (26), and s can be obtained as defined s=s′/T. According to Table 2, the mean stress value of σ(ε) can be achieved. The value of n varying with strain can be derived from the slope of the lines in ln σ(ε)−ln (ε). Subsequently, the value of n varying with strain rate and temperature can be derived from the slopes of lines in ln σ(ε,ε˙)−ln(ε) and ln σ(ε,T)−ln (ε), respectively. The parameters m, s varying with strain, strain rate and temperature can be obtained in the same way, as shown in Figure 9.

Figure 9:

n, m, s changing with strain, strain rate and temperature: (a) n(ε), n(ε˙), n(T); (b)m(ε), m(ε˙), m(T); and (c)s(ε), s(ε˙), s(T).

The n, m, and s varying with strain, strain rate and temperature can be expressed by fifth power of polynomial. Coefficients of the polynomial are presented in Table 3.

Table 3:

The fitting coefficients of the fifth power of polynomial about n, m, s.

Parameter	C0	C1	C2	C3	C4	C5
n(ε)	0.2454	−3.9845	21.7928	−56.3611	66.8725	−29.2930
n(log(ε˙))	0.0279	0.0222	−0.0194	−0.0137	−0.0048	−0.0010
n(T/1000)	−127.3865	972.3961	−2938.2428	4396.6689	−3260.3587	959.0222
m(ε)	0.0408	0.3524	−1.5632	3.3889	−3.3830	1.2235
m(log(ε˙))	−0.0196	−0.0344	0.1117	0.1346	0.0376	0
m(T/1000)	52.0217	−413.4907	1300.2062	−2021.8458	1556.2107	−474.4889
s(ε)	2.7070	17.1580	−95.9430	235.2326	−258.9123	104.5667
s(log(ε˙))	3.3478	−0.0220	0.7333	−0.2673	−0.5868	−0.1609
s(T/1000)	3596.2293	−23,929.0729	59,170.2136	−64,342.1430	25,951.5028	0

Three curves of n, m and s varying with strain, strain rate and temperature intersected almost at one point, with red marked in Figure 9. The n, m and s values of intersection point were 0.024, 0.077 and 3.62, respectively. Then the rule of n(ε,ε˙,T), m(ε,ε˙,T) and s(ε,ε˙,T) can be obtained as follows:

(29)n(ε,ε˙,T)=n(ε)+n(ε˙)+n(T)−2n0

(30)m(ε,ε˙,T)=m(ε)+m(ε˙)+m(T)−2m0

(31)s(ε,ε˙,T)=s(ε)+s(ε˙)+s(T)−2s0

where n₀, m₀ and s₀ were values of intersection point.

n′(ε,ε˙,T)=∂n(ε,ε˙,T)∂ε+∂n(ε,ε˙,T)∂ε˙+∂n(ε,ε˙,T)∂T

m′(ε,ε˙,T)=∂m(ε,ε˙,T)∂ε+∂m(ε,ε˙,T)∂ε˙+∂m(ε,ε˙,T)∂T

s′(ε,ε˙,T)=∂s(ε,ε˙,T)∂ε+∂s(ε,ε˙,T)∂ε˙+∂s(ε,ε˙,T)∂T

3D energy dissipation maps and 3D instability maps

It can be considered that it is beneficial to develop the hot processing map for the metals if the corresponding flow stress data were achieved from an extensive scale of deformation temperature and strain rate [29]. Energy dissipation rate η was obtained in eq. (7); Figure 10 shows 3D energy dissipation maps at different strains, temperatures and strain rates, and different gray grid point represented energy dissipation value in the energy dissipation maps. In Figure 10(a), it was found that the distribution of energy dissipation rates was similar to that of energy dissipation maps at different strains. However, energy dissipation rate η was still increasing with increasing of strain, due to energy participating in the increased microstructure evolution. In Figure 10(b), the region at temperature of 523 K, strain rate of 1 s⁻¹ showed lower energy dissipation rate of −17 %, the energy which participated into the microstructure evolution was little, and this was easy to cause deformation microdefects. The forming process energy input was mainly used for microstructure evolution of pure aluminum including DRV (Dynamic Recovery) and DRX. As shown in Figure 10(c), the region at strain rate of 10 s⁻¹ showed high-energy dissipation rate of 38 %, and the region at temperature of 823 K, strain rate of 0.005 s⁻¹ showed higher energy dissipation rate of 42 %. The corresponding process parameters indicated that the area should be of pure aluminum alloy having optimum parameters within the range of the test parameters. Figure 11 showed the cracking occurred at 623 K/1 s⁻¹, with the strain 0.9, and it can be seen that the cracking initially occurred at the phase interface because of the stress concentration. Once the material was hot processed in the instable region, it was undesirable to obtain the perfect mechanical properties. As a result, the proper process parameters were ought to be kept away from this region.

