Anisotropy

During the rolling process, thin sheet metal obtains a texture through grain orientation, which the mechanical properties become anisotropic (direction-dependent). This plays an important role in sheet metal forming.

A measure of the anisotropy of plastic properties of sheet metal materials is the r-value. It describes the so-called vertical or plastic anisotropy, the ratio of the deformation degrees in surface direction to the thickness direction.

The plastic anisotropies at angles of 0° and 90° to the rolling direction are calculated as follows:

Here, φ_l φ_b means the degrees of deformation in the longitudinal and width directions, φ_s the natural strain in the thickness direction. Numerical indices indicate the angle between the sample position and the rolling direction.

• r = 1 material isotropic, same true strain in width and thickness directions
• r > 1 true strain primarily in the width direction
• r < 1 true strain primarily in the thickness direction

To determine the average vertical anisotropy, an anisotropy value is also determined using a 45° sample. The mean vertical anisotropy is given by:

The mean vertical anisotropy r_m is a measure of the unevenness. A good deep-drawing steel has an average vertical anisotropy value of r_m ≥ 1.25.

Regarding spring back , it is recommended to use a low vertical anisotropy as this has a positive influence on stability.

The planar anisotropy Δris a measure of the unevenness:

• Δr > 0 corners in 0° and 90° directions
• Δr ≤ 0 corner in 45° direction