Research on micro strain and sub grain size of each texture in 6A16 Al sheet

The micro strain and sub grain size of each texture type in cold rolled 6A16 Al alloy sheet were calculated using X-ray line broadening method, and the effects on the texture transformation during recrystallization process were investigated. The results showed that strain in R/S was the largest, and Brass, Copper, Goss in sequence, the sub grain size in R/S was the least, and Brass, Goss, Copper in sequence, which was coincident with the texture transformation speed during solid solution process, meanwhile, the contents of recrystallization texture, such as R/S, Cube and CubeND20 reduced obviously as the cold rolling stored energy released when recovery process imported before solid solution. It was conformed that the recrystallization texture transforming was influenced by stored energy significantly.


Introduction
As high strength-to-weight ratio, good formability after solid solution, baking hardening performance, 6XXX Al alloys (Al-Mg-Si) are chosen to stamp automotive body panels so as to reduce weight, it is quite attractive to enhance the range per charge for the electric vehicles.However, the deep drawing ability, flanging and earing still need improving to fit the existing production line, the texture, as one key influence factor, is got more attention consequently [1,2] Abstract:The micro strain and sub grain size of each texture type in cold rolled 6A16 Al alloy sheet were calculated using X-ray line broadening method, and the effects on the texture transformation during recrystallization process were investigated.The results showed that strain in R/S was the largest, and Brass, Copper, Goss in sequence, the sub grain size in R/S was the least, and Brass, Goss, Copper in sequence, which was coincident with the texture transformation speed during solid solution process, meanwhile, the contents of recrystallization texture, such as R/S, Cube and CubeND20 reduced obviously as the cold rolling stored energy released when recovery process imported before solid solution.It was conformed that the 3 State Key Laboratory of Nonferrous Metals and Processes, Beijing 100088, China Email: xiongbq@grinm.comrecrystallization texture transforming was influenced by stored energy significantly.
It's known that the main driving force for recrystallization is the stored strain energy accumulated during cold rolling process, which is in the form of dislocations, sub-grain boundaries etc. [10] .Therefore, it is natural that the strain energy storage and release should be paid more attention.
In this paper, the 6A16 Al alloy was chosen to try to find the difference of strain energy in each texture type by X-ray diffraction line broadening method statistically, and discussed the effect on the recrystallization texture transformation during the solid solution process.2. Theoretical considerations X-ray diffraction line pattern analysis is an effective method to describe the micro strain (II strain, local strain), sub-grain size as which cause the diffraction peak broadening.Early workers, such as Delhez, Rosenthal etc. [11,12] , have demonstrated the theories systematically.
The Full width at half maximum intensity of the diffraction peak (FWHM) is always used to express the diffraction peak broadening, which caused by the three parts mainly, 1. sub-grain size, 2. micro strain, 3. the intrinsic divergence.In this paper, the peak shape is close to Gaussian distribution [11] , which can be described by function (1).
Where βm is the measured broadening (FWHM); βt is the true broadening; βi is the broadening caused by intrinsic divergence of the instrument; βs is the broadening caused by sub-grain size which is too fine for X-ray diffraction; βd is caused by the micro strain.
βi can be measured using standard sample; βs and βd have been illuminated by Scherrer [14] and Warren [15] , which are given by the following empirical formulation (2) and (3).
Where Κ is related to sub grain shape, which is 1 in this paper; λ is X-ray wavelength, which is 0.154 nm; θ is the Bragg angular; L is the sub-grain size; εg is the micro strain.
From equation ( 1)~(3), the following relationship is induced: Therefore, we take sinθ as X-axis, βcosθ as Y-axis, then the statistical sub grain size and micro strain will be calculated after the linear least squares fit the values [16] .
In order to deduce the error, the experiment was set close to the perfect Bragg-Brentano geometry as far as possible.The incident slit was 1/3, the receiving slit was 1/3, and the Graphite bending monochromator was added.Besides that, we still paid more attention to the sample preparation.
It was known that the meticulous experiment and error minimizing are important to the line broadening analysis.In this paper, the aim was to measure the strain and sub grain size in each texture individually.Usually, the sample had to be rotated multi-dimensionally in order to move each crystalline plane of the texture perpendicular to the diffracting vector, however, it was too complex and unclear to correct the line broadening caused by the defocusing.Therefore, a rotating platform was set on the electric spark cutting machine, so as to get the required crystalline plane by rotating the polar angle(α) and auxiliary angle(β) of the sample.The α and β of each crystalline plane in all texture types were shown in Tab.1.Took the Brass texture as an example, first, the working face of electric spark cutting machine was set parallel to the normal face of the rotating platform.Second, the sample was fix on the rotating platform with rolling normal direction (ND) parallel to the platform normal direction, and the rolling direction (RD) was set to the origin direction.Third, the sample was rotated 35.27°(α) along ND, and 35.27°(β) along the transverse direction(TD)(see Fig. 1).Finally, the {111} crystalline plane was bared after cutting.
The plates cut with special crystalline plane were stuck together side by side, then ground and polished so as to remove the surface machining strain, see Fig. 2. Similarly, the {111}, {222}, {200}, {400} and {220} planes of each texture were obtained and tested.

