ABSTRACT: The GLEEBLE-1500 hot compression test scheme was developed based on continuous extrusion process, the flow stress of H62 brass was measured, the constitutive relation of H62 brass was described by Arrhenius equation in exponential form, and the hot working diagram of H62 brass was drawn, the distribution of power dissipation factor and microstructure, as well as the location of plastic instability region during continuous extrusion of H62 brass alloy were predicted. The optimum thermal deformation parameters of H62 brass alloy were determined as strain rate 0.01 s-1 and temperature 400ー500 °C. Key Words: Metal Material; Brass Alloy; continuous extrusion; hot working drawing; Constitutive Relation; Middle Diagram of flow stress classification number: TG14611; TG11325 Reference Number: A article number: 1001-0211(2010)02-0007

The flow stress in hot deformation of metal is one of the basic properties of material at high temperature. It is not only affected by the deformation temperature, the degree of deformation, the strain rate and the chemical composition of alloy, but also the comprehensive reflection of the microstructure evolution in the deformed body. The accurate numerical value or expression of the flow stress is the key to improve the accuracy of the theoretical calculation, both in the formulation of the reasonable hot working process and in the modern plastic working mechanics represented by the plastic finite element method. Therefore, in recent years, the domestic and foreign research in this area is very active. The rheological stress of hot compression deformation of KFC copper alloy was analyzed by Zhang Honggang et Al. . The flow stress of several copper alloys at high temperature was also studied by Zhou Xiaohua and Liu Ruiqing. However, few studies have been reported on the flow stress of H62 brass alloy. Using Gleeble-1500 thermal simulator and combined with continuous extrusion process, the process scheme was developed. The ISOTHERMAL hot compression test of H62 brass alloy was carried out under the deformation temperature of 100 ~ 800 °C and strain rate of 0.01 ~ 1s-1, based on the analysis of the relationship between flow stress and deformation degree, strain rate and deformation temperature in hot compression deformation of brass alloy, the constitutive equation and hot working diagram are established, and to provide accurate data or mathematical model for further analysis of finite element numerical simulation.

1. Flow stress curve analysis

In the continuous extrusion process, the rotating speed of the extrusion wheel is generally 6r/min ~ 10r/min, which is in the order of 1s-1, so the flow stress curve with the strain rate of 1s-1 is analyzed as shown in Fig. 1.

The results show that the flow stress of H62 brass has a peak at 400 °C and then a straight line. It can also be seen from Fig. 1 that the strain corresponding to the peak stress decreases with the increase of temperature. The True stress-true strain curve can be divided into three stages. When the deformation is small in the first stage, the dislocation density increases and the velocity of dislocation disappearance increases with the increase of strain. On the true stress-true strain curve, the work hardening rate decreases with the increase of the deformation amount, but in the first stage, the general trend is that the work hardening exceeds the dynamic softening, so as the deformation amount increases, the deformation stress is still increasing. In the second stage, when the strain exceeds a certain value, the stress decreases, which indicates that the material has undergone dynamic recrystallization at this temperature. In the third stage, when the strain reaches a certain value, the stress and strain present the characteristics of steady state rheology. As the flow stress maintains a stable value under this condition, the work hardening and dynamic recrystallization softening reach a balance. The lower the strain rate is, the lower the flow stress is when the deformation temperature remains unchanged. As can be seen from Fig. 2, temperature and strain rate are important factors affecting flow stress. At the same temperature, the peak value of stress increases with the increase of strain rate. It is generally believed that the storage energy in the material is higher at lower temperature, which is beneficial to the dynamic recrystallization of the material during thermal deformation. At higher strain rates, the deformation time of the unit strain is shortened and the number of dislocations that can move is increased. At the same time, the time of softening process provided by dynamic recovery and dynamic recrystallization is shortened, and the plastic deformation is not sufficient, which leads to the increase of flow stress. At the same strain rate, the higher the temperature, the greater the role of the thermal activation energy of atoms, the stronger the atomic vibration, and the decrease of the critical shear stress between atoms, in addition, the softening degree caused by dynamic recovery and dynamic recrystallization also increases with the increase of temperature, which leads to the decrease of peak stress, and the critical strain of dynamic recrystallization decreases with the increase of temperature and the decrease of deformation rate, this means that the dynamic recrystallization of the material takes place very quickly at high temperature.

2. The constitutive equation of H62 brass alloy is sensitive to the deformation temperature and strain rate in the process of deformation. It is shown that [7] , Z follows a relation (1) in which Z is Zener-Hollomon parameter, Z = EXP (Q/RT) , a and is a function of material constant or strain Q is the activation energy of deformation, K j mol-1; flow stress, MPA;'is the strain rate, s-1. Formula (1) can be expressed as Z = A ′ N and Z = AEXP () , defined by Zener-Hollomon parameter, and'can be expressed as formula (2) ~ (4) , respectively.

ε′ = A1［sinh( аσ) ］nexp( -Q / RT) ( 2)

ε′ = g Ag′σnexp( -Q / RT) ( 3)

ε′ = Aexp( βσ) exp( -Q / RT) ( 4)

When the constitutive equation of H62 alloy is regressed, the slopes of LN ′-LN and LN ′-graphs can be obtained by replacing the data of hot compression test of H62 alloy with the logarithms of LN ′-LN and LN ′-graphs according to Formula (3) and formula (4) , and then the slopes of LN ′-LN and LN ′-graphs can be expressed approximately as n and n respectively. The value of and N is replaced by equation (5) , which is obtained by logarithm on both sides of equation (2) . The deformation activation energy q = 214644kj is obtained

Q = R{ γln［sinh( аσ) ］/ ( 1 / T) }ε′·{ ln( ′ / ln［sinh( аσ) ］}T( 5)

z = ε′·exp( 214 644 / RT) ( 6)

lnz = ln A′ + nln［sinh( аσ) ］ ( 7)

lnz = ln A′ + nlnσ ( 8)

lnz = ln A′ + βσ ( 9)

Q = ［lnσ / ( 1 / T) ］ε′·［lnε′ / lnσ］T·R( 10)

The flow stress equation (11) of H62 brass alloy during hot compression deformation is obtained by substituting the obtained parameters of a, N and q into equation (3) .

