Simulation of cold-rolled 2024 Al alloy thick plate based on visco-plastic self-consistent model

2024 Al has been used in various fields. However, most cold-rolled Al has poor strength and plasticity, so it needs a solution and aging treatment. The rolled reduction has an important influence on microstructure. For different rolled reductions, microstructure has different evolution rules even under the same solution and aging treatment. Therefore, different rolled reduction has a great influence on the subsequent treatment. In this paper, deform simulation analysis technique was used to study the changes of strain of 2024 Al alloy during rolling deformation, and visco-plastic self-consistent was used to study the texture evolution of 2024 Al alloy, which provided a new method for the study of deformation behavior and anisotropy during rolling.


Introduction
2024 Al alloy is a typical Al-Cu-Mg series wrought Al alloy, which has been used in aerospace and transportation fields, such as powertrains and automobile bodies, owing to their high strength, good plasticity, and lightweight [1] .Currently, with the development of the aerospace field, higher requirements are put forward for the properties and process of aluminum alloys [2] .The research of aluminum alloys with both excellent strength and ductility via severe plastic deformation has been a hotspot, previously [3] .Most aluminum sheets were deformed by rolling to obtain high strength.However, the application is limited due to the poor cold forming ability and low production.The mechanical properties of cold rolled 2024 Al need to be further improved via appropriate heat treatment.The microstructure and mechanical properties after annealing are related to the rolling reduction.During the cold rolling, the higher rolling reduction of 2024 Al will introduce more dislocation density, which lead to an increase of the stored energy.After heat treatment, microstructure and mechanical properties vary due to the various recrystallization grain growth rates caused by the difference in stored energy.Therefore, the microstructure evolution at different rolling reductions plays an important role in the microstructure and mechanical properties after heat treatment.
Recently, with the development of the texture theory and computer technology, the visco-plastic selfconsistent (VPSC) model as an accurate and effective way was used to predict the texture evolution in alloy after deformation.In recent years, V.V. Mishin has studied the evolution of texture during cold rolling of beryllium foils about the planar anisotropy of mechanical properties by VPSC modeling [4] .Li et al. [5] simulated the texture evolution at the center and edge of the TC18 Titanium alloy bar during forging using the mesoscopic visco-plastic self-consistent model.Maldar et al. [6] investigated the effect of alloying elements on Mg's tensile behavior under the relative activity of different slip and twinning modes by VPSC modeling.Then, VPSC as an effective way to predict texture evolution can reduce the repeated experiments and increase efficiency.The research about predicting the microstructure evolution on cold rolling 2024 Al using the VPSC model is still absent.
To reveal the microstructure evolution of 2024 Al during cold rolling, deform simulation analysis was used to study the changing of temperature and strain at the core, 1/4, and surface positions during rolling deformation under 30%, 60%, and 90% thickness reduction.The texture evolution at different positions was studied with visco-plastic self-consistent finite elements.It provides a new method for studying the deformation behavior and anisotropy of aluminum alloy during rolling.

developing finite element model
Most of the plastic deformation areas in the rolling process are triaxial compressive stress, and the stressstrain relationship is relatively close to the upsetting process.Then, the constitutive equation was constructed under the hot compression behavior.In this paper, the deform simulation analysis of 2024 aluminum alloy uses the constitutive equation established by Zhang during the hot compression process.The constitutive equation is shown in Equation ( 1).
The deformation process in hot rolling is a coupling relationship between plastic deformation and temperature.During hot rolling, plastic deformation work and frictional heat are considered internal heat sources, and the relationship is as follows.
is the shear stress during rolling, ∆ is relative sliding speed of the contact surface between roll and plate.In the temperature field solving of hot rolling, the boundary conditions of heat transfer mainly include heat radiation, natural convection, and heat contact between sheet and roll.
In the rolling process, the sheet is set as a plastic body, and the roll is set as a rigid body.The sheet needs to be meshed in pre-treatment.Hypermesh software is used to divide the hexahedral mesh and then imported into Deform for calculation.The friction type between billet and roll is set as shear friction, and the friction coefficient is set at 0.7 to ensure sufficient friction between plate and roll, and no skid occurs between billet and roll.Rolling deformation is set at 30%, 60%, and 90%, respectively.

