Three dimensional full-ﬁeld velocity measurements in shock compression experiments using stereo digital image correlation Suraj Ravindran1aVatsa Gandhi2aAkshay Joshi2and Guruswami Ravichandran2 3

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Three dimensional full-ﬁeld velocity measurements in shock compression

experiments using stereo digital image correlation

Suraj Ravindran,1, a) Vatsa Gandhi,2, a) Akshay Joshi,2and Guruswami Ravichandran2, 3

1)Aerosapce Engineering and Mechanics, University of Minnesota, Minneapolis, Minnesota 55455,

USA

2)Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California 91125,

USA

3)Jio Institute, Ulwe, Navi Mumbai, Maharashtra 410206, India

(*Author to whom correspondence should be addressed: sravi@umn.edu)

(Dated: 25 October 2022)

Shock compression plate impact experiments conventionally rely on point-wise velocimetry measurements based on

laser-based interferometric techniques. This study presents an experimental methodology to measure the free surface

full-ﬁeld particle velocity in shock compression experiments using high-speed imaging and three-dimensional (3D)

digital image correlation (DIC). The experimental setup has a temporal resolution of 100 ns with a spatial resolution

varying from 90 to 200 µm/pixel. Experiments were conducted under three different plate impact conﬁgurations to

measure spatially resolved free surface velocity and validate the experimental technique. First, a normal impact ex-

periment was conducted on polycarbonate to measure the macroscopic full-ﬁeld normal free surface velocity. Second,

an isentropic compression experiment on Y-cut quartz-tungsten carbide assembly is performed to measure the particle

velocity for experiments involving ramp compression waves. To explore the capability of the technique in multi-axial

loading conditions, a pressure shear plate impact experiment was conducted to measure both the normal and transverse

free surface velocities under combined normal and shear loading. The velocities measured in the experiments using

digital image correlation are validated against previous data obtained from laser interferometry. Numerical simulations

were also performed using established material models to compare and validate the experimental velocity proﬁles for

these different impact conﬁgurations. The novel ability of the employed experimental setup to measure full-ﬁeld free

surface velocities with high spatial resolutions in shock compression experiments is demonstrated for the ﬁrst time in

this work.

Keywords: Shock Compression, Full-ﬁeld measurements, High Speed imaging, Stereo Digital image correlation

I. INTRODUCTION

Plate impact experiments, generating shock compression,

are employed to understand the high pressure and high strain-

rate behavior of broad classes of materials, including met-

als, glasses, ceramics, and composites1. In these exper-

iments, the free surface velocities are typically measured,

which provide insights into various phenomena, such as equa-

tion of state1, inelastic material behavior2, polymorphic phase

transformations3, and spall failure4. Laser interferometric

techniques are the commonly used method for determining

free-surface velocities due to their high sensitivity, accuracy,

time resolution, and non-intrusiveness towards propagating

shock waves. In these techniques, Doppler-shifted light re-

ﬂected from the target free surface is superposed with either

a delayed version of itself (velocity interferometer) or a refer-

ence light beam (displacement interferometer), and the phase

difference of the interfered beams is used to obtain the nor-

mal and transverse free surface velocities. The most well-

known interferometry techniques that are employed for mea-

suring point-wise normal particle velocity are the Velocity

Interferometer System for Any Reﬂector (VISAR)5, and the

Photon Doppler Velocimetry (PDV)6,7. The point-wise trans-

a)These authors contributed equally to this work.

verse particle velocities are measured using a transverse dis-

placement interferometer (TDI)8or its corresponding PDV,

a heterodyne transverse velocimetry (HTV)9interferometer.

Despite its high temporal resolution (∼ns), common laser in-

terferometry techniques provide only point-wise velocimetry

and are unable to capture the spatial heterogeneity in the shock

wave. This limits the utility of such techniques in the context

of shock compression experiments on heterogeneous materi-

als such as composites, granular, and architected lattice ma-

terials, where characterization of the material requires mea-

surement of spatio-temporally resolved free surface velocities.

This issue can be partly addressed by employing a variant of

VISAR known as Optically Recording Velocity Interferome-

ter System (ORVIS)10, where velocity measurements are con-

ducted along a line to provide improved spatial resolution11.

