19 Tensile Hopkinson Bar Analysis of Additively Manufactured Maraging Steel 113 The first imaged the entire gauge length and tracked the evolution of necking as the sample failed. This provided useful information for developing a constitutive model, but was not especially novel [7]. The second used a significantly reduced field of view to increase the camera’s frame rate. The technique resembles that of [8], significantly modified to account for the camera’s low resolution. While still imaging the entire length of the gauge section, the camera’s vertical field of view was set to 32 pixels, the smallest possible. By careful lighting, small irregularities in the sample surface were highlighted. Vertically averaging the field of view then produced a streak image of the sample surface over time. Figure 19.3 illustrates these images. Tracing streaks on this image using a zero-normalized sum-squared-differences system provided sample surface longitudinal displacement u as a function of position x and time t. In principle strain ε could be calculated using ε = du dx . However, in practice this was unacceptably noisy, and any filter broad enough to eliminate the noise also eliminated any strain localization. Instead a functional form of ε =ln ! m+exp " − x −μ s 2#$ for localized strain was chosen and fitted to the measured displacements. This gave acceptable results; Fig. 19.4 gives an example. Uncertainty was assessed by bootstrapping [9]. Fig. 19.3 Illustration of image processing on oxygen free high conductivity copper C103. (a) Camera field of view, (b) Streak image, (c) Streak image with traced flow lines -150 -100 -50 0 50 100 150 200 250 Time / µs -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 Peak true strain Fig. 19.4 Maximum true strain for C103 copper experiment shown in Fig. 19.3
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