developing VPSC modeling procedures
Visco-plastic Self-consistent (VPSC) was first developed by Lebensohn and Tomé, and it takes into account the slip, twin, and anisotropy of polycrystalline materials, and can calculate and analyze the deformation behavior, deformation mechanism, and texture evolution behavior of polyphase polycrystalline materials during plastic deformation.The viscoplastic constitutive mechanical behavior of single crystals in the VPSC model can be described by a nonlinear rate-sensitive equation, as shown in Equation ( 4).
where ( ̅ ) and ( ̅ ) are the deviatory strain rate and stress, respectively; , , , is positive integer variable; is slip/twin system; represents the threshold stress; is the Schmid factor tensor in ij direction of deformation systems; = ( + ) is the symmetric Schmid tensor of slip/twin system, respectively ( and are the normal vector and Burgers vector of the slip/twin systems, respectively) is shear rate acting on the slip/twin system, is the strain rate sensitivity exponent.
In the VPSC model, each grain is regarded as having a uniform ellipsoidal orientation, and the polycrystalline constitutive relationship is deduced from the single-crystal constitutive model according to the self-consistent principle.
where ( ) and ( ) are respectively partial strain tensor and partial stress tensor； ( ) is Schmid tensor, ( ) is partial strain tensor of a single crystal.
The VOCE hardening model is used in the VPSC model to describe the mechanical response of a single crystal during plastic deformation.The hardening characteristics of a single deformation system change with the critical stress of the accumulated shear strain of each grain.For the slip system and twin system, shear stress ( ) during deformation can be expressed by the VOCE hardening model.
where is the accumulated shear amount in the grain, represents the CRSS in the initial slip system or twin system, + is the value corresponding to the epitaxial shear stress of the slip system/twin system, and are the initial hardening rate and saturation hardening rate of slip system/twin system, respectively.1a-c show the simulation analysis results of equivalent strain under different rolling reduction rates.According to the analysis, the strain of the plate shows an upward trend with an increase in the rolling process.Related research on thick plate rolling shows that the phenomenon of rolling plate cannot be rolled easily occurs in the first few passes of initial rolling.With the increase of the rolling pass, the reduction rate increases.The strain accumulates at each position of the rolled plate, and the plastic deformation expands from the surface to the deep part of the core, resulting in the cumulative strain gradually increasing.From the cumulative strain of different reduction rates, it can be seen that the cumulative strain of the surface in the plate is not much different, which is because, during the rolling process, the surface metal of the rolled piece is subjected to the normal (ND) compressive stress and the larger shear stress along the rolling direction (RD).In particular, obvious shear deformation occurred in the process of multi-pass cumulative deformation.However, due to the lack of function of restriction in the rolling process, the deformation of the two parts at the head and end of the rolled parts shows greater non-uniformity than that at the other parts.Fig. 2 is the polar diagrams of the (100), ( 110) and (111) crystal faces of the rolled piece at the 30% rolling reduction rate.It can be seen that when the rolling deformation amount is 30%, the typical Copper {112} <111>, Brass {011} <012} and S {123} <634> textures are formed on the surface and in the middle of the plate, and the maximum texture density is 5.3.Fig. 5 shows the standard polar projection diagram of Copper, Brass and S texture respectively.Through comparison, it can be seen that the rolled plate at different rolling reduction rate has typical copper texture {112}<111>, brass texture {011}<211> and S texture {123}<634>.The maximum texture strength is 14.By studying the rolling process of 7056 aluminium alloy thick plate, Chang found that the core of thick plate presented three textures (Brass{011}<211>, S{123}<634> and Copper{112}<111>), but the volume fraction distribution of the three textures was no uniformity.These three textures locate on the β-oriented lines of face-centered cubic metals.With the continuous increase of rolling reduction rate (from 30% to 90%), the volume fraction of typical rolling texture becomes more obvious, and thus the texture strength gradually increases.

Result and discussion
At the same time, aluminum alloy belongs to high fault energy metal, which has high layer-fault energy.it is difficult for dislocations to expand to form partial dislocations, and layer faults are not easy to occur in crystal defects.Therefore, dislocation slip is the main deformation mechanism in high-fault energy FCC metals.The common slip system is {111}<110>, which has 12 equivalent slip systems.With the increase in rolling reduction rate, the number of slip systems that can be activated in the crystal increases, showing an increase in macroscopic texture strength.

Conclusion
1.During the rolling process, the surface of the rolled piece has more obvious shear deformation than the core of the plate due to the normal (ND) compressive stress and the larger shear stress along the rolling direction (RD).The strain increases with an increase in the rolling process from 30% to 90%.The contact surface of rolled parts has the highest strain subjected to greater stress, and the local rolled parts show obvious uniformity distribution.2. By comparing the changes of the three textures under different rolling reduction rates, it is found that the texture of S shows an obvious upward trend with the increase of strain, which further indicates that the texture of S is more sensitive to the strain process than the other two textures.

Figure 1
Figure 1 Simulation results of equivalent strain fields under different rolling reduction rates.(a) 30%; (b) 60%; (c) 90%.Figures.1a-cshow the simulation analysis results of equivalent strain under different rolling reduction rates.According to the analysis, the strain of the plate shows an upward trend with an increase in the rolling process.Related research on thick plate rolling shows that the phenomenon of rolling plate cannot be rolled easily occurs in the first few passes of initial rolling.With the increase of the rolling pass, the reduction rate increases.The strain accumulates at each position of the rolled plate, and the plastic deformation expands from the surface to the deep part of the core, resulting in the cumulative strain gradually increasing.From the cumulative strain of different reduction rates, it can be seen that the cumulative strain of the surface in the plate is not much different, which is because, during the rolling process, the surface metal of the rolled piece is subjected to the normal (ND) compressive stress and the larger shear stress along the rolling direction (RD).In particular, obvious shear deformation occurred in the process of multi-pass cumulative deformation.However, due to the lack of function of restriction in the rolling process, the deformation of the two parts at the head and end of the rolled parts shows greater non-uniformity than that at the other parts.Fig.2is the polar diagrams of the (100), (110) and (111) crystal faces of the rolled piece at the 30% rolling reduction rate.It can be seen that when the rolling deformation amount is 30%, the typical Copper {112} <111>, Brass {011} <012} and S {123} <634> textures are formed on the surface and in the middle of the plate, and the maximum texture density is 5.3.

Figure 2
Figure 2 Texture distribution of each part for a rolled piece with a rolling reduction rate of 30%.

Figure 3
Figure 3Texture distribution of each part for a rolled piece with a rolling reduction rate of 60%.Fig.3is the polar diagrams of the (100), (110) and (111) crystal faces of the rolled piece at the 60% rolling reduction rate.The typical Copper {112} <111>, Brass {011} <012} and S {123} <634> textures are formed on the surface and in the middle of the plate, and the maximum texture density is 8.9.

Figure 4 Figure 5
Figure 4 Texture distribution of each part for a rolled piece with a rolling reduction rate of 90%.Fig. 4 is the polar diagrams of the (100), (110) and (111) crystal faces of the rolled piece at the 90% rolling reduction rate.The typical Copper {112} <111>, Brass {011} <012} and S {123} <634> textures are formed on the surface and in the middle of the plate, and the maximum texture density is 14.