Texture-hardening Al, however, has a high fault energy and because of

7.6.3.2 Texture-hardening Al, however, has a high fault energy and because of

The flow stress in single crystals varies with orienta- the limited solid solubility it is difficult to lower by

tion according to Schmid’s law and hence materials alloying. The extreme types of rolling texture, shown

with a preferred orientation will also show similar by copper and 70/30 brass, are given in Figures 7.44a

plastic anisotropy, depending on the perfection of the and 7.44b.

texture. The significance of this relationship is well In bcc metals there are no striking examples of

illustrated by a crystal of beryllium which is cph and solid solution alloying effects on deformation texture,

capable of slip only on the basal plane, a compres- the preferred orientation developed being remarkably

sive stress approaching ³2000 MN/m 2 applied normal insensitive to material variables. However, material

to the basal plane produces negligible plastic defor- variables can affect cph textures markedly. Variations

mation. Polycrystalline beryllium sheet, with a texture in c/a ratio alone cause alterations in the orientation

such that the basal planes lie in the plane of the sheet,

Table 7.3 Deformation textures in metals with common crystal structures

Structure Wire (fibre texture)

Sheet (rolling texture)

bcc [1 1 0]

f1 1 2g h1 1 0i to f1 0 0g h0 1 1i

fcc [1 1 1], [1 0 0] double fibre

f1 1 0g h1 1 2i to f35 1g h1 1 2i

cph [2 1 0]

f0 0 0 1g h1 0 0 0i

234 Modern Physical Metallurgy and Materials Engineering shows a correspondingly high strength in biaxial ten-

sion. 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. Dur- ing deformation there is little thinning of the sheet, because the h1 1 20i directions are aligned in the plane of the sheet. Other hexagonal metals, such as tita- nium 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 con- sideration 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

Figure 7.45 Schematic diagram of the deep-drawing the basal planes are normal), in an fcc crystal m can

operations indicating the stress systems operating in the vary only by a factor of 2 with orientation, and in bcc flange and the cup wall. Limiting drawing ratio is defined as crystals the variation is rather less. In extending this the ratio of the diameter of the largest blank which can

satisfactorily complete the draw ⊲D max ⊳ to the punch approach to polycrystalline material certain assump-

diameter (d) (after Dillamore, Smallman and Wilson, 1969; tions have to be made about the mutual constraints

courtesy of the Canadian Institute of Mining and between grains. One approach gives m D 3.1 for a

Metallurgy) .

random aggregate of fcc crystals and the calculated strain in the through-thickness direction, indicating a

is 20% stronger than a random structure; the cube tex- high through-thickness strength. In deep-drawing, schematically illustrated in

If conventional mechanical properties were the sole Figure 7.45, the dominant stress system is radial criterion for texture-hardened materials, then it seems

tension combined with circumferential compression in unlikely that they would challenge strong precipitation-

the drawing zone, while that in the base and lower hardened alloys. However, texture-hardening has more

cup wall (i.e. central stretch-forming zone) is biaxial subtle benefits in sheet metal forming in optimizing

tension. The latter stress is equivalent to a through- fabrication performance. The variation of strength in

thickness compression, plus a hydrostatic tension the plane of the sheet is readily assessed by tensile

which does not affect the state of yielding. Drawing tests carried out in various directions relative to the

failure occurs when the central stretch-forming zone rolling direction. In many sheet applications, however,

is insufficiently strong to support the load needed to the requirement is for through-thickness strength (e.g.

draw the outer part of the blank through the die. to resist thinning during pressing operations). This is

Clearly differential strength levels in these two regions, more difficult to measure and is often assessed from

leading to greater ease of deformation in the drawing uniaxial tensile tests by measuring the ratio of the

zone compared with the stretching zone, would enable strain in the width direction to that in the thickness

deeper draws to be made: this is the effect of increasing direction of a test piece. The strain ratio R is given by

the R value, i.e. high through-thickness strength relative to strength in the plane of the sheet will favour

RDε w /ε t

D ln⊲w 0 /w⊳/ ln⊲t 0 /t⊳

drawability. This is confirmed in Figure 7.46, where deep drawability as determined by limiting drawing

ratio (i.e. ratio of maximum drawable blank diameter where w 0 ,L 0 ,t 0 are the original dimensions of width,

D ln⊲w 0 /w⊳/ ln⊲wL/w 0 L⊳

to final cup diameter) is remarkably insensitive to length and thickness and w, L and t are the corre-

ductility and, by inference from the wide range of sponding dimensions after straining, which is derived

materials represented in the figure, to absolute strength assuming no change in volume occurs. The average

level. Here it is noted that for hexagonal metals slip strain ratio R, for tests at various angles in the plane of

occurs readily along h1 1 20i thus contributing no strain the sheet, is a measure of the normal anisotropy, i.e. the

in the c-direction, and twinning only occurs on the difference between the average properties in the plane

f1 0 12g when the applied stress nearly parallel to p of the sheet and that property in the direction normal to

the c-axis is compressive for c/a > p p 3 and tensile the sheet surface. A large value of R means that there

3, has a high is a lack of deformation modes oriented to provide

for c/a <

3. Thus titanium, c/a <

strength in through-thickness compression, whereas

Mechanical behaviour of materials 235 deep-drawing properties in terms of strain ratio mea-

surements made in a uniaxial tensile test as high R and low R. Much research is aimed at improving forming properties through texture control.