Texture Definition and Classification

Describing Texture: Pole Figures, ODFs, and Key Components

• Pole figures (PFs): These are stereographic projections showing the distribution of a given crystallographic pole (e.g., {111} in fcc, {0001} in hcp) relative to sample coordinates (rolling direction RD, transverse direction TD, normal direction ND). Pole figures are intuitive, widely used in sheet metallurgy, and directly relate to anisotropy in forming.
• Orientation Distribution Function (ODF): The ODF provides a complete, quantitative description of the probability density of orientations in orientation space (often parameterized by Euler angles). ODFs allow the identification and quantification of “texture components” and fibers and enable computation of macroscopic properties through homogenization models.
• Inverse pole figures (IPFs): These indicate which crystal directions align with a chosen sample direction, often used in EBSD maps to visualize grain orientation.
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Crystallographic texture refers to the non-random distribution of crystal grain orientations within a polycrystalline material. The term encompasses several interconnected concepts:

• fcc (Al, Cu, Ni alloys): Rolling textures often involve the Copper {112}〈111〉, Brass {011}〈211〉, S {123}〈634〉 components, and associated fibers. Recrystallization textures may include Cube {001}〈100〉, which is especially important in aluminum sheet due to its effect on formability and surface quality.
• bcc (ferritic steels): Typical rolling textures include α-fiber (〈110〉 || RD) and γ-fiber ({111} || ND), with the γ-fiber strongly linked to good deep drawability in low-carbon steels.
• hcp (Ti, Mg, Zr): Textures are often described in terms of basal pole alignment; for rolled Mg, a strong basal texture (basal planes parallel to sheet surface) can severely limit room-temperature formability. Alloying, thermomechanical routes, and recrystallization can weaken or tilt basal texture, improving ductility.

Texture Components: Discrete orientation groups characterized by sharp maxima in orientation space, typically represented in Euler angle space (φ₁, Φ, φ₂). In cubic systems, common texture components are named conventionally using Miller indices. For rolling of FCC metals, significant components include:

- Copper component: {112}‖(111), a dominant rolling texture in FCC metals
- Brass component: {110}‖(111), associated with particular slip system combinations
- S component: {123}‖(634), intermediate orientation
- Cube component: {001}‖(100), dominant recrystallization texture in high SFE FCC materials

For BCC metals, rolling produces {110}‖ rolling direction fiber textures, while recrystallization often yields {100}‖ cube textures.

Fiber Textures: Continuous distributions of orientations in which a specific crystallographic axis or plane maintains a fixed angular relationship to a sample direction. Rolling typically produces α-fiber ({110}‖ND, normal direction) and β-fiber ({111}‖ND) in cubic materials, representing incomplete fiber distributions that can be superimposed to approximate rolling textures.

Texture Strength: Quantified by the fraction of material exhibiting specific orientations. Sharp textures show high orientation concentration (high peak values in ODF space), while weak textures exhibit more uniform orientation distributions approaching random (isotropic). Texture intensity is frequently characterized by extreme values of the ODF.