Cold Rolling

Cold rolling is one of the most important processes in metal forming. Metal sheets are drawn back and forth between two rotating rolls. The gap between the rolls is smaller than the sheet thickness and the resulting strain state is plane strain compression:

ǫ=











ǫ 0 0 0 0 0 0 0 −ǫ











(2.1)

This corresponds to tensile deformation in x-direction (RD) and compression in z-direction (ND) without any lateral expansion. Often deviations of this ideal strain state exist, e.g. lateral expansion or shear may occur.

The plastic deformation of metals takes place by the movement of dislocations. If the applied stress is high enough dislocations will move on crystallographic glide systems, what leads to a shape change of the crystal in accordance with the applied stress. In fcc crystals the glide, or slip, plane is the close packed {111} plane and the glide, or slip, direction is h110i. Taking into account crystal symmetry 12 different slip systems exist in fcc crystals. Von Mises demonstrated that at least five slip systems are necessary to allow an arbitrary shape change of a cubic crystal [33]. The shear stress τ that acts on

2.2. Thermomechanical Processes dislocations in a certain glide system depends on the orientation of a crystal as shown by Schmid [34]:

τ = σm ⊗ n, (2.2)

where σ is the tensile stress, m the slip plane and n the slip direction.

In a polycrystal glide is not simply activated on the system with the highest τ since this would lead to the formation of voids. Instead a compromise between the shape change of neighbored crystals will be established. After Taylor the set m of all glide systems will be activated which requires least energy A for the plastic deformation [35]:

A^(m)= τ₀

n=n5

X

n=n¹

γ_n^(m)

= min . (2.3)

where n1 to n5 are permutations of five out of all possible glide systems and γ_n^m is the amount of slip in the glide system n. With the Taylor approach the rotations of grains caused by dislocation movement, i.e. the texture development, during deformation can be adequately described [36].

During deformation additional dislocations are generated and act as obstacles for disloca-tion movement what results in work hardening of the material. If the dislocadisloca-tion density becomes so large that dislocation movement is virtually suppressed, other deformation mechanisms like mechanical twinning or shear banding can occur. The magnitude of these other deformation mechanisms depends on the necessary energy to form stacking faults γSF.

Common inhomogeneities of deformed microstructures are:

Transition bands Due to the ambiguity of Eq. (2.3) different slip systems can be acti-vated in the same grain. The different rotations lead to a orientation spread inside a grain.

Subgrains Metals with medium to high stacking fault energy form cell structures where thick dislocation walls surround regions with a low density of statistical

disloca-tions. These subgrains play an important role in the nucleation of new grains during recrystallization.

Deformation twins By lattice shearing a part of a grain can flip into a twin orientation in which it shares a mirror plane with the parent grain. The coherent twin bound-ary has a very low energy and mobility and can act as an obstacle for dislocation glide.

Shear bands When strong deformation obstacles develop during deformation non-crys-tallographic slip on other planes than {111} (fcc) can occur. In materials with low stacking fault energies these obstacles are twin-matrix lamellae which already develop at early stages of deformation. For medium to high stacking fault energy materials the obstacles are formed by dislocation walls and cell blocks at later stages of deformation [37]. Because of the non-crystallographic slip shear band formation strongly affects the texture development. Shear bands are often inclined by 35^◦ to RD and are supposed to interfere with the nucleation of Cube grains during recrystallization [38].

Grain fragmentation By severe plastic deformation grains may fragment into smaller parts, especially if the initial grain size was rather large. The orientation of the grain fragments can diverge further during subsequent deformation.

In fcc metals two main texture types develop during cold rolling:

Copper or Pure Metal type This texture is favored by medium to high stacking fault fcc metals (like Copper) and consists out of Copper, S and Brass orientations dis-tributed along the β-fiber. The formation of a Copper type texture is related to the formation of subcells during deformation [39]. For details about ideal orientations and fibers see Tables 2.1 and 2.2.

Brass or Alloy type In fcc metals with low stacking fault energy (like Brass) a texture out of the ideal orientations Brass and Goss develops along the α-fiber. Since

2.2. Thermomechanical Processes

Figure 2.5.: {111} pole figures of a Copper type (a) and an Alloy type (b) rolling textures.

the stacking fault energy can be strongly decreased by alloying the term Alloy type is used. Mechanical twinning is enhanced by a low stacking fault energy as less cross-slip occurs and higher stress levels are reached during deformation [40].

It is assumed, that the generation of new orientations by twinning leads to the development of alloy type rolling textures [40]. For details about ideal orientations and fibers see Tables 2.1 and 2.2.

An example of both texture types is given in Figure 2.5. If the ratio of volume fractions calculated from the ODF is

VCopper+ VS > 2 · V^Brass (2.4)

the rolling texture is considered to be of the Copper type and else of the Alloy type [41].

The stacking fault energy is not the only parameter influencing this texture transition but also the work hardening behavior, shear banding and grain fragmentation can contribute [42].