Crack Propagation Velocity Determination by High-speed Camera Image Sequence Processing

Abstract

The determination of crack propagation velocities can provide valuable information for a better understanding of damage processes of concrete. The spatio-temporal analysis of crack patterns developing at a speed of several hundred meters per second is a rather challenging task. In the paper, a photogrammetric procedure for the determination of crack propagation velocities in concrete specimens using high-speed camera image sequences is presented. A cascaded image sequence processing which starts with the computation of displacement vector fields for a dense pattern of points on the specimen's surface between consecutive time steps of the image sequence chain has been developed. These surface points are triangulated into a mesh, and as representations of cracks, discontinuities in the displacement vector fields are found by a deformation analysis applied to all triangles of the mesh. Connected components of the deformed triangles are computed using region-growing techniques. Then, the crack tips are determined using the principal component analysis. The tips are tracked in the image sequence and the velocities between the time stamps of the images are derived. A major advantage of this method as compared to the established techniques is in the fact that it allows spatio-temporally resolved, full-field measurements rather than point-wise measurements. Furthermore, information on the crack width can be obtained simultaneously. To validate the experimentation, the authors processed image sequences of tests on four compact-tension specimens performed on a split-Hopkinson tension bar. The images were taken by a high-speed camera at a frame rate of 160,000 images per second. By applying the developed image sequence processing procedure to these datasets, crack propagation velocities of about 800 m/s were determined with a precision in the order of 50 m/s.

Keywords: crack analysis; crack propagation velocity; deformation measurement; high-speed camera; image sequence analysis; material testing.

Figure 1

Displacement field, exaggerated using a vector scale factor of 6, from a bend test.

Figure 2

(a) Relative translation vector of a divided triangle; (b) color-coded map of the relative translation vector length $\left|\left|{\overrightarrow{t}}_{rel}\right|\right|$ for each triangle.

Figure 3

Connected components of crack triangles where $\left|\left|{\overrightarrow{t}}_{rel}\right|\right|>\delta$ according to [19].

Figure 4

(a) The crack width r is computed by the projection of ${\overrightarrow{t}}_{rel}$ onto the normal $\overrightarrow{n}$; (b) crack normal estimation according to [19,20].

Figure 5

Connected components (in blue) of crack triangles.

Figure 6

Neighborhood analysis: The bold red triangle is the crack candidate that is considered; darker blue triangles are non-deformed neighbor triangles: (a) Standard case with two components; (b) crack junction; (c) crack tip; (d) crack candidate at the mesh boundary.

Figure 7

(a) False crack tip detection with the neighborhood analysis; (b) experimental example with false detections.

Figure 8

(a) Connected components of the deformed triangles in red, of which the center points are colored green, the mean and the principal directions magenta; (b) rotated bounding box computed using the principal component analysis (PCA); (c) crack tip detection by means of PCA. The yellow triangle is detected as a mesh boundary triangle, the green triangle shows the detected crack tip.

Figure 9

Experimental setup: Split-Hopkinson tension bar used for performing dynamic tests on compact-tension specimens: (a) Schematic view of the setup; (b) main components of the assembly; (c) specimen and its dimensions.

Figure 10

(a) Specimen in the test setup. (b) Front side of the specimen; (c) back side with four conductive lacquer barriers.

Figure 11

Color-coded maps of $\left|\left|{\overrightarrow{t}}_{rel}\right|\right|$ of a sequence of one of the experiments at the 160 kHz imaging rate, time stamps in milliseconds.

Figure 12

Crack triangles (blue) with crack tips, i.e., green colored triangles and the yellow-colored mesh border triangles for the experiment presented in Figure 11.

Figure 13

Crack length over time plots using the photogrammetric method with different thresholds for deformed triangles (red, green, blue) and using the conductive lacquer barriers (magenta): (a) 1st sample; (b) 2nd sample; (c) 3rd sample; (d) 4th sample.

Figure 14

Crack propagation velocities and the corresponding error bars (±one standard deviation) obtained using the photogrammetric technique with different thresholds for deformed triangles (red, green, blue) and using the conductive lacquer barriers (magenta): (a) 1st sample; (b) 2nd sample; (c) 3rd sample; (d) 4th sample.

Figure 15

Least-squares velocities obtained using all data points as average velocities and the corresponding standard deviations (error bars: ±one standard deviation) for all specimens.