Full-field imaging of dynamic ruptures using ultrahigh-speed digital image correlation
Quantifying the full-field behavior of shear ruptures poses a significant metrological challenge due to the time- and length-scales involved in the rupture process. Spontaneously propagating shear ruptures with the speeds in excess of 2 km/s require a minimum temporal sampling of the order of 1-2 million frames/s to capture their temporal evolution, as well as an adequate spatial sampling to resolve their features. At the same time, the noise level needs to be maintained at a minimum in order to analyze the images with pattern-matching algorithms. These specifications make the high-speed camera selection a particularly difficult task. Further, the presence of a displacement discontinuity at the interface poses an additional challenge to the digital image correlation (DIC) analysis, since most DIC approaches are based on continuity assumptions.
Recently, we have been able to address these issues and to image and quantify the full-field experimental behavior of dynamic shear ruptures at a level of detail that, until now, was only possible to achieve with numerical simulations (Rubino, Rosakis, Lapusta, Experimental Mechanics, 2019).
Laboratory earthquake setup. Dynamic ruptures, used to mimic earthquakes in the lab, are produced along the frictional interface of two polymer plates and are initiated by the small burst of a nickel-chromium wire placed across the interface. Once nucleated, dynamic ruptures propagate spontaneously under the pre-applied static loading. The experimental setup features an ultrahigh-speed camera (Shimadzu HPV-X), capable of recording up to 10 million frames per second, a high-speed white light source (Cordin 605), capable of providing adequate illumination during the small exposure times, and a high-voltage capacitor (Cordin 640) to trigger the ruptures. The high-speed digital images are analyzed with pattern-matching algorithms to produce the sequence of displacement, velocity and strain fields. Credit: Rubino, Rosakis, Lapusta, Nature Communications (2017) and Experimental Mechanics (2019).
An example of the displacement, velocity and stress fields of a supershear rupture is reported below. The figure shows the dynamic shear rupture entering the field of view from the left hand side and propagating at a constant speed of 2.3 km/s.
Full-field quantification of dynamic ruptures. Experimentally determined snapshots of (a) interface-parallel displacement, (b) interface-parallel velocity, and (c) shear stress associated to a supershear rupture. Displacement time-histories are produced by processing the sequence of ultrahigh-speed images with digital image correlation. Velocity fields are computed as the displacements time derivatives. The strain fields (not shown here) are obtained by spatial derivatives of the displacement fields. The stress components are computed using linear elastic plane-stress constitutive equations with the dynamic Young's modulus of Homalite to account for its strain-rate dependent behavior. Credit: Rubino, Rosakis, Lapusta, Experimental Mechanics (2019).
Using the new ultrahigh-speed digital image correlation technique we can track the time evolution of a broad range of field quantities. The movie below shows the interface-parallel velocity of a superstar rupture, obtained by analyzing digital images acquired at 2 million frames/sec.
Interface-parallel velocity of a supershear rupture
In our laboratory, dynamic shear ruptures are used to mimic earthquakes, occurring as frictional ruptures propagating along pre-existing interfaces in the Earth's crust. Dynamic ruptures are produced along the inclined frictional interface of two quadrilateral plates of a polymer (usually either Homalite-100 or PMMA), pre-stressed in compression and shear.
Previous versions of this setup, developed by the group of Professor Rosakis [1,2], have been used to address important issues in earthquake dynamics, including the sub-Rayleigh to supershear transition, the bimaterial effects on rupture directionality and speed, the change of rupture mode from pulse-like to crack-like with decreasing fault pre-stress, and rupture interaction with the free surface [1-8].
However, earlier studies could not quantify the temporal evolution of the full-field displacements, velocities, strains and stresses, as they were based on temporally sparse photoelastic measurements, providing the maximum shear stress, or on temporally accurate, but spatially sparse, velocity measurements obtained with laser velocimeters (available at only 2-3 locations). Our first progress towards spatially continuous mapping was to quantify the full-field behavior of arrested ruptures using low-frame cameras .
