Research on Modeling Crystallographic Texture Evolution of Al Alloy 7075

Crystallographic texture is related to the anisotropy or isotropy of material physical properties, including mechanical performance. The crystallographic effect in micromachining is more significant than that in macro-processing owing to that the depth of the cut and the grain size are in the same order. It is of great significance to model the crystallographic texture evolution induced by mechanical and thermal load during micro-machining to investigate the surface integrity and performance of the finished product. This study performed hot deformation experiments of Al alloy 7075 (AA7075) under various input parameters, including the temperature, temperature rate, stain rate, and strain, which was designed using the Taguchi method. Following that, crystallographic orientation of the samples before and after the deformation was tested using electron back-scattered diffraction (EBSD). Then, the crystallographic texture evolution was modeled with the parameters obtained by fitting a part of the experimental data. The crystallographic texture evolution of AA7075 under different levels of input parameters is studied and analyzed. Finally, the sensitivity of crystallographic orientation evolution to the process parameter is analyzed. The results indicate that these four input parameters have a significant impact on some crystallographic texture of the specimens. The proposed model is instructive in the future investigation of micromachining and microstructure evolution.


INTRODUCTION
Aluminum is the most abundant metal material in the Earth's crust. It is easy to process and has high corrosion resistance, electrical conductivity, and thermal conductivity. Alloying aluminum with other elements can obtain better mechanical properties. Alloy aluminum 7075 (AA7075) is used as the main structural material for aviation applications and has been the first choice for the aircraft industry for decades (Yasakau et al., 2014). AA7075, which has high strength-to-density ratio, high ductility, light weight, corrosion resistance, and superior mechanical properties, is widely used in the automotive and aerospace industries (Puchicabrera et al., 2006).
The microstructure of the material includes grain orientation, grain size, dislocation density, and phase transition. During micromachining, the quality of the workpiece will be affected by the microstructure of the workpiece material . The machining surface quality has an important impact on the performance of the part, and many scholars have done some research around the machining surface quality . Guo et al. (2021) proposed a new surface roughness prediction system with good prediction performance, which has certain feasibility and practicality. Li et al. (2021) found that grinding assisted by graphene oxide coolant could improve the surface quality of grinding. The influence mechanism of surface generation and the generation mechanism of residual stress in the grinding process have attracted the attention of many researchers Ding et al., 2020;Sun et al., 2021;Xiao et al., 2021). For the surface quality requirements of precision machining of complex parts, robotic grinding is also used as a method to control the surface integrity (Lv et al., 2020;Xie et al., 2020;Zhu et al., 2020). The grain orientation is a key parameter in the analysis of the microstructure effect. The study of the evolution of the grain orientation during processing is of great significance for obtaining better machining quality.
The importance of texture in materials science stems from "anisotropy". The properties of single crystals such as mechanical, thermal, magnetic, optical, and chemical can be very different in different crystallographic directions. For example, rotation of the axis of loading can result in a 15% increase in the Young's modulus of commercial pure aluminum from 63 to 72 GPa. Simoneau et al. (2007) through the orthogonal micromachining of normalized AISI 1045 steel and refined AISI 1045 steel found that the small grain size will reduce the maximum plastic strain during chip formation. If the orientation of the grain boundary is not parallel to the shear surface, it can reduce the size of the pits on the processed surface. Cho et al. (2004) studied the effect of initial crystallographic orientation on the microstructure evolution of Ni-30 Fe alloy and found that the development of the deformed microstructure will be affected to a certain extent by the initial grains. Wu et al. (2015) found through copper microcutting experiments that the grain orientation has a great influence on the cutting force and the formation of burrs. The movement direction of the dislocation is obliquely forward of the cutting direction, which is beneficial to reduce the cutting force and the formation of burrs. Lin and Shiu (2016) used molecular dynamics methods to study the nanogrooving of single-crystal copper, and the results showed that the grain orientation has a significant effect on the cutting force and groove morphology. As a typical micro-part processing technology, microgrinding will be significantly influenced by the microstructure effect of the workpiece material. Min et al. (2006) used the tool at different angles relative to the workpiece direction to micro grind face centered cubic (FCC) single crystal materials and found that due to different crystal grain orientations, the activated slip system is different, which will have a significant effect on the surface and edges. Zhao et al. (2021) found that the grain orientation has a significant effect on the residual stress of microgrinding. Aicheler (2010) found that [111] surface grains produced much greater damage and roughness than the oriented surface grains in [100] through surface thermal fatigue experiments of polycrystalline copper. This is because the grains of the two orientations of <111> and <100> had different evolution during the thermal fatigue test of polycrystalline copper, and the surface with a grain orientation of <111> was severely deformed, while the surface with a grain orientation of <100> remained almost unchanged (Aicheler et al., 2011).
The texture evolution of aluminum alloys is mainly caused by the rotation of the operating slip system towards the direction of the applied external force. Also, twinning is considered to contribute to the texture evolution of AA7075 (Tabei 2015). Zhang and Li (2008) studied the grain orientation evolution of extruded magnesium alloy AZ31B sheets under uniaxial stretching at room temperature and found that the twin behavior is also different due to different initial orientations of the grains. Fang et al. (2011) carried out tensile tests on high manganese TWIP steel at different temperatures and found that temperature has a certain effect on the grain orientation evolution and twinning. Chen et al. (2018) studied the effect of strain rate and temperature caused by friction during high-speed sliding on the evolution of copper microstructure, and the results showed that the deformation is dominated by dislocation movement and twinning at lower or higher strain rates. Peng et al. (2018) conducted a uniaxial tensile test on a pure copper sample. In the experiment, with the increase of strain, the crystal grains with orientation <110> gradually rotated to the <111> orientation, and finally found that there were three main grain orientations. The ratio of <111> oriented grains increased significantly, the ratio of <110> oriented grains decreased significantly, and the ratio of <100> oriented grains hardly changed. Sun et al. (2019) studied the Cu-Sn low-temperature TLP-bonding solder joints and observed the grain orientation of the samples at 235, 250, and 265°C reflow and found that Cu 6 Zn 5 and Cu 3 Zn grains showed the preferential orientations of [001] and [100]. Parajuli et al. (2018) found that after annealing the gold film along the <111> direction, the grain orientation changed significantly. The proportion of <111> oriented grains increased from 50 to 70% because <111> is the preferred orientation of the gold film under certain conditions. Zhang et al. (2018) conducted stress fracture experiments on Waspaloy alloy and found that the grain orientation evolution behavior is related to the initial grain size of the sample. Zhang et al. (2021) conducted cold rolling experiments on ultra-thin grain-oriented silicon steel and found that changing the shear distribution during the rolling process would change the evolution of grain orientation. Wang et al. (2021) combined the VPSC model and the finite element cutting simulation model to study the texture changes during Ti-6Al-4V processing and found that the slip system plays an important role in the formation of shear texture. Gong et al. (2017) studied the effect of microgrinding parameters on the ground surface and microstructure through a nickel-based single-crystal superalloy microgrinding experiment. Riyad et al. (2021) established a simulation framework based on multilevel crystal plasticity to study the texture evolution of Ti-6Al-4V in tension and compression. Tang  Researchers concur that crystallographic texture evolutions are important microstructural evolutions occurring in the processing of materials. The above literature mentioned several experimental observations of the abovementioned phenomena. To the best of my belief, the predictive model of crystallographic texture evolution is not presented, which takes the effect of strain rate, strain, temperature, and temperature rate induced by the thermalmechanical load in machining of different types of metals and alloys. This work focused on analytically modeling the crystallographic texture evolution in microgrinding of AA7075 and developed an empirical model considering the effect of the strain rate, strain, temperature, and temperature rate with the parameters obtained by fitting the experimental data.

