r-Value Determination to ISO 10113

"The r-value is the “ratio of the true plastic width strain to the true plastic thickness strain” in a metal specimen that has been subjected to uniaxial tensile stress (definition from DIN EN ISO 10113).

To calculate the r-value, one would therefore need the measurement of the true plastic width- and thickness-strain during uniform elongation. However, since it is much easier to measure the change in length than the change in thickness, the standard is based on the model of constant volume in the range up to maximum force Ag (uniform elongation). If we assume that the volume is constant up to the plastic extensometerr- strain at maximum force Ag, we can replace the change in thickness with the change in length to determine the r-value.

If the r-value is 1, then we are looking at an isotropic material in which the deformation in terms of width and thickness changes to the same extent. If the value is greater than 1, we have a greater deformation in width. If the value is smaller than 1, we have a greater deformation in thickness.

The ISO 10113 standard also defines three procedures and two methods for determination of the r-value.

Three procedures: In the automatic procedure, both the extension as well as change in width are measured with an extensometer. In addition, there is a semi-automatic procedure, where only the extension is measured with an extensometer, and the manual procedure where both the change in width and the extension are measured manually.

For the manual and semi-automatic procedures, the r-value is determined according to the single point method. Here, the r-value is determined at a certain degree of plastic stretch (e.g., through value determination at 2% and 5% plastic elongation).

The automatic procedure additionally provides the option of the regression method, which covers a course of development, that is, a full strain range. The data obtained from the true plastic longitudinal strain and true plastic width strain in a specified strain range is used to determine the slope.

The regression method is recommended as it provides more reliable r-values because it is averaged over a complete range and not just a snapshot, as is the case with the single point method (where determination is usually based on 2 or 5% plastic elongation).

Since the 2020 edition, ISO 10113 (2020-08) recommends the use of “extensometers for measurement of the instantaneous width reduction which are able to measure the change in width in multiple locations ideally evenly distributed across the entire gauge length.”

With this change of standard, realistic specimen results shall be determined and the reproducibility shall be increased. In addition, the method is easier to understand, since the same specimen volume is used for change in width and extension.

ZwickRoell offers the videoXtens T-160 HP specifically for this recommendation of the standard. It measures over 10 measurement axes, equally distributed over the entire measurement range. It not only produces realistic r-values to ISO 10113, but also precise, highly accurate values, since it was specially designed for this test.