{11¯24} deformation twinning in commercial purity titanium at room temperature

Figures & data

Table 1. Crystallography of possible deformation twinning modes in CP titanium using standard nomenclature for the twin plane K₁, shear direction η₁, second undistorted plane K₂ and direction η₂ lying in K₂ and the plane of shear [5–7]. For each deformation twinning mode a specific K₁ is selected to emphasize the crystallographic relations between K₁, η₁, K₂ and η₂. q is the complexity of the shuffles required to ensure all atoms in the twin are carried into their final correct positions [5–7]. ‘T’ and ‘C’ refer to the nomenclature of tension (T) and compression twins (C), which define whether the shape change produced by the twinning mode causes extension or contraction along the c-axis, respectively [5,6].

Type	K1	η1	K2	η2	Misorientation angle/axis (for c/a = 1.588)	Shear magnitude |S|	q	Refs.
T					85.03°	0.174	4	[5,6]
T					34.96°	0.630	2	[5,6]
C^a					76.89°	0.219	6	[5,6]
C					64.40°	0.219	6	[5,6]
C					57.22°	0.099	8	[5,6]

^a is a compression twinning mode despite the assertions by Yoo [5] and Christian and Mahajan [6] that it is a tension twinning mode. See the text for details.

Figure 1. (colour online) Geometry of (a) and (b) twinning in a single crystal of titanium viewed normal to . The composition plane K₁, twinning direction η₁, conjugate twinning direction η₂ and shear magnitude S are labelled. The shaded regions represent the super cell that undergoes the shear. The lattice point labelling system is that specified by Crocker and Bevis [26]. Using the ABAB stacking sequence designation of the h.c.p. crystal structure of α-titanium, the atom positions are represented by circles and squares for the A layer and triangles for the B layer. The atom positions displayed represent the projection of four planes: circles lie on the plane of the page, squares are one d-spacing below the page, upright triangles two d-spacings below the page and inverted triangles three d-spacings below the page. Representations of the macroscopic shape change to a single crystal of titanium deformed by twinning on and are shown in (c) and (d), respectively. It is evident that these twinning modes facilitate a macroscopic compression in line with the c-axis as in both cases; the pre-twinning crystal length l₀ is greater in magnitude than the post-twinning crystal length l₁.

Table 2. CP titanium impurity levels for C, H, N and O determined from combustion analysis and for Fe determined from inductively coupled plasma optical emission spectrometry.

Element	C	Fe	H	N	O	Ti
Wt.%	0.037	0.027	0.0005	0.012	0.389	99.535

Figure 2. (colour online) (a) EBSD scan of an individual deformation twin and smaller twins acquired at 25 kV with a 0.5 μm step size, inverse pole figure colouring and band contrast, with the twin outlined in white and the smaller twins outlined in black. The loading direction is in the horizontal direction. (b) Bright field image of the TEM specimen taken from the boxed region in (a). (c) Electron diffraction pattern from (b) viewed down the zone ( in the three index notation) common to both the matrix and the twin confirming twinning on . This electron diffraction pattern has been image processed to highlight the and twin spots, which have a low intensity because of their large .

Figure 3. Electron diffraction patterns from Figure 2(b), (a) viewed down the zone ([2 1 0] in the three index notation) (b) viewed down the zone ( in the three index notation) and (c) viewed down the zone ( in the three index notation) common to both the matrix and the twin confirming twinning on . As in Figure 2, the electron diffraction patterns have been image processed to highlight the and twin spots, which have a low intensity because of their large .

Figure 4. (colour online) (a) EBSD scan of a longitudinally sectioned ballistically tested projectile acquired at 25 kV with a 15 μm step size, inverse pole figure colouring and band contrast. The loading direction is in the horizontal direction, with the impact face on the right-hand side. (b) Band contrast with grains whose c-axes were within 6° of the loading direction highlighted in green. (c)–(e) EBSD scans of the highlighted green grains in (b) acquired at 25 kV with a 0.5 μm step size, with inverse pole figure colouring and band contrast, showing large twins outlined in white and smaller twins outlined in black.

Table 3. Area fractions of deformation twins in Figures 2(a) and 4(c)–(e) as percentages of the EBSD scan area of a grain, and area percentage of twinned area for and deformation twins.

	Area fractions expressed as a percentage
	Figure 2(a)	Figure 4(c)	Figure 4(d)	Figure 4(e)
Percentage of EBSD scan area	2.5%	23.2%	17.8%	7.7%
Percentage of EBSD scan area	2.2%	0.5%	0%	0.4%
Percentage of twins	53.1%	97.8%	100%	95.2%
Percentage of twins	46.9%	2.2%	0%	4.8%

Table 4. Highest Schmid factors for twinning within each possible deformation twinning mode for the grains shown in Figures 2(a) and 4(c)–(e), assuming plane strain compression loading in the x-direction which is horizontal across the page in each of these figures, compressing the crystal c-axis.

Deformation twin mode	Highest Schmid factor, x-direction, plane strain
	Figure 2(a)	Figure 4(c)	Figure 4(d)	Figure 4(e)
	0.399	0.498	0.500	0.497
	0.443	0.477	0.485	0.474
	0.468	0.452	0.462	0.449

Note:

The operative twinning modes are in bold.

Table 5. Schmid factors for the six and deformation twin variants for the grains shown in Figures 2(a) and 4(c)–(e), assuming plane strain compression loading in the x-direction which is horizontal across the page in each of these figures, compressing the crystal c-axis.

Deformation twin variant	Schmid factor, x-direction plane strain
	Figure 2(a)	Figure 4(c)	Figure 4(d)	Figure 4(e)
V1:	0.377	0.493	0.472	0.494
V2:	0.223	0.478	0.455	0.481
V3:	0.253	0.466	0.467	0.469
V4:	0.398	0.474	0.490	0.475
V5:	0.390	0.490	0.500	0.489
V6:	0.399	0.498	0.494	0.497
V1:	0.379	0.430	0.463	0.431
V2:	0.443	0.461	0.485	0.457
V3:	0.441	0.477	0.470	0.474
V4:	0.339	0.466	0.428	0.467
V5:	0.126	0.436	0.399	0.441
V6:	0.163	0.416	0.420	0.422

Note:

The operative twinning modes are in bold.

Figure 5. (colour online) (a) and (b) The variation of positive Schmid factors for loading in compression for twinning on ; the position where the Schmid factor is at a maximum of 0.5 is 6.5° away from [0 0 0 1] and 45° from the pole. (c) and (d) Maximum positive Schmid factors for loading in compression for twinning on . In (a)–(d) the [0 0 0 1] pole is indicated by a black dot.

M.H. Yoo, Metall. Trans. A 12 (1981) p.409. 10.1007/BF02648537

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J.W. Christian and S. Mahajan, Prog. Mater. Sci. 39 (1995) p.1. 10.1016/0079-6425(94)00007-7

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A.G. Crocker and M. Bevis, Deformation and Fracture, in The Science, Technology and Application of Titanium, R.I. Jaffee and N.E. Promisel, eds., Pergamon Press, Oxford, 1970, p.453.

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