Representation of Crystallographic Texture
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 , V, 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. V 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 V is [0, π].

Modeling of Crystallographic Texture Evolution
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 CRSS . 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 c ij of the crystal explains that the crystallographic texture evolution can be found using the following formula: 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 c ij 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): 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 CRSS . The Johnson-Cook model can be used to obtain the constitutive behavior of AA7075 at each temperature.
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 FIGURE 1 | Schematic illustration of Euler angles defined by Bunge's notation. 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: 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: where a ij is the constant and exponents.
To convert the nonlinear model to a linear model, logarithmic transformation is used. lnf ( φ 1 , ∅, φ 2) lna k1 + a k2 lnT + a k3 ln _ T + a k4 ln _ ε + a k5 lnε . (6) For model simplification, Eq. (6) can be given as follows: 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.

EXPERIMENTS METHOD Hot Compression Test
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 thermalmechanical 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.

Microstructure Observation
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.

EBSD Measurement Result
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 threedimensional spatial distribution of a crystal and represents the FIGURE 2 | Samples before and after the hot compression test.  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.

The Linear Regression Analysis
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 ( 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.

Sensitive Analysis
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 FIGURE 5 | Initial microstructure of AA7075. 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 ( 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.  3) 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. 4) The thermo-mechanical load in micromachining is closely related to the process parameters. This study will be instructive for the crystallographic texture evolution in micromachining. This paper focuses on crystallographic orientation evolution under the thermo-mechanical load, and it is important to examine the

DATA AVAILABILITY STATEMENT
The raw data supporting the conclusion of this article will be made available by the authors, without undue reservation.

AUTHOR CONTRIBUTIONS
MZ, HL, and YZ contributed to conception and design of the study. MZ and HL participated in the experimental data acquisition and data analysis. HL wrote the first draft of the manuscript. MZ, GL, and YZ wrote sections of the manuscript. All authors contributed to manuscript revision, read, and approved the submitted version.

FUNDING
This work was supported by the Shanghai Pujiang Program (20PJ1404700) and the Young Scientific Research Team Cultivation Program of SUES (QNTD202112).