 '= e-97795 EXP (- 215517 RT)(11)

3. Heat map theory

The dynamic material model considers the thermal deformation of materials as an energy dissipation system. The External Input Energy P (formula (12)) can be divided into two parts, namely dissipation (g) and dissipation covariance (j) . The dissipation G is the energy dissipated by the plastic deformation of the material, most of which is converted into heat energy, and a small part is stored in the form of crystal defect, the dissipative COVARIANCE J is the energy dissipated by the microstructure evolution during the deformation process. Under certain conditions of strain and temperature, the ratio of these two energy changes is strain rate sensitive factor M, see formula (13)[10] .

p = σε′ = G + J = ∫ σ·d( ′ + ( ε′·dσ ( 12)

m = d J / d G = ［( logσ) / ( logε′) ］ε，T ( 13)

When m = 1, the thermal deformation process is an ideal linear dissipative system, and the maximum value of the dissipative covariance J is (Jmax = ′/2) . The power dissipation factor (= j/Jmax) is the ratio of the energy dissipated by the microstructure evolution in the process of deformation to the ideal linear dissipation energy [11] . The expressions are (14) and (15) .

η = ( p-G) / Jmax= 2-2G / ( σε′) ( 14)

G = ∫ σ · dε′ ( ε′ = 0 ～ ε′min) + ( σ·dε′( ε′ =ε′min～ ε′) = ［

σε′ / ( m + 1) ］ε′ = ε′min+ ( σ·dε′( ε′= ε′min～ ε′) ( 15)

In general physical simulation experiments, the strain rate usually'≥0.001s-1, so'= 0001s-1 is preferable. When the constitutive relation of the material satisfies = K ′ , the power dissipation factor can be expressed as a formula (16) . The power dissipation factor with the variation of deformation temperature and strain rate forms the power dissipation diagram. Due to the dissipation of energy in various damage and metallurgical processes during plastic forming, the deformation mechanism in different regions can be analyzed by means of metallographic observation and power dissipation diagram.

= J/JMAX = 2m/(m + 1)(16) 

Prasad instability criterion is described in formula (17) . The stress values of H62 brass alloy under true strain of 0.5 at 5 temperatures and 3 strain rates are listed in Table L. The data in table L show that the flow stress log and log ′ are fitted by cubic spline function, the strain rate sensitive index M is calculated according to formula (13) , and then the dissipation efficiency factor is obtained by formula (16) . Using Matlab software to draw the CONTOUR curve of the equal power dissipation efficiency factor in the plane composed of t and log ′ , and according to the criterion of the rheologic instability in the machining drawing given by formula (17) , it can be concluded that rheological instability will occur in the zone of deformation () at different deformation temperatures. The hot working drawing of H62 brass alloy is shown in Fig. 3.

ξ( ε′) = log［m / ( m + 1) ］/ ( logε′) + m < 0( 17)

As can be seen from Fig. 3, the dynamic energy consumption behavior of the alloy is obviously different with different deformation temperature and strain rate. With the increase of deformation temperature and the decrease of strain rate, the value of H62 increases obviously, that is, the dynamic energy consumption of the alloy is enhanced, and the strain rate of H62 is 0. 01s-1, the energy dissipation factor reaches a peak of about 40% . At 350 ~ 650 °C, the energy dissipation factor appears a plateau of equal height, about 30% . According to the curves, this region may be the one in which dynamic recrystallization occurs. The dynamic recrystallization softening is beneficial to the uniform deformation of the alloy. Hot working in this region yields defect-free and excellent mechanical properties. The microstructure at typical temperature is shown in Fig. 4. According to the results of microstructure observation, the complete recrystallization zone at 400600 °C during hot working can be determined.

In figure 3, the thick solid line is the region where the Level is negative, which is calculated according to the Prasad instability criterion. In the instability diagram, when the instability criterion is negative, the region is said to be rheologic unstable. The larger the absolute value of the negative instability criterion is, the greater the probability of rheological instability is. To be on the safe side, unstable zones should be avoided in the development of hot working processes. It can be seen that the rheologic instability of H62 alloy occurs in the region of 0.1 ~ 1 strain rate below 500 °C, and the grain boundary cracking is easy to occur according to the microstructure observation. These working conditions should be avoided when working out the hot working parameters, when the strain rate of H62 alloy is 0.001 s-1 and the temperature is 400 ~ 500 °C, the dissipation factor of H62 alloy is the largest.

 4. Conclusion

The exponential form of Arrhenius equation can well describe the flow stress behavior of H62 brass alloy during high temperature deformation. The analysis of high temperature deformation behavior of material by hot working drawing theory can reflect the microstructure evolution rule of material under different deformation conditions exactly and directly. The optimum thermal deformation parameter of h 62 is that the strain rate is 0. 01s-1, the deformation temperature is 400 ~ 500 °C. 

Source: Chinanews.com, by Wang Yanhui