The new measurements, based on ultrahigh-speed digital image correlation, constitute a significant advancement compared to those obtained with previous diagnostics , as they allow to quantify a broad range of field quantities and they have already allowed us to discover new phenomena, undetectable with previous techniques. For example, we have recently been able to visualize the formation of pressure shock fronts (in addition to the shear ones) associated to the propagation of supershear ruptures in viscoelastic materials . Another important advancement in the study of dynamic ruptures has been tracking the evolution of dynamic friction of spontaneously propagating dynamic ruptures .
Validation of the digital image correlation measurements with laser velocimeters. (a) Schematics of the configuration employed. (b) Comparison of the interface-parallel time-histories obtained with the velocimeters (colored curves) and DIC (black curves) at the same locations. The two measurements are in excellent agreement. However, while it is only possible to employ 2-3 velocimeters (which are quite expensive) in each experiment, the DIC measurements provide a near-continuous mapping. Credit: Rubino, Rosakis, Lapusta, Nature Communications (2017).
From photoelasticity to ultrahigh-speed digital image correlation. Maximum shear stress for a supershear rupture obtained with (a) photoelasticity and (b) digital image correlation. (a) is modified from Xia, Kanamori, Rice, Science, 2005. The new approach allows us to make the leap form qualitative observations to fully quantitative measurements: photoelasticity is sensitive to the maximum shear stress and allows observing qualitative rupture features; digital image correlation enables quantification of individual components of displacements, strains and stresses and better characterization of the full-field rupture behavior. Credit: Rubino, Rosakis, Lapusta, Experimental Mechanics (2019).
The temporal evolution of the maximum shear stress of a supershear rupture obtained with the ultrahigh-speed digital image correlation method shows the well developed Mach cones. The movie below was captured with a temporal sampling rate of 2 million frames/sec.
Maximum shear stress of a supershear rupture
- Xia K, Rosakis AJ, Kanamori H (2004) Laboratory earthquakes: the sub-Rayleigh-to-supershear rupture transition. Science 303(5665):1859–1861.
- Rosakis AJ, Xia K, Lykotrafitis G, Kanamori H (2007) Dynamic shear rupture in frictional interfaces-speeds,directionality, and modes. In: Treatise on Geophysics, vol 4. Elsevier, pp 153-192 .
- Xia K, Rosakis AJ, Kanamori H, Rice JR (2005) Laboratory earth- quakes along inhomogeneous faults: directionality and supershear. Science 308(5722):681–684.
- Lu X, Lapusta N, Rosakis AJ (2007) Pulse-like and crack-like rup- tures in experiments mimicking crustal earthquakes. Proc Natl Acad Sci USA 104(48):18931–18936.
- Lu X, Rosakis AJ, Lapusta N (2010) Rupture modes in laboratory earthquakes: Effect of fault prestress and nucleation conditions.J Geophys Res Solid Earth 115(B12).
- Gabuchian V, Rosakis AJ, Lapusta N, Oglesby DD (2014) Experimental investigation of strong ground motion due to thrust fault earthquakes. J Geophys Res Solid Earth 119(2):1316–1336.
- Mello M, Bhat HS, Rosakis AJ (2016) Spatiotemporal properties of Sub-Rayleigh and supershear rupture velocity fields: Theory and experiments. J Mech Phys Solids 93:153–181.
- Gabuchian V, Rosakis AJ, Bhat HS, Madariaga R, Kanamori H (2017) Experimental evidence that thrust earthquake ruptures might open faults. Nature 545(7654):336.
- Rubino V, Lapusta N, Rosakis AJ, Leprince S, Avouac JP (2015) Static Laboratory Earthquake Measurements with the Digital Image Correlation Method. Exp Mech 55(1):77–94.
- Rubino V, Rosakis A, Lapusta N (2019) Full-field ultrahigh-speed quantification of dynamic shear ruptures using digital image correlation. Exp Mech 8:15991.
- Gori M, Rubino V, Rosakis A, Lapusta N (2018) Pressure shock fronts formed by ultra-fast shear cracks in viscoelastic materials. Nat Commun 9(1):4754.
- Rubino V, Rosakis A, Lapusta N (2017) Understanding dynamic friction through spontaneously evolving laboratory earthquakes. Nat Commun 8:15991.