3.3.1. Non-Necking Area

A square area of 8 × 8 pixels, as shown in Figure 12a, was selected instead of a single point in the non-necking area to reduce the influence of noise on the data. Each pixel represents 0.2 mm. The calculation results for the traditional and proposed methods are shown in Figure 13. According to the definition of R-value, the R-value for DP980 is equal to the slope of these two curves. It can be seen from the figure that the relationship between thickness strain and width strain is approximately linear, and the amount of noise in the data is low. Therefore, the least squares principle can be used to calculate the slope of the two curves. The directly measured R-value is 0.8546, while the indirectly measured R-value is 0.8656. Based on previous research of the properties of DP980 material, its

R-value generally ranges between 0.7–1.0, depending on the material's composition [24]. The results measured by both methods can be considered reasonable because they both fall within this range, and the difference in the results between the two methods is very small. Therefore, both methods are acceptable. – .0, depending on the material's composition [24]. – .0, depending on the material's composition [24].


**Figure 13.** The R-value curve by two different measurement methods in the non-necking area. -

## 3.3.2. Necking Area

When necking occurs during a tensile test, a large amount of strain is disproportionately distributed in a central location of the material. As the deformation continues, the strain in the necking area continues to increase until the material ruptures. In the necking stage, the cross-sectional area of the material decreases drastically, while the strain in the thickness and width directions increases sharply. Figure 14 displays an example of the sharp strain increase that can occur during the necking stage.

**Figure 14.** Width and Thickness strain history.

An 8 × 8 pixel square area was selected in the necking area to obtain strain data, as shown in Figure 12b. Figure 15 illustrates the R-value measured by the two methods in the necking area. In the linear elastic deformation stage, the thickness strain is proportional to the width strain. The R-value at this time is a constant, and the results measured by the two methods are 0.8471 and 0.8526, respectively; these results are similar to those measured in the non-necked area. This shows that the material is uniformly distributed, stable in nature, and isotropic. When the width strain exceeds 60 mm/m, the strain value increases rapidly, and the material deformation enters the necking stage. It is worth noting that the direct method measurement curve no longer increases linearly; the growth rate reduces, and the R-value correspondingly becomes smaller. This shows that the ability of the material to resist strain in the thickness direction is reduced. Compared to the curve for the direct measurement method, the curve for the indirect measurement method remains linear in the early necking stage, and the R-value does not decrease significantly until the later necking stages. This result further confirms some researcher opinions that the material does not necessarily follow the constant volume assumption in the necking stage [12]. Therefore, the R-value measured by the direct measurement method is more reliable and accurate in the necking stage. It should be noted that some materials do follow the assumption of constant volume in the necking stage. The R-values for DP980 in the three rolling directions are displayed in Table 1. The R-values in the three rolling directions are very similar, indicating that the material has similar resistance to thickness deformation in different rolling directions.