X-ray line broadening analysis
The {111} diffraction peak in Brass texture was measured and shown as red line in Fig. 3, the peak shown as green was Gaussian fitted after the background removed and Kα2 skipped (shown as blue), then the FWHM was deduced finally.The others diffraction peaks were similar as this pattern.The data points distribution were shown in Fig. 4, and the βtcosθ~sinθ linear least squares fitting results were shown in Tab.3.It was clear that the strain in Cube was the least as 0.23% after solid solution and the sub grain size was the largest.Among the deforming texture types, the strain in R/S was the largest as 1.79%, and Brass, Copper, Goss in sequence, sub grain size in R/S was the least as 47.8nm, and Brass, Goss, Copper in sequence.The strain and sub grain size were very little different between each deforming texture type.The possible reasons were the content of Cube texture in 3mm annealing hot rolled plate was little, only about 25% [17] , and the rolling reduction was also small, only about 66%.The texture developed from Cube texture not lonely, but multiply [18] .Besides that, the second phase particle and inclusion always pinned the vacancy, tangled the dislocation, and disturbed the normal micro plastic deformation and strain energy storage [19] .However, it still could be deduced that the stored energy in R/S was a little more than Brass and Copper, and the Goss was the least.

Texture analysis
In order to clarify the effect of stored energy on the texture development, first, the 30min recovery at 280℃ was imported to release part of stored energy before 20min solid solution at 550℃, and the recrystallization textures were compared.Second, the texture transformation process during solid solution was investigated, and each deformation texture transforming speed was compared.The results were shown as below.

Comparison of recrystallization texture with or without recovery process.
The ODF sections of phi2=0°/45°/70°after 280℃-30 min recovery + 550℃-20min solid solution were shown in Fig. 5, and the ODF after only 550℃-20min solid solution were shown in Fig. 6j.there were both R/S, Cube and CubeND20 textures after recrystallization.The intensity of each texture decreased obviously when the recovery process was imported.The content of each texture was calculated and shown in Tab.4.The R/S and Cube reduced substantially from 9% and 10% to 4% and 5% respectively, and CubeND20 was also reduced from 13% to 8%.without recovery 9 10 13 with recovery 4 5 8 There were fixed texture transforming relationships between deformation and recrystallization, such as Cube and Copper, R and S, Cube and S. Therefore, the contents of recrystallization texture grew with deformation texture increasing generally.From the comparison of the texture results with and without recovery process, it could be deduced that the hereditary potency of texture transformation during recrystallization process weaken as the stored energy reduced after recovery.

