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Typical Textures, part 2:Thermomechanical Processing (TMP)

of bcc Metals

27-750

Advanced Characterization and Microstructural Analysis

A.D. RollettCarnegie

Mellon

MRSEC

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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.

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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.

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Why does deformation result in texture development?

• Deformation means that a body changes its shape, which is quantified by the plastic strain, p.

• Plastic strain is accommodated in crystalline materials by dislocation motion, or by re-alignment of long chain molecules in polymers.

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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

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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.

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Texture Development in Low C Steel During Cold Rolling & Annealing

(R.K. Ray et al., International Materials Reviews, 1994, Vol.39, p. 129)

rolling and recrystallization texture - to - transformation

Transformed hot band texture

Cold rolling texture

Cold Rolling

ND fiber, <111> ND RD fiber, <110> RD

Annealing textureND fiber sharpens RD fiber weakens

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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.)

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Axisymmetric deformation: Extrusion, Drawing

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05.00

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bcc uniaxial textures

92% rolled TaTensile test inoriginal RD tostrain 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).

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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.

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Rolling Textures

bcc

{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]

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{100} Pole figure for certain components of rolled bcc metals

Note how very different components tend to overlap in a pole figure.

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Fiber Texture in bcc Metals

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bcc fibers: the 2 = 45° section

<111>||ND<110>||RD

<110>||TD

Goss

Bunge Euler angles

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Theoretical bcc rolling

textureCalculated 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

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Dependence on Rolling Reduction

TD

RD

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Crystallite Orientation Distribution in Polar Space

RD

TD

-fiber

-fiber

-fiber

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Alpha fiber plot, <110> // RD

0

2

4

6

8

10

12

14

0 20 40 60 80

Alpha fiber

20% CR50 % CR60% CR80 % CR70% CR BA

Inte

nsity

Phi (°)

{001}<110> {112}<110> {111}<110> {110}<110>

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Gamma Fiber, <111> ND

0

1

2

3

4

5

6

60 65 70 75 80 85 90

Gamma Fiber

20% CR50% CR60% CR80% CR70% CR BAIn

tens

ity

1 (°)

{111}<110> {111}<112>

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Ta, Fe rolling textures

Note: in these plots, the Euler anglesare Roe angles:axes transposedwith horizontal, (=1-90°)vertical.

45° sections, contours at 1,2 … 7(a) low-C steel before cold rolling(b) Low-C steel reduced 90%(c) Tantalum rolled to 91%

45° sections, contours at 1,2,3,4 … (a) 0% Si steel before cold rolling(b) 2% Si steel before cold rolling(c) 0% Si steel cold rolled 75 %;

{112}<110> strongest(d) 2% Si steel cold rolled 75 %;

{111}<110> strongest

a b

c dmax

max

<111>//ND

<110>//RD

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Fe, Fe-Si rolling,

fiber plots

Note the marked alloy dependencein the alpha fiber;smaller variationsin the gamma fiber.

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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)

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Mechanical Properties

Plastic Strain Ratio (r-value)

)2(2

1)(

)2(4

1)(

)/ln(

)/ln(

)/ln(

)/ln(

90450

90450

rrranisotropyplanarr

rrrvaluerr

WLWfL

WfW

TfTi

WfWr

m

iif

ii

Large rm and small ∆r required for deep drawing

LiWi

Rolling Direction

4590

0

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Correlation between rm and I{111}/I{100} texture ratio in Steels

(J.F. Held, 'Mechanical Working and Steel Processing IV', 1965)

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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

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Shear Texture• Shear strain means that displacements are tangential

to the direction in which they increase.• Shear direction=1, Shear Plane 2-axis

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1 = Shear Direction = <uvw>

2 =Torsion

Axis= {hkl}

d 0 0

0 0 0

0 0 0

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Torsion Textures: twisting of a hollow cylinder specimen

(a)

(b)(c)

Torsion Axis

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{100} Pole figuresMontheillet et al.,

Acta metall., 33, 705, 1985

fcc bcc

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bcc torsion textures: Fe

Ideal |{100} pole figures

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bcc torsion textures: Ta

(a) initial texturefrom swaged rod;(b) torsion texture

Ideal |{100} pole figures

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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).