Modeling the Controlled Recrystallization of Particle-Containing Aluminum Alloys

Abstract

The recrystallized fraction for AA7050 during the solution heat treatment is highly dependent upon the history of deformation during thermomechanical processing. In this work, a state variable model was developed to predict the recrystallization volume fraction as a function of processing parameters. Particle stimulated nucleation (PSN) was observed as a dominant mechanism of recrystallization in AA7050. The mesoscale Monte Carlo Potts model was used to simulate the evolved microstructure during static recrystallization with the given recrystallization fraction determined already by the state variable model for AA7050 alloy. The spatial inhomogeneity of nucleation is obtained from the measurement of the actual second-phase particle distribution in the matrix identified using backscattered electron (BSE) imaging. The state variable model showed good fit with the experimental results, and the simulated microstructures were quantitatively comparable to the experimental results for the PSN recrystallized microstructure of 7050 aluminum alloy. It was also found that the volume fraction of recrystallization did not proceed as dictated by the Avrami equation in this alloy because of the presence of the growth inhibitors.

Appendix

In the hot rolling stage of high-strength aluminum alloys, recovery and perhaps some recrystallization can take place between stands in a rolling mill. Therefore, it is presumed that deformation goes to increase dislocation density, but immediately after unloading as result of the deformation temperatures, recovery begins to take place. These events continually influence the stored energy rate in hot deformation. As stated in section 3 (Eq 1 and 2), the assumption is that the recrystallization kinetics follow a law similar to that proposed by Johnson, Mehl, Avrami, and Kolmogorov with the exception that complete recrystallization will not take place. In this state variable model, developed specifically for this study, the total fraction of recrystallization is equal to K _o , where

$$K_{0} = B_{1} \left( {\frac{S}{{S_{C} }}} \right)^{m} \left[ {\tanh \left( {C_{1} \ln \left( {1 + Z} \right)} \right)} \right]^{{m_{1} }} \left( {\frac{{T_{{\text{rex}}} }}{{T_{m} }}} \right)^{{n_{1} }}$$

(5)

T_rex is the recrystallization temperature which is an external variable, while Z is the Zener-Hollomon parameter, $S$ is stored energy and is an internal state variable that tracks evolution of the structure during deformation and annealing, and T _m is the melting temperature.

$$Z = \dot{\varepsilon }\exp \left( {\frac{Q}{{RT_{{\text{def}}} }}} \right)$$

(6)

$$S_{c} = 1000$$

(7)

${\text{S}}_{\text{c}} \varvec{ }$ is an arbitrary value representing the highest possible value for stored energy in the metal at any condition.

During hot deformation, the stored energy evolves following the relationship:

$$\dot{S} = C\left( Z \right)\dot{\varepsilon }\left[ {1 - \frac{S}{{S_{\hbox{max} } \left( Z \right)}}} \right]$$

(8)

where

$$C\left( Z \right) = B_{3} \left[ {\ln \left( {Z + 1} \right)} \right]^{{m_{3} }}$$

(9)

And the maximum equilibrium stored energy attainable at any given Z value is:

$$S_{\hbox{max} } = S_{c} \left[ {\tanh \left( {B_{4} \ln \left( {Z + 1} \right)} \right)} \right]$$

(10)

Constants determined from experimental measurements of recrystallization at various deformation and annealing conditions were determined as follows: m = 0.48, B ₁ =2.12, B ₃ = 0.015 (fixed), m₃= 3.9, B₄= 0.79, C₁= 0.03 (fixed), Q = 50000 JK/mole (not a fitting parameter), R = 8.314 J/mole (not a fitting parameter), and with the initial condition, S (0) = 1 for hot-deformed AA7050 at a position in the center of the plate (t/2).