Figure 10:

3D energy dissipation maps at different strains, temperatures and strain rates: (a) at strain of 0.02, 0.04, 0.06, 0.08, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8 and 0.9; (b) at temperature of 523, 573, 623, 673, 773 and 823 K; and (c) at strain rate of 0.005, 0.01, 0.1, 1, 5 and 10 s⁻¹.

Figure 11:

Surface cracking of pure aluminum deformed at 623 K/1 s⁻¹.

Then, the 3D dynamic instability maps can be obtained by plotting the relationship between n, m, s and strain, strain rate and temperature on the base of MATLAB, as shown in Figure 12. The color section was responsible for instability regions corresponding to n, m, s stability criterion, instead, the blank section was stability regions. As shown in Figure 12(a), the strain hardening exponent n reflected the work-hardening effect of material. It was well known that the strain hardening exponent n resulted from a competition between thermal softening and work hardening. Figure 12(a) shows that when strain was over 0.1, n decreased sharply which was associated with bulging deformation or thermal softening effect. Strain rate sensitivity exponent m reflected the viscous flow ability in material processing, which was very important in determining the tensile ductility of superplastic material [30]. Figure 12(b) showed the variation of strain rate sensitivity exponent m with strain, strain rate and temperature in isothermal compression of pure aluminum. The variation of strain rate sensitivity exponent m with strain was controlled by three aspects: (i) thermal softening related to dislocation annihilation; (ii) work hardening due to dislocation accumulation and dislocation–dislocation interaction; (iii) microstructure evolution. In Figure 12(b), it was shown that m increased slowly with increasing strain firstly and then almost remained stable. It was proved that the strain rate sensitivity exponent m increased with increasing temperature and decreasing strain rate [31]. The instability region about strain rate sensitivity exponent m was determined in the strain rate range of 0.01–1 s⁻¹. Temperature sensitivity exponent s was used to characterize the sensitivity of the flow stress on deformation temperature. Figure 12(c) showed the variation of temperature sensitivity exponent s with strain, strain rate and deformation temperature in isothermal compression of pure aluminum. The instability region about temperature sensitivity exponent s was determined as the temperature range of 723–823 K. Moreover, s decreased gradually with increasing strain rate at the same deformation temperature, since deformation temperature increased quickly at high-strain rate, while the actual temperature fluctuation was smaller compared with that at low-strain rate, it resulted that the value of temperature sensitivity exponent s was lower at high-strain rate.

Figure 12:

3D dynamic instability maps: (a) n(ε,ε˙,T); (b) m(ε,ε˙,T); (c) s(ε,ε˙,T).

Conclusions

Isothermal compression tests were carried out on pure aluminum at the temperatures of 523–823 K and strain rates of 0.005–10 s⁻¹. The traditional processing maps and 3D dynamic processing maps were constructed to evaluate the efficiency of energy dissipation and recognize the flow instability regions. The following conclusions were drawn from this research:

1. It was found that stability regions determined by Malas was mainly located at two domains for the pure aluminum: one located in the strain rate range of 0.1–0.3 s⁻¹ and temperature of 673–773 K with energy dissipation of 30 %, the other located in the strain rate range of 0.005–0.01 s⁻¹ and temperature range of 773–823 K with energy dissipation of 42 %.

2. 3D processing maps considering the strain variable were developed, and the energy dissipation maps and the dynamic instability maps were changed with the strain increasing. The stability region occurred in the temperature range of 773–823 K and strain rate range of 0.005–0.01 s⁻¹ with the peak energy dissipation rate of 42 %.

3. 3D processing maps showed that region at strain rate of 10 s⁻¹ and the region at temperature of 823 K, strain rate of 0.005 s⁻¹ showed high-energy dissipation rate. The 3D dynamic instability maps showed instability region of different parameters, the proper process parameters were ought to be kept away from this region. The conditions of the cracking microstructure occurred proving that the region was determined by the 3D instability maps.