Development of preferred orientation

6.6.3 Development of preferred orientation

6.6.3.1 Crystallographic aspects

When a polycrystalline metal is plastically deformed the individual grains tend to rotate into a com- mon orientation. This preferred orientation is developed gradually with increasing deformation, and although it becomes extensive above about 90% reduction in area, it is still inferior to that of a good single crystal. The degree of texture produced by a given deformation is readily shown on a monochromatic X-ray transmission photograph, since the grains no longer reflect uniformly into the

342 Physical Metallurgy and Advanced Materials

Rolling direction

Rolling direction

Figure 6.43 (1 1 1) pole figures from copper (a) and α-brass (b) after 95% deformation (intensities in arbitrary units).

Table 6.3 Deformation textures in metals with common crystal structures. Structure

Sheet (rolling texture) Bcc

Wire ( fiber texture)

[1 1 1], [1 0 0] double fiber

diffraction rings but only into certain segments of them. The results are usually described in terms of an ideal orientation, such as [u, v, w] for the fibre texture developed by drawing or swaging, and {h k l} plane and a direction of the type the ideal orientation can only be represented by means of a pole figure, which describes the spread of orientation about the ideal orientation for a particular set of (h k l) poles (see Figure 6.43).

In tension, the grains rotate in such a way that the movement of the applied stress axis is towards the operative slip direction as discussed in Section 6.3.5 and for compression the applied stress moves towards the slip plane normal. By considering the deformation process in terms of the particular stresses operating and applying the appropriate grain rotations it is possible to predict the stable end-grain orientation and hence the texture developed by extensive deformation. Table 6.3 shows the predominant textures found in different metal structures for both wires and sheet.

For fcc metals a marked transition in deformation texture can be effected either by lowering the deformation temperature or by adding solid solution alloying elements which lower the stacking-fault energy. The transition relates to the effect on deformation modes of reducing stacking-fault energy or thermal energy, deformation banding and twinning becoming more prevalent and cross-slip less important at lower temperatures and stacking-fault energies. This texture transition can be achieved in most fcc metals by alloying additions and by altering the rolling temperature. Al, however, has a high fault energy and because of the limited solid solubility it is difficult to lower by alloying. The extreme types of rolling texture, shown by copper and 70/30 brass, are given in Figure 6.43a and b.

In bcc metals there are no striking examples of solid solution alloying effects on deformation texture, the preferred orientation developed being remarkably insensitive to material variables. However,

Mechanical properties I 343 material variables can affect cph textures markedly. Variations in c/a ratio alone cause alterations

in the orientation developed, as may be appreciated by consideration of the twinning modes, and it is also possible that solid solution elements alter the relative values of critical resolved shear stress for different deformation modes. Processing variables are also capable of giving a degree of control in hexagonal metals. No texture, stable to further deformation, is found in hexagonal metals and the angle of inclination of the basal planes to the sheet plane varies continuously with deformation. In general, the basal plane lies at a small angle (<45 ◦ ) to the rolling plane, tilted either towards the rolling direction (Zn, Mg) or towards the transverse direction (Ti, Zr, Be, Hf).

The deformation texture cannot, in general, be eliminated by an annealing operation even when such a treatment causes recrystallization. Instead, the formation of a new annealing texture usually results, which is related to the deformation texture by standard lattice rotations.

6.6.3.2 Texture hardening

The flow stress in single crystals varies with orientation according to Schmid’s law and hence materials with a preferred orientation will also show similar plastic anisotropy, depending on the perfection of the texture. The significance of this relationship is well illustrated by a crystal of beryllium, which is cph and capable of slip only on the basal plane, a compressive stress approaching ≈2000 MN m −2 applied normal to the basal plane produces negligible plastic deformation. Polycrystalline beryllium sheet, with a texture such that the basal planes lie in the plane of the sheet, shows a correspondingly high strength in biaxial tension. When stretched uniaxially the flow stress is also quite high, when additional (prismatic) slip planes are forced into action even though the shear stress for their operation is five times greater than for basal slip. During deformation there is little thinning of the sheet, because the and zirconium, show less marked strengthening in uniaxial tension because prismatic slip occurs more readily, but resistance to biaxial tension can still be achieved. Applications of texture hardening lie in the use of suitably textured sheet for high biaxial strength, e.g. pressure vessels, dent resistance, etc. Because of the multiplicity of slip systems, cubic metals offer much less scope for texture hardening.

Again, a consideration of single-crystal deformation gives the clue; for, whereas in a hexagonal crystal m can vary from 2 (basal planes at 45 ◦ to the stress axis) to infinity (when the basal planes are normal), in an fcc crystal m can vary only by a factor of 2 with orientation, and in bcc crystals the variation is rather less. In extending this approach to polycrystalline material certain assumptions have to be made about the mutual constraints between grains. One approach gives m = 3.1 for a random aggregate of fcc crystals and the calculated orientation dependence of σ/τ for fiber texture shows that a rod with the cube texture (σ/τ = 2.449) is 20% weaker.

