In this part, the stereovision technique is applied to analyze a cylinder expansion caused by blast loading. It is worth noting that other types of loading configurations have been used in the literature [13, 20]. First, a synthetic case representative of the experiment is studied to estimate the performances of the technique and in particular the resolution of the reconstruction. This enables for the evaluation of the minimum size of observable and quantifiable defects. In the present experiments, the observed surface undergoes important deformations (beyond 100% strain). This is the reason why the computation is not carried out with the initial reference but rather with an updated reference that causes a cumulation of measurement errors. A reduction in the size of the reconstructed surface is observed since the points that leave the initial region of interest are not taken into account. To improve the performances of the approach, a precorrection for large displacements is performed. It consists in seeking a uniform translation to apply to the images so that, on average, the region of interest is motionless. Then the DIC algorithm is run using the prior translation as an initialization of the displacement field. This procedure makes the computation faster, more stable and more accurate. Finally, the stereovision technique is applied to the experiment itself [21–24].

### 5.1. Detection Level

Before applying the stereo-correlation procedure to an experimental case, it is important to evaluate the size and amplitude of defects that can be detected. The hydrodynamic code HESIONE [25] predicts the shape of the specimen at different stages of evolution. For any instant of time, , the predicted surface is projected onto the actual surface by least squares minimization.

Figure 10(a) shows one picture of the specimen in its reference state. The surface texture is artificially created by mimicking laser marking (i.e., with parallel rays) based on a computerized pattern. The picture of the surface deformed by the computed displacement field, and onto which the original surface marking has been projected, is shown in Figure 10(b). In addition to the smooth displacement field, some additional perturbations are superimposed to check the resolution of the analysis. They would correspond to localized "bumps" of various diameters (0.5, 1, 5, 10, and 30 mm) and amplitudes (0.125, 0.25, 0.5, 1, 2.5, and 5 mm) as illustrated in Figure 10(c). A total of 15 different perturbations are introduced.

Based on the knowledge of the transformation matrix, each point of the 3D surface is projected onto the two image planes to create synthetic left and right stereoscopic image pairs as close as possible to experimental images. When compared with the experimental geometry, the mean distance between the projection into the image of a known 3D point and the corresponding image-point extracted in the image is equal to pixels. The blurring effect of the entire optical chain is taken into account through convolution with a Gaussian filter. 16 image pairs are generated, one of them (reference) containing no perturbation. Two examples of left-right pairs are shown in Figures 11(a)–11(d) and 11(b)–11(e). To appreciate the effect of the bumps on the images, the same figure shows the difference between two similar images with and without the perturbations. Figures 11(c) and 11(f) correspond, respectively, to the left and right views. It is to be emphasized that no noise has been added to the images in order to focus on detection issues.

A DIC analysis was performed on those artificial images, based on the same choice of parameters as the one used in the experiment, namely, pixel elements are selected based on the signal-to-noise ratio. A comparison between the measured and prescribed displacements for each bump allows for the evaluation of the resolution. To carry out this analysis, the measured and imposed shapes are unfolded onto a plane as suggested by Luo and Riou [26].

Figure 12(a) shows the prescribed perturbation for the easiest cases (amplitudes of 2.5 mm and 5 mm, left and right, respectively, for a 30 mm diameter bump), while Figure 12(b) is the measured shape. In spite of a large noise affecting the shape of the bump, this perturbation is rather well captured by DIC computations. Figures 12(c) and 12(d) correspond to smaller perturbations (amplitudes of 125 m and 250 m, left and right respectively, for a 5 mm diameter). Although the perturbations are detected, their sizes and amplitudes cannot be estimated reliably. The reason for this lies in the intrinsic resolution of the DIC analysis performed here with elements of size 16 pixels or 2.9 mm. Thus the entire bump can fit in a two-element wide square. A summary of the results is presented in Figures 13(a) and 13(b) where measured amplitudes and diameter, respectively, normalized by the prescribed counterpart, are shown for all tested cases.

It is concluded that for very severe experimental conditions (rotating mirror high-speed camera at 16 m optical distance from the specimen, magnification of 22, small radius of curvature, and poorly contrasted surface texture), the limit of detection of such bumps is of the order of 5 mm, and a minimum size of about 10 mm is needed to allow for a reliable quantification of the perturbation. Moreover, 250 m amplitudes are resolved reliably for those conditions. These conclusions hold for a fixed element size of 16 pixels. Smaller elements lead to too noisy measurements to secure the determination, whereas larger elements are too coarse. This level is to be compared with the 3D reconstruction uncertainty achieved herein. A level of m is estimated by randomly perturbing the position of the calibration points, and reconstructed points with realistic values [19].

Possible improvements involve drastic changes in the experimental set-up. CCD camera could offer images in digital format directly, thus limiting the digitation step in the analysis. However, access to similar pixel sizes still represents a technical challenge. A better resolution could also be obtained through a higher magnification, at the expense of a smaller frame.

