AA7075 is a FCC metal, and there is no phase transformation in the microgrinding process. The texture research of materials is mainly focused on microtexture analysis. Electron backscatter diffraction (EBSD) is the main tool for microtexture analysis.

Euler angles are about Cartesian axes of the rotation required, and it can be obtained in the desired direction from a reference direction. The work follows Bunge’s notation; the Euler angles are represented by φ 1 , Ф, and φ 2 . The definition of Bunge’s notation is shown in Figure 1. In order to get to the desired orientation,   φ 1 is rotated around the z axis. Ф is rotated around the x axis that has already been rotated, as shown by x ′ in Figure 1. φ 2 is the rotation about the z ′ axis (the z axis after the first two rotations).

Each crystallite’s orientation coordinates are called the “crystal” frame. In Bunge’s notation of Euler angles, the range of φ 1 and φ 2 is [0, 2π] while the range of Ф is [0, π].

Experimental results show that twinning is mostly suppressed in FCC metals such as aluminum, and the major mechanism of inelastic deformation is slip (Barlat et al., 1997). The reason for the change of the crystallographic orientation in slip deformation is explained by Schmid’s law (Schmid and Boas 1950). From the perspective of thermodynamics, the direction of the normal slip plane (n) of the crystal should be consistent with the direction of the externally applied load(s). The activation of any slip system requires that the shear stress acting on the slip system to reach a critical value, the so-called “critical resolved shear stress” or τ C R S S . Eshelby proposed the strain and rotation fields in the ellipsoidal grain (Eshelby 1957). Therefore, the rotation of each grain can be determined. Following that, “self-consistent” approaches were introduced to solve the crystal plasticity problem (Hutchinson 1970). The spin (rotation rate) Ω i j c of the crystal explains that the crystallographic texture evolution can be found using the following formula: Ω i j c − Ω ¯ i j = ∏ : S − 1 :   ( ε ˙ i j c − ε ˙ ¯ i j ) , (1) where S is the fourth-order Eshelby tensor that is only a function of the shape of the ellipsoid particle, and ∏ is the skew-symmetric fourth-order Eshelby tensor (Eshelby 1957). ε ˙ i j c is the strain rate in the crystal; the overline denotes the value of the medium. The self-consistent approach leads to the following (Molinari et al., 1987): ε ˙ i j c − ε ˙ ¯ i j =   M ¯ c : ( σ c − σ ¯ ) , (2) where M ¯ c is the secant modulus associated with the rate.

Feng et al. (2018) used the modified Johnson–Cook flow stress law to calculate the cutting and plowing forces considering the grain size and proposed an analytical model for predicting the milling temperature of Inconel 718 considering the effect of dynamic recrystallization. In this study, we consider only the effect of grain orientation. In this process, the hardening behavior of the material is taken into account and is used to update τ C R S S . The Johnson–Cook model can be used to obtain the constitutive behavior of AA7075 at each temperature. σ = ( A + B ε n ) ( 1 + C ⁡ ln ε   ˙ ε 0 ˙ ) ( 1 − ( T 0 − T w T m − T w ) m ) , (3) where A, B, C, m, n, and ε 0 ˙ are material constants, ε is the plastic strain, ε   ˙ is the plastic strain rate, T 0 is the workpiece temperature, T w is the ambient temperature, and T m is the material melting temperature. The values of Johnson–Cook model parameters are from Flores-Johnson et al. (2014) in Table1.

From the theoretical analysis, it is captured that crystallographic texture evolution is related to the strain rate, strain, temperature, and temperature rate. Therefore, the empirical model can be expressed as follows: Ω i j C = f ( T , T ˙ , ε ˙ , ε ) . (4)

For polycrystalline material, crystallographic texture is represented by COs and the corresponding orientation distribution functions (ODFs). Crystallographic texture evolution can be represented by the ODF variation of main COs, as follows: f ( φ 1 ,   ∅ ,   φ 2 ) = a k 1 T a k 2 T ˙ a k 3 ε ˙ a k 4 ε a k 5 , (5) where a i j is the constant and exponents.

To convert the nonlinear model to a linear model, logarithmic transformation is used. ln f ( φ 1 ,   ∅ ,   φ 2 ) = ln a k 1 + a k 2 ln T   + a k 3 ln T ˙   + a k 4 ln ε ˙   + a k 5 ln ε   . (6)

For model simplification, Eq. (6) can be given as follows: y = β 0 + β 1 A + β 2 B + β 3 C + β 4 D + δ , (7) where y is logarithmic transformations of the measured surface roughness, and A ,    B ,   C , and D are temperature, temperature rate, strain rate, and strain on a logarithmic scale, respectively; β 0 ,   β 1 ,   β 2 ,   β 3 , etc., are coefficients to be estimated by the least squares method, and δ is the randomly distributed error terms.