If conventional mechanical properties were the sole criterion for texture-hardened materials, then it seems unlikely that they would challenge strong precipitation-hardened alloys. However, texture hardening has more subtle benefits in sheet metal forming in optimizing fabrication performance. The variation of strength in the plane of the sheet is readily assessed by tensile tests carried out in various directions relative to the rolling direction. In many sheet applications, however, the requirement is for through-thickness strength (e.g. to resist thinning during pressing operations). This is more difficult to measure and is often assessed from uniaxial tensile tests by measuring the ratio of the strain in the width direction to that in the thickness direction of a test piece. The strain ratio R is given by

R =ε w /ε t = ln (w 0 / w)/ ln (t 0 / t)

= ln (w (6.31)

0 / w)/ ln (wL/w 0 L 0 ),

where w 0 ,L 0 and t 0 are the original dimensions of width, length and thickness, and w, L and t are the corresponding dimensions after straining, which is derived assuming no change in volume occurs.

344 Physical Metallurgy and Advanced Materials

zx

Figure 6.44 Schematic diagram of the deep-drawing operations, indicating the stress systems operating in the flange and the cup wall. Limiting drawing ratio is defined as the ratio of the diameter of the largest blank which can satisfactorily complete the draw (D max ) to the punch diameter (d) (after Dillamore, Smallman and Wilson, 1969; courtesy of the Institute of Materials, Minerals and Mining).

The average strain ratio R, for tests at various angles in the plane of the sheet, is a measure of the normal anisotropy, i.e. the difference between the average properties in the plane of the sheet and that property in the direction normal to the sheet surface. A large value of R means that there is a lack of deformation modes oriented to provide strain in the through-thickness direction, indicating a high through-thickness strength.

In deep drawing, schematically illustrated in Figure 6.44, the dominant stress system is radial tension combined with circumferential compression in the drawing zone, while that in the base and lower cup wall (i.e. central stretch-forming zone) is biaxial tension. The latter stress is equivalent to a through-thickness compression, plus a hydrostatic tension which does not affect the state of yielding. Drawing failure occurs when the central stretch-forming zone is insufficiently strong to support the load needed to draw the outer part of the blank through the die. Clearly, differential strength levels in these two regions, leading to greater ease of deformation in the drawing zone compared with the stretching zone, would enable deeper draws to be made: this is the effect of increasing the R value,

i.e. high through-thickness strength relative to strength in the plane of the sheet will favor drawability. This is confirmed in Figure 6.45, where deep drawability as determined by limiting drawing ratio (i.e. ratio of maximum drawable blank diameter to final cup diameter) is remarkably insensitive to ductility and, by inference from the wide range of materials represented in the figure, to absolute strength level. Here it is noted that for hexagonal metals slip occurs readily along contributing no strain in the c-direction, and twinning only occurs on √ {1 0 ¯1 2} when the applied stress √ nearly parallel to the c-axis is compressive for c/a >

3 and tensile for c/a < √ 3. Thus, titanium, √ c/a <

3 has low through-thickness strength when the basal plane is oriented parallel to the plane of the sheet. In √ contrast, hexagonal metals with c/a >

3, has a high strength in through-thickness compression, whereas Zn with c/a <

3 would have a high R for {1 0 ¯1 0} parallel to the plane of the sheet.

Texture hardening is much less in the cubic metals, but fcc materials with {1 1 1} system and bcc with {1 1 0} with {1 1 1} and {1 1 0} parallel to the plane of the sheet. The range of values of R encountered

Mechanical properties I 345

4 Tensile elongation

Plastic anisotro

2.0 2.2 2.4 2.6 2.8 3.0 L.D.R.

Figure 6.45 Limiting draw ratios (LDR) as a function of average values of R and of elongation to fracture measured in tensile tests at 0 ◦ , 45 ◦ and 90 ◦ to the rolling direction (after Wilson, 1966; courtesy of the Institute of Materials, Minerals and Mining).

in cubic metals is much less. Face-centered cubic metals have R ranging from about 0.3 for cube texture, {1 0 0} are sometimes obtained in body-centered cubic metals. Values of R in the range 1.4–1.8 obtained in aluminum-killed low-carbon steel are associated with significant improvements in deep-drawing performance compared with rimming steel, which has R-values between 1.0 and 1.4. The highest values of R in steels are associated with texture components with {1 1 1} parallel to the surface, while crystals with {1 0 0} parallel to the surface have a strongly depressing effect on R.

In most cases it is found that the R values vary with testing direction and this has relevance in relation to the strain distribution in sheet metal forming. In particular, ear formation on pressings generally develops under a predominant uniaxial compressive stress at the edge of the pressing. The ear is a direct consequence of the variation in strain ratio for different directions of uniaxial stressing,

= (R max −R min ) generally correlates with a tendency to form pronounced ears. On this basis we could write a simple recipe for good deep-drawing properties

research is aimed at improving forming properties through texture control.