### 5.2. Large Displacement Handling

In the context of detonics, very high strain levels between consecutive images have to be captured. This fact is a major difficulty for DIC. A specific procedure has been designed to allow for a much more robust analysis in this context. As a side benefit, displacement fields appear to be less subjected to noise.

The principle of the method is simply to initialize the DIC analysis, which is in the present case an iterative procedure, by a prior determination of the displacement field obtained via a simulation of the experiment. This allows for a convergence of the displacement determination into the deepest minimum, and avoids trappings into secondary minima. Let us note that a multiscale strategy is adopted in the DIC analysis for the same purpose of limiting secondary minima trappings [16]. However, at the largest scales, the contrast of the images is significantly reduced and hence some nodes or zones may be polluted by such artifacts. In contrast, a fair prior estimate of the displacement field, which may still be inaccurate, requires DIC to address only the remaining corrections displacements and hence can be tackled with less coarsened images. As this procedure only affects the initial displacement field, it does not affect the final one at convergence as can be checked by perturbing this prior determination, and checking that the final determination is unaffected. This robustness allows for some tolerance on the quality of this first displacement field, and hence, small effects such as the motion of the cylinder axis are neglected.

In the DIC procedure, the deformed image is corrected at each iteration by the current determination of the displacement field. Hence, any displacement field can be used at initialization, and no subsequent modification of the DIC algorithm is needed. When the initial field is close to the final solution, convergence is fast and accurate. The only operation needed is to transform the 3D displacement field from HESIONE code [25] into both the right and left 2D displacement fields used for the time registration of the DIC procedure. This projection is performed as in the previous subsections using the transformation matrices introduced in Section 2 once the 3D frames used in the code and in the stereo-correlation procedure coincide. This is achieved by a least squares minimization between the initial experimental and numerical shapes. A mispositioning error of the order of 1 mm is achieved. Figure 14 illustrates the effect of the prior correction of a late image onto reference one. It can be seen that most of the displacement has been accounted for, and only small differences remain to be determined (by DIC). When this prior determination is not taken into account, a larger element size (24 pixels) has to be chosen to limit the uncertainty level. With the present initialization, a 16 pixel element can be dealt with.

### 5.3. Experimental Reconstruction

After the experiment, the film composed of 25 acquisitions is developed and the 25 images are digitized independently from each other. From the fixed elements of the scene (yellow paper in Figure 1(a) or the calibration target shown in Figure 14), repositioning of images is performed by adjusting a translation correction so that the elements remain motionless [19].

Reconstruction of the surface is given in Figure 15 for three different times. In these figures, the result of the stereo-correlation is shown in blue, while the computed one (given by HESIONE) is in red. Apart from some slight positioning differences between experimental and computed geometries, the two surfaces superimpose quite well for the entire duration of the experiment. Displacement corrections of at most pixels need to be measured. With the multiscale algorithm used herein, this level is easily measured. Moreover, in the last picture, a clear defect can be identified, which is interpreted as a local thinning of the specimen, that is, an example of necking. The image pair shown in Figure 16 supports that statement.

In order to investigate on a quantitative basis the onset of necking, it is proposed to base the analysis on the standard deviation of the normal surface displacements. This standard deviation can be seen as a measure of the roughness of the expanding surface, which is expected to remain small for a uniform strain of the surface, and to display a sudden increase when necking (at least necking that can be captured by the DIC analysis, i.e., at a large enough scale). The standard deviation is expected to be sensitive to the sampled surface as the lower part of the specimen is subjected to a larger strain. Thus the standard deviation is estimated over three regions, namely, first globally over the entire field of analysis, second over a central zone (where edge effects are avoided), and third on a zone located at the bottom of the specimen where necking is seen to occur first.

The first two standard deviations are shown as functions of time (through the image number) in Figure 17(a). A steady increase is observed with an acceleration taking place for the two last stages, although the level of fluctuation of this curve makes this last observation questionable. The central zone shows a smaller roughening, which is consistent with the lower strain level reached in this zone. Let us emphasize the fact that the displacement field is computed from the reference image to the current one, and hence the steady increase cannot be attributed to a cumulation of measurement errors. Note also that the initial image has already a significant roughness because it has suffered a significant expansion prior to be captured in the first image. The third standard deviation computed over the bottom part of the specimen is shown in Figure 17(b). The sudden acceleration of the standard deviation for the last images seems to depart clearly from the previous steady evolution and supports the previous discussion on a detectable necking occurring in this zone. This also supports the idea that the global standard deviation is affected by the necking of the lower part, and that the sudden rise is actually meaningful. Moreover, the a priori uncertainty is estimated to amount to 0.5 pixel, or 90 m. The impact of image noise has been estimated to amount to an additional 100 m [19]. The sum of these uncertainties is well below the fluctuation level reported in those graphs.