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Rock Fracture Under dynamic loading

Full-field deformation and fracture characterisations of rocks under dynamic loads using high-speed three-dimensional digital image correlation

Haozhe Xing

Department of Civil Engineering, Monash University, Clayton, VIC 3800, Australia

This project uses high speed imaging combined with the three-dimensional digital image correlation (3D-DIC) method to study the full-field strain and strain-rate fields of rock materials under dynamic compression and penetration tests. A series of dynamic tests were conducted on Hawkesbury sandstones using a split Hopkinson pressure bar (SHPB) and gas gun. The real-time images of the loaded specimen were captured by two high-speed cameras at a frame rate up to 200,000 frames per second (fps) with a resolution of 256×256 pixels.

Fig.1 Setup of the SHPB coupled with high-speed imaging

 

Dynamic uniaxial compression test

The dynamic loading was applied by a striker launched via the gas gun which impacts the incident bar to generate a compressive wave which propagates through the specimen and afterwards to the transmitted bar. Two high-speed CMOS cameras (Phantom V2511) to reconstruct a stereo-vision were triggered by two synchronous transistor-transistor logic (TTL) signals. The sample was speckled to be tracked by the digital image correlation (DIC).

 

Fig 2. Compressive wave propagating through the specimen causing negative strain field movement within the sandstone at a strain rate of 120 s−1

Empowered by the high-performance high-speed cameras and DIC, the full-field stress wave propagation in rock material is visualised for the first time. The frame rate is 200,000 frames per second (fps), the resolution is 256×256 pixels and the P- wave velocity is 2034m/s.

Fig.3 (a) Images of cracks developing at a strain rate of 120 s−1 (b) Initiation of strain localisation under the strain rate of 120 s−1 in axial (exx), vertical (eyy) and shear (exy) directions at different stages

High-speed imaging enables capturing the initiation moment of the crack caused by the tension and shear. Coupled with the 3D-DIC, the strain localisation prior to the visible crack is available to be monitored with the quantitative information.

Fig. 4 3D out-of-plane displacement field at t=220 μs with the strain rate of 70 s−1.

Through the reconstruction of 3D-DIC the surface of the rock can be easily reconstruct to calculate the out-of-plane displacement.

It was found that the strain field during the pre-failure stage shows the wave propagation and dispersion proving the existence of the radial inertial effect on the specimen. The strain rate field on the specimen presents a significant vibration pattern which is caused by the axial inertial effect. The strain extracted from DIC has an elastic recovery after peak which is not reflected by one-dimensional wave method. Hence, the actual strain on the brittle material especially after the peak stress cannot be accurately revealed by strain gauge signals.

High impact penetration tests

In penetration experiments, two cameras are involved to capture the rear surface of the rock target and projectile status, respectively. The frame rate is 200,000 fps and the resolution is 256×256 pixels. A sequence of side photos can provide the velocity and the trajectory of the projectile.

Fig. 5: Setup of the two cameras in penetration test
Fig. 6: The side view of the projectile at a velocity of 350 m/s, the interval time of the photos is 240 µs

The damages of the rear face of sandstone and gabbro show quite different patterns which has a relationship between the parameters of projectile and the mechanical properties of the rock.

Fig. 7: The rear view of the sandstone plate (left) and gabbro plate (right) the interval time is 240 µs

In the compression test, wave propagation, dispersion and radial inertial effect on the specimen were found from DIC results. The strain rate vibration pattern on the specimen, which was visualised by DIC, found to be dependent on the input waveform. A recovery of strain in the post-peak stage was detected on the specimen by DIC, which is unrevealed in the traditional one-dimensional theory method (i.e., strain gauge signals). The results showed that strain localisation initiated from the interface of the bar and specimen with the order of tensile, shear and vertical. The initiation of crack from strain localisation is found rate independent. Comparison between 2D- and 3D-DIC in strain measurement of the same experiment showed that the error in the strain obtained by 2D-DIC could be up to 32%. In the penetration test, two different fracture modes were visualised in different types of rock. More investigation is in progress.