ORVIS requires an elaborate arrangement of optics and high-

speed streak cameras in order to provide the desired horizontal

scan of the laser needed for the measurement12. Additionally,

this technique only offers insight into the velocity variation

along a line on the free surface and not on the entire free

surface. Such full-ﬁeld free surface velocity measurements

can be achieved using the Digital Image Correlation (DIC)

technique13,14.

Digital image correlation is well established as a full-ﬁeld

measurement technique for both in-plane and out-of-plane

displacement measurements14. This technique involves taking

a series of images of a deforming randomly speckled sample

arXiv:2210.12568v1 [physics.app-ph] 22 Oct 2022

and is cross-correlated to extract displacement ﬁelds across

the entire sample surface13,14. Therefore, a single experi-

ment yields thousands of displacement measurements over

the entire ﬁeld of view, with sub-pixel accuracy, which can

be further used to obtain the velocity, acceleration, and strain

ﬁelds15,16. While DIC is well-suited for quasi-static experi-

ments, advances in high-speed imaging capabilities have en-

abled DIC in the dynamic regime. For example, high-speed

imaging in conjunction with two-dimensional DIC was uti-

lized to study the dynamic micro- to macro-scale deformation

behavior of materials17–21. Recently, Rubino et al.16 com-

bined high-speed photography, and 2D DIC to characterize

deformation ﬁelds around dynamically propagating shear rup-

tures in laboratory earthquake experiments. In addition to in-

plane deformation ﬁelds, out-of-plane deformation can be re-

solved using two cameras and high-speed three-dimensional

(stereo) digital image correlation, which is used in blast, bal-

listic and low velocity impact applications. For instance, Ti-

wari et al.22 conducted 3D DIC to measure the deformation

of aluminum plates subjected to blast loading, while work by

Jannotti et al.23 investigated anisotropic ballistic response of

rolled AZ31B magnesium plates. Additionally, Gupta et al.24

conducted 3D DIC to understand the physical processes as-

sociated with the implosion of cylindrical tubes submerged

underwater. Pankow et al.25 implemented stereo DIC with a

single camera by using a series of mirrors to split the image

into two different views and examined the out-of-plane ﬂexu-

ral response of a dynamically loaded thin aluminum plate. In

these studies, the authors use the extracted full-ﬁeld displace-

ment and strain ﬁeld to analyze the deformation mechanisms

at time scales ranging from 25 −150 µs. Overall, previous

impact studies using full-ﬁeld measurements have focused on

longer time scale behavior of materials compared to the shock

compression behavior where the total event duration is typi-

cally smaller than 5 µs.

The present study extends the applications of high speed

3D DIC to plate impact experiments for the ﬁrst time to under-

stand material behavior in the shock regime (strain rates >106

s−1). In Section II, details of the experimental setup, accuracy

and resolution of measured data, and the methodology of post-

processing the acquired data are discussed. In Section III, the

feasibility of the developed experimental setup for measuring

full-ﬁeld free surface velocity measurements and is ﬁrst val-

idated against point-wise PDV measurements in normal and

pressure-shear plate impact experiments. In Section IV, con-

cluding remarks are presented and potential future directions

are discussed.