In the research process, AA7075 is used as the experimental material. The dimension of samples is a diameter of 8 mm and the height of 12 mm as shown in Figure 2.

In order to simulate the microgrinding process and study the flow behavior and crystallographic texture evolution of AA7075, the isothermal compression test was carried out on the G1eeble-3800 thermo-mechanical simulator as shown in Figure 3, and each parameter was set to 3 levels, respectively; the temperature was 350, 400, and 450°C, and the temperature rate was 1, 10, and 100°C/s; the strain rate was 0.01, 0.1, and 1 s-1, and the strain was 0.5, 0.6, and 0.7. The hot compression tests were designed according to the Taguchi method, as shown in Table 2.

The G1eeble-3800 thermo-mechanical simulator is composed of a computer control system, mechanical control system, and thermal control system, which can simulate various thermal-mechanical processes, such as thermal tension, thermal compression, and plane deformation. For the hot compression test, each sample was heated to the target temperature according to the respective set temperature rate in Table 1 and then held for 2 min, after which the specimens were compressed according to the respective corresponding strain rate and strain.

The details of the hot compression process are shown in Figure 4.

To study the microstructure evolution during hot compression, the microstructure of the samples before and after the test was observed by EBSD. The surface of the compressed sample was polished before the EBSD examination. EBSD data were taken from the center of the polished surface. The samples were polished and tested as depicted in Figure 5.

Inverse pole diagrams (IPFs) of nine samples were obtained from EBSD, as shown in Figure 6, which can be used as a qualitative description of microtexture.

The COs and the corresponding distributions of the nine samples were analyzed by TSL OIM Data Collection 5 software and depicted by the OIM micrographs, as shown in Figure 7.

The ODF is a preferred orientation representation of the three-dimensional spatial distribution of a crystal and represents the odds of a particular crystal orientation defined by the Euler angles. The COs and the corresponding ODFs of the nine samples were obtained by EBSD tests. The top 11 ODFs and COs are listed in Table 3.

For comparing the variance of microtexture intuitively, the ODFs of nine specimens are described in Figure 8.

Form Figure 8, it is found that the ODFs of specimens are completely different, which indicates that crystallographic texture evolution is conspicuous.

In the research process, the crystallographic texture evolution is represented by the main COs evolution of specimens. To determine the main COs, the calculated method was developed. In the method, the ODF variation of each CO is obtained by calculating the difference value between the specimens before and after hot deformation. Then, the sum for ODF variation of each CO was calculated, and the top three variations represent COs evolution. The ODF variation of each specimen is listed in Table 4.

It is found that the top three COs are (270.0, 35.3, and 45.0), (35.3, 90.0, and 45.0), and (270.0, 25.2, and 45.0). To connect the crystallographic texture evolution to the process parameters of hot deformation intuitively, the process parameters and ODF variation of the top three COs are listed in Table 5.

The coefficients of the three CO evolutions are determined by fitting predictions with 9 groups of experimental data, with the R-squares of 0.8460, 0.9575, and 0.7064, respectively. f ( 270.0 ,   35.3 , 45.0 ) = − 4.1189 T 0.0536 T ˙ 0.9495 ε ˙ 0.0202 ε 0.6141 , f ( 35.3 , 90,45.0 ) = − 10.0246 T 0.1197 T ˙ 2.4915 ε ˙ 0.0619 ε 1.6069 , f ( 270.0 , 25.2 , 45.0 ) = 25.9283 T − 0.0372 T ˙ − 7.1702 ε ˙ 0.2640 ε − 4.7421 .

The sensitivity analysis of crystallographic orientation evolution to the parameters of the hot deformation process was carried out to investigate the significance of input parameters. Four input parameters were selected for sensitivity analysis, including temperature, temperature rate, strain rate, and strain. The influence of each main input on the three crystallographic orientations (270.0, 35.3, 45.0), (35.3, 90.0, 45.0), and (270.0, 25.2, 45.0) was shown in Figure 9.

The results show that the process parameters have a greater impact on the crystallographic orientation evolution within the scope of the experimental exploration. The three crystallographic orientations (270.0, 35.3, 45.0), (35.3, 90.0, 45.0), and (270.0, 25.2, 45.0) have negative correlation with temperature, temperature rate, and strain. The grain orientations of (270.0, 35.3, 45.0) and (35.3, 90.0, 45.0) also show negative correlation with the strain rate, while grain orientations of (270.0, 25.2, and 45.0) are positively correlated with the strain rate. Therefore, to obtain the two crystallographic orientations (270.0, 35.3, 45.0) and (35.3, 90.0, 45.0), lower temperature, temperature rate, strain rate, and the strain are required. To obtain crystallographic orientation of (270.0, 25.2, 45.0), low temperature, small temperature rate, small strain, and large strain rate are required. At the same time, it can be seen that the effect of temperature on the evolution of grain orientation is almost linear, and as the strain rate increases, the rate of grain orientation evolution slows down.