1. Advanced Characterization and Microstructural Analysis
Typical Textures, part 2: Thermomechanical Processing (TMP) of bcc Metals
27-750
Advanced Characterization and Microstructural Analysis
A.D. Rollett

2. Objectives
Introduce you to experimentally observed textures in a wide range of (bcc) materials.
Develop a taxonomy of textures based on deformation type.
Prepare you for relating observed textures to theoretical (numerical) models of texture development, especially the Taylor model.
See chapter 5 in Kocks, Tomé & Wenk.

3. Taxonomy Deformation history more significant than alloy.
Crystal structure determines texture through slip (and twinning) characteristics.
Alloy (and temperature) can affect textures, e.g. through planarity of slip; e.g. through frequency of shear banding.
Annealing (recrystallization) sometimes produces a drastic change in texture, although this is less important than in fcc alloys.

4. Why does deformation result in texture development?
Deformation means that a body changes its shape, which is quantified by the plastic strain, ep.
Plastic strain is accommodated in crystalline materials by dislocation motion, or by re-alignment of long chain molecules in polymers.

5. Dislocation glide  grain reorientation
Dislocation motion at low (homologous temperatures) occurs by glide of loops on crystallographic planes in crystallographic directions: restricted glide.
Restricted glide throughout the volume is equivalent to uniform shear.
In general, shear requires lattice rotation in order to maintain grain alignment: compatibility

6. Re-orientation  Preferred orientation
Reorientations experienced by grains depend on the type of strain (compression versus rolling, e.g.) and the type of slip (e.g. {110}<111> in bcc).
The Taylor model is a useful first order (crystal plasticity) model that correctly predicts the main features of deformation textures, although more sophisticated models are required for quantitative matching.
In general, some orientations are unstable (f(g) decreases) and some are stable (f(g) increases) with respect to the deformation imposed, hence texture development.

7. Texture Development in Low C Steel During Cold Rolling & Annealing
 rolling and recrystallization texture
 - to -  transformation
Transformed  hot band texture
Cold Rolling
Cold rolling texture
ND fiber, <111> ND
RD fiber, <110> RD
ND fiber sharpens
Annealing texture
RD fiber weakens
(R.K. Ray et al., International Materials Reviews, 1994, Vol.39, p. 129)

8. Deformation systems (typical)
In deformed materials, texture or preferred orientation exists due to the anisotropy of slip. While slip in bcc metals generally occurs in the <111> type direction, it may be restricted to {110} planes or it may involve other planes (T. H. Courtney, Mechanical Behavior of Materials, McGraw-Hill, New York, 1990.)

9. Axisymmetric deformation: Extrusion, Drawing

10. bcc uniaxial textures
92% rolled Ta Tensile test in original RD to strain of 0.6: <110> fiber
(a) Normal and rolling direction inverse pole figures (equal area projection) of 92% rolled Ta and (b) Prior normal and rolling direction inverse pole figures for (a) tested in tension to a strain of 0.6 (tensile direction coincident to prior rolling direction).

11. Rolling RD ND
Rolling ~ plane strain deformation means extension or compression in a pair of directions with zero strain in the third direction: a multiaxial strain.

12. Rolling Textures bcc [Kocks]
{110} and {100} pole figures (equal area projection; rolling direction vertical) for (a) low-carbon steel cold rolled to a reduction in thickness of 80% (approximate equivalent strain of 2); (b) tantalum, unidirectionally rolled at room temperature to a reduction in thickness of 91%.
[Kocks]

13. {100} Pole figure for certain components of rolled bcc metals
Pole figures are evidently less than ideal for distinguishing particular components!
Note how very different components tend to overlap in a pole figure.

14. Fiber Texture in bcc Metals

15. bcc fibers: the f2 = 45° section
e, <110>||TD
g, <111>||ND a,
<110>||RD
Goss
Bunge Euler angles

16. Theoretical bcc rolling texture
Calculated using LApp, starting from a random texture with a strain of 50% (about 35% reduction). The gamma fiber is approximately in the center of each section.
The 45° section of the COD shows a strong alpha fiber and only partial development of the gamma fiber at this low strain

17. Dependence on Rolling ReductionRD TD

18. Crystallite Orientation Distribution in Polar Space
h-fiber
a-fiber
g-fiber RD TD

19. Alpha fiber plot, <110> // RD

20. Gamma Fiber, <111>  ND

21. Ta, Fe rolling textures g, <111>//ND a,<110>//RD b a c d
45° sections, contours at 1,2 … 7
low-C steel before cold rolling
Low-C steel reduced 90%
Tantalum rolled to 91%
a,<110>//RD
Note: in these plots, the Euler angles are Roe angles: axes transposed with Q horizontal, y (=1-90°)vertical. b a
g, <111>//ND
45° sections, contours at 1,2,3,4 …
0% Si steel before cold rolling
2% Si steel before cold rolling
0% Si steel cold rolled 75 %; {112}<110> strongest
2% Si steel cold rolled 75 %; {111}<110> strongest
max c d
max

22. Fe, Fe-Si rolling, fiber plots
Note the marked alloy dependence in the alpha fiber; smaller variations in the gamma fiber.

23. Parameters for Optimizing <111> Fiber Texture
Fine hot band grain size
Low concentrations of C, N, Mn
Additions of Ti, Nb
Long holding times in annealing
High annealing temperatures
Large cold reduction ratio
Control of coiling & rolling temperatures
Anneal before Cold Rolling (austenite)

24. Mechanical Properties
Plastic Strain Ratio (r-value)
Rolling Direction 45 Li 90 Wi
Large rm and small ∆r required for deep drawing

25. Correlation between rm and I{111}/I{100} texture ratio in Steels
(J.F. Held, 'Mechanical Working and Steel Processing IV', 1965)

26. Variation of r-value with Texture
These plots make it clear that the two main gamma fiber components complement each other to give high r-values; other components in the alpha fiber tend to lower the r-value and make it anisotropic

27. Shear Texture e12 2 = Torsion Axis = {hkl}
Shear strain means that displacements are tangential to the direction in which they increase.
Shear direction=1, Shear Plane  2-axis
e12
2 = Torsion Axis = {hkl}
1 = Shear Direction = <uvw>

28. Torsion Textures: twisting of a hollow cylinder specimen
Torsion Axis
(c)
(b)

29. {100} Pole figures Montheillet et al., Acta metall., 33, 705, 1985
fcc
bcc

30. bcc torsion textures: Fe
Ideal |{100} pole figures

31. bcc torsion textures: Ta
(a) initial texture from swaged rod;
(b) torsion texture
Ideal |{100} pole figures

32. Summary: part 2
Typical textures illustrated for shear textures and for bcc metals.
Pole figures are recognizable for standard deformation histories but orientation distributions provide much more detailed information.
For bcc rolling textures, the 45° section often provides most of the information needed.
As an example of the connection to mechanical properties, the plastic strain ratio (r-value) is highly sensitive to texture. For deep drawing, the gamma fiber should be optimized. For use in motors as electrical sheet steel, the <100>//ND fiber should be optimized (not yet a solved problem).