s ¼ Kε_m ð19Þ

where K is the constant and m is the strain rate sensitivity which can be calculated as follows    [30]:

5。2。Establishment  of  hot  processing map

The flow stress  used for establishing  the hot processing map  can be obtained by means of the isothermal compression test, as shown in Table 2。 According to the data illustrated in Table 2, the relation- ship between lgs and lgε_ can be obtained, as shown in Fig。 10。 The relationship between lgs and lgε_ can be fitted by means of cubic spline。 Simultaneously, the strain rate sensitivity m can be calculated according to Eq。 (20)。 Asa result, the efficiency of power dissipation η can be further calculated according to Eq。 (23)。 Therefore, the power dissipation map with respect to T and lgε_ can be established in the case of the different true strains, as shown in Fig。 11。 Furthermore, the

values  of  ξ  based  on  the  different  temperatures  and  the  different

m ¼ dG  ¼ sdε_  ¼  sε_dlnε_ ≈  Δlgε_

ð20Þ

strain rates can be obtained by substituting the values of lgε_  and m

At the given strain and temperature, the dissipated co-content  J

can be expressed by the following equation:

into Eq。 (25)。 Consequently, the instability processing map of 7A09 aluminum alloy can be established through the  interpolation method,  as shown  in Fig。 12。  In the end, the hot processing  map    of

7A09 aluminum alloy can be obtained by means of superimposition

of the power dissipation  map and the instability  processing  map,   as

It can be emphasized that Eq。 (21) is based on the constant m。 In general, the m value varies nonlinearly with the temperature and the strain rate。 When the m value is equal to 1, the metal material belongs to the perfectly linear dissipation state, in which the dissipated  co-content  J  amounts  to  the  maximum  value  Jmax [31]:

J sε_ 22

max  ¼  2 ð   Þ

According to the  combination  of Eq。  (21) and  Eq。  (22),   the

shown in Fig。 13。 It can be found that the power dissipation generally decreases with the increase in the strain, while the instability flow zone gradually expands。 If 7A09 aluminum alloy is subjected to plastic deformation in the case of the process parameters corre- sponding to the instability flow zone, microstructural defects are possible to take place。 Therefore, it is necessary to avoid hot working

Table 2The values of the flow stress of 7A09 aluminum alloy  (MPa)。

efficiency of power dissipation  η can be obtained  as     follows:

300 350 400 430 460

where η is closely related to the temperature, the  strain  and  the strain rate。 At the given strain, the isoline map of η with respect to the strain rate ε_ and the temperature T can be plotted to obtain the power dissipation map。 The power dissipation map represents the relative rate of internal entropy production during  hot  deformation and characterizes the dissipative microstructure in the case of the different temperatures and the different strain rates [17]。 However, in the  power  dissipation  map,  the  large  η value  represents  either the