*3.2. Experiment System*

The experimental system is shown in Figures 8 and 9. Four GigE cameras (maximum resolution 2752 × 2200) were used to form two independent DIC binocular measurement systems. One DIC system was placed in front of the test sample, while the other DIC system was placed behind the test sample. Two pairs of 50 mm fixed focus lenses were used to achieve a 20 mm × 20 mm field of view. The spatial resolution was 0.08 mm/pixel and the acquisition rate was 10 Hz. Two powerful LED lights provided sufficient illumination for the front and back DIC measurement systems. A 50 KN MTS tensile test machine was used to do the tensile test, and a 1 mm thick dog bone shape sample made from DP980 sheet metal was prepared for the test. The tensile speed was set at 3 mm/min. The slow tensile rate used for the test enabled more images to be taken before the sample cracked, thus providing more data to analyze. Figure 10 is a schematic diagram of this sample. Current limitations with this system include the cost of the cameras used for the DIC systems and the large amount of space required to accommodate the front and rear camera groups.

**Figure 8.** Schematic diagram of the experimental system.

**Figure 9.** Experimental set-up of the R-value measurement.

<sup>1</sup> <sup>2</sup> <sup>3</sup>

<sup>3</sup> = −(<sup>1</sup> + <sup>2</sup>

2 −(<sup>1</sup> + <sup>2</sup>

=

)

)

**Figure 10.** The schematic diagram of DP 980.

1 2 3

#### *3.3. Experimental Results Analysis and Discussion*

The 3D contour and strain distribution on the surfaces of the DP980 was obtained through DIC measurement. Figure 11 illustrates the simultaneous measurement results of length strain (*ε*1) map, width strain (*ε*2) map and thickness strain (*ε*3) map before fracture in the tensile test. The necking area, which is indicative of a strain concentration, is clearly visible. <sup>1</sup> <sup>2</sup> <sup>3</sup>

R-value measurements were taken using two different methods, and these results were compared and analyzed. The first method is the traditional measurement, or indirect measurement, method based on the constant volume assumption. According to the assumption of constant volume, *ε*1+ *ε*2+ *ε*<sup>3</sup> = 0; thus, the thickness strain can be derived from measurements of the length and width strain: 1 2 3

)

$$
\varepsilon\_{\mathfrak{Z}} = - (\varepsilon\_1 + \varepsilon\_2) \tag{10}
$$

Based on the definition of R-value: <sup>3</sup> = −(<sup>1</sup> + <sup>2</sup>

$$\mathcal{R} = \frac{\varepsilon\_2}{- (\varepsilon\_1 + \varepsilon\_2)} \tag{11}$$

The other method used is the direct measurement method, or the direct thickness strain measurement method proposed in this paper. The calculation method is shown in Equation (8). Data in both the non-necking and necking area was selected for analysis to better show the difference between the two measurement methods.

**Figure 11.** Full field strain distribution of sample surface measured by DIC system: (**a**) distribution of length strain; (**b**) distribution of width strain; (**c**) distribution of thickness strain.