II. MATERIALS AND METHODS

A. Experimental Setup

In this study, plate impact experiments were conducted us-

ing a powder gun facility at Caltech. Four materials, polycar-

bonate (PC), tungsten carbide (WC), Y-cut quartz, and D2 tool

steel, were investigated in different experimental conﬁgura-

tions to demonstrate the reliability, advantage, and robustness

of the high-speed stereo (3D) DIC for measuring full-ﬁeld free

surface velocities in plate impact experiments. The schematic

of the experimental setup with high-speed imaging-based full-

ﬁeld diagnostics is shown in Fig. 1a. Also, the images of

the stereo high speed imaging DIC setup and the components

inside the vacuum chamber are shown in Fig. 1b. Samples

were shocked using the 38.7 mm slotted powder gun capa-

ble of launching projectiles at velocities ranging from 0.2-1.5

km/s. Two Hyper Vision HPV-X2 high-speed cameras (Shi-

madzu, Kyoto, Japan) capable of capturing 5 million frames/s

at full resolution (400 ×250 pixel2) and 10 million frames/s

at half resolution (400 ×250 pixel2, where missing pixels are

interpolated) were used to capture the image of the free sur-

face, see Fig. 1a. These cameras were placed at a stereo an-

gle between 15◦−16◦and were calibrated by capturing the

image of the standard laser engraved calibration grids (Corre-

lated Solutions Inc., Columbia, SC), to facilitate stereo DIC

measurement14. A total of 45 image pairs were collected by

tilting and rotating the calibration grid within the ﬁeld of view

of both the cameras. It was ensured that the images were

within the depth of ﬁeld of the imaging system to obtain accu-

rate calibration of the stereo camera system. The image of the

camera arrangement and a typical calibration grid used for cal-

ibration are shown in Fig. 1a. The images of the rear surface

of the sample were observed through a large mirror (50 mm

× 100 mm) arranged at 45◦with respect to the loading direc-

tion. A CAVILUX Smart laser (Cavitar, Tampere, Finland),

which provides high-speed incoherent laser (wavelength, 640

nm) pulses as short as 10 ns, was used to illuminate the sample

during loading. The short duration laser pulses avoid blurring

due to the transients in the high-speed impact experiments.

These laser pulses were synchronized with the exposure of

the camera sensor during the image acquisition. An image of

the complete target assembly, mirrors, and illumination using

laser inside the vacuum chamber is shown in the Fig. 1b. Im-

pact velocities of the experiments were measured using Pho-

tonic Doppler velocimetry6(PDV). The PDV probe was at-

tached to the target holder and the optical return was checked

during the target alignment. In the pressure shear plate impact

experiment, a heterodyne PDV was used to simultaneously

measure normal and transverse velocities9.

The materials used in this study were obtained from various

commercial vendors. Polycarbonate and D2 tool steel mate-

rials were procured from McMaster-Carr (Los Angeles, CA)

while the tungsten carbide was acquired from Basic Carbide

Corporation (Lowber, PA), ARMCO iron from AK Steel In-

ternational (Breda, The Netherlands), and Y-cut quartz from

University Wafer (South Boston, MA). The ﬁnal dimensions

of the ﬂyers and target materials are shown in Table II.

The ﬂyers and targets were lapped parallel to less than 10

µm and ﬂat to within 0.5 µm variation across the surface.

Four encapsulated copper shorting pins (tilt pins) were glued

to the target and lapped ﬂush to the target surface; see in-

set in Fig. 1b. These pins were connected to a digital cir-

cuit, which was connected to a high-speed digital oscilloscope

sampling at 20 GigaSamples/s (MSO9404A, Keysight Tech-

nologies, Inc., Santa Rosa, CA) to determine the contact time

of the ﬂyer with the target. The contact time of each pin with

Projectile

First surface mirror

Target

Vacuum chamber

Mirror

HPVX-2

Lens

Transparent

window

Vaccum chamber

332 mm

High speed

cameras

Laser

control box

Calibration grid

PDV probe for impact

Flyer

velocity measurment

Aluminum ring

Cavilux laser (640 nm)

with shorting pins

450

Mirror

Laser

Target holder

Target front

Tilt pins

PDV optical cable

Target rear

Inside vaccum chamber

Laser

Powder gun

Projectile

0.2 - 1.5 km/s X

Optically clear

window

9 mm

Field of view and speckles

Polycarbonate D2 Tool Steel PSPI

36.8 mm

23.0 mm

96.0 mm

60.0 mm

Stereo DIC camera arrangement

FIG. 1: a) Schematic of the experimental setup with powder gun, camera arrangements for 3D digital image correlation, b) image of the components inside the

vacuum chamber and the high-speed camera arrangement for stereo DIC set up for imaging through the transparent window, c) representative speckle patterns

on the free surface of the sample.

the ﬂyer was used to calculate the impact tilt in the exper-

iment. The ﬂyer and target assemblies were aligned in the

experiment using an auto-collimator and an optically ﬂat mir-

ror assembly prior to the shot26. This alignment ensures the

impact tilt between the ﬂyer and target below 2