4.2.2
Texture transformation via solid solution process.In order to analyze the texture transformation via solid solution process, the plate was polished first, and put into the muffle furnace which had already been heated to 550 ℃ .After holding special time, the plate was cooled in the water immediately.Then the texture in the sample was measured and analyzed.The ODF sections were shown in Fig. 6, from which we could find the Cube, CubeND20 recrystallization texture were increased, and the cold deformation texture, Brass, Copper, Goss were decreased with the holding time increase.In order to compare the transforming speed, the deformation texture was normalized to 100%, and each texture content changed with holding time was calculated and shown in Fig. 7.After about 5 seconds for breeding and nucleation, The Copper, Brass, Goss and R/S decreased rapidly in the next 10 seconds, and the texture transformation nearly completed at 30 seconds.The transforming speed still had some difference between each other.Besides R/S transformed into Cube which caused the content reduce, R/S still transformed into R which did not change the content, therefore, the real transforming speed was faster than which analyzed only by content change [20] .Goss breeding time was nearly 10 seconds which was longer than the others, and did not complete until 60 seconds.Above all, the transforming speed of R/S was the fastest, and Goss was the slowest, which were consistent with the stored energy results.Therefore, it could be deduced that the stored energy influenced significantly on the recrystallization texture transforming speed.The stored cold rolling strain energy of each texture type in 6A16 Al alloy, which were in the form of micro strain and sub grain size, were calculated by X ray line broadening analysis, the results showed that, the strain in R/S was the largest as 1.79%, and Brass, Copper, Goss in sequence, the Goss was the least as 1.54%, the sub grain size in R/S was the smallest as 47.8nm, and Brass, Goss, Copper in sequence, the Copper was the largest as 65.3nm.
The cold rolling stored energy played an important role in the recrystallization texture transformation.First, the hereditary potency of recrystallization texture transformation was weaken as cold rolling stored energy reduced.As the contents of recrystallization texture, R/S, Cube and CubeND20 were reduced from 9%, 10%, 13% to 4%, 5%, 8% obviously when 280℃-30 min recovery process was imported before solid solution.Second, the relative speed of each texture transforming was affected by the stored energy greatly.Goss was the slowest, as the stored energy in which was the least, meanwhile, R/S was the fastest as the stored energy was the most.

Figure 3 .
Figure 3.The schematic of sample final prepared The βi and βt of each crystalline plane in all texture types were measured and shown in Tab.2, βi were calculated by interpolation method from Si standard sample pattern.It was easily found that the βt of Copper, R/S, Brass and Goss were larger than Cube after solid solution(SS).

Figure 6 .
Figure 6.ODF sections of cold rolled plate via 550℃ solid solution process (a: 0 (cold plate); b: 5; c: 8; d: 10; e: 12; f: 15; g: 25; h: 30; i: 60; j: 1200;(seconds))After about 5 seconds for breeding and nucleation, The Copper, Brass, Goss and R/S decreased rapidly in the next 10 seconds, and the texture transformation nearly completed at 30 seconds.The transforming speed still had some difference between each other.Besides R/S transformed into Cube which caused the content reduce, R/S still transformed into R which did not change the content, therefore, the real transforming speed was faster than which analyzed only by content change[20] .Goss breeding time was nearly 10 seconds which was longer than the others, and did not complete until 60 seconds.Above all, the transforming speed of R/S was the fastest, and Goss was the slowest, which were consistent with the stored energy results.Therefore, it could be deduced that the stored energy influenced significantly on the recrystallization texture transforming speed.

Figure 7 .
Figure 7. Content change of each texture via 550℃ solid solution process5.SummaryThe stored cold rolling strain energy of each texture type in 6A16 Al alloy, which were in the form of micro strain and sub grain size, were calculated by X ray line broadening analysis, the results showed that, the strain in R/S was the largest as 1.79%, and Brass, Copper, Goss in sequence, the Goss was the least as 1.54%, the sub grain size in R/S was the smallest as 47.8nm, and Brass, Goss, Copper in sequence, the Copper was the largest as 65.3nm.The cold rolling stored energy played an important role in the recrystallization texture transformation.First, the hereditary potency of recrystallization texture transformation was weaken as cold rolling stored energy reduced.As the contents of recrystallization texture, R/S, Cube and CubeND20 were reduced from 9%, 10%, 13% to 4%, 5%, 8% obviously when 280℃-30 min recovery process was imported before solid solution.Second, the relative speed of each texture transforming was affected by the stored energy greatly.Goss was the slowest, as the stored energy in which was the least, meanwhile, R/S was the fastest as the stored energy was the most.

Table 1 .
The α and β of each crystalline plane in all texture types

Table 2 .
The FWHM of each crystalline plane in all texture types