increase in the energy storage is caused。 On the other hand, the

where A1  remains the material constant and A1 ¼ Aαn 。

When the high stress level results in αs 41:2, Eq。 (1) can be approximately expressed as

。 Q  。

high  strain  rates  cause  the  great  temperature  effect  and conse-

quently the heat quantity from plastic deformation work is unable

to dissipate rapidly。 The temperature effect similarly leads to the sharp temperature rise in the aluminum alloy, which can be validated by the experimental results as shown in Fig。 7。 Fig。 7 indicates the curves of the temperature rise versus the time during hot compression of 7A09 aluminum alloy at the different   strain

rates  at  400 1C。  It  can  be  found  from  Fig。  7  that  there  is    no

temperature rise at the low strain rates of 0。01 s−1 and 0。1 s−1 and there is slight temperature rise at the strain rate of 1 s−1。 However,

where  A2   and  β  remain  the  material  constant  and  A2 ¼ A=2n,

β ¼ nα。

The values of A, α, n and Q can be determined according to the experimental data and thus the constitutive equation of 7A09 aluminum alloy can be obtained。

To obtain the value of n, the natural logarithm of Eq。 (2) results in Eq。 (4):

there is sharp temperature rise at the strain rate of 10 s−1。 The influence  of  the  strain  rate  on  the  temperature  rise  can        be

explained as follows。 In the case of the high strain rate,  the thermal energy derived from the plastic deformation work cannot be diffused outward in time and consequently the temperature increases rapidly。 However, in the case of the low strain rate, the thermal energy derived from the plastic deformation work has sufficient time to dissipate and thus the temperature does not exhibit the sharp increase。 It can be proposed that the energy storage and the temperature rise are responsible for dynamic recrystallization of 7A09 aluminum alloy at the high strain   rates。

4。2。Constitutive equation

According to the true stress–strain curves of 7A09 aluminum alloy as shown in Fig。 5, it can be found that the flow behavior of 7A09 aluminum alloy under hot deformation is related  closely to the strain rates and the deformation temperatures。 It is necessary to establish the constitutive equation in order to obtain mathe- matical description of the constitutive behavior of 7A09   aluminum

It can be seen from Eq。 (4) that n is the linear proportion  factor of lnε_ with respect to ln s and thus can be determined by the slope of the lines derived from linear fitting method in Fig。 8(a)。 The value of n is calculated as the average values of slope of the lines at the different deformation temperatures and thus is determined as 6。3141。

In the same manner, in order to obtain the value of α, the value of β is first determined according to the natural logarithm of Eq。 (3), which leads to Eq。 (5):

Q

lnε_ ¼ lnA2  þ βs− RT ð5Þ

Eq。 (5) indicates that β is the linear proportion factor of lnε_ with respect to s and thus can be determined by  the  slopes  of  the lines derived from linear fitting method in Fig。 8(b)。 The value of β is calculated as the average value of slope of the lines at the different deformation temperatures and thus is determined as 7。8325 ~ 10−2  MPa−1。 As a result, the value of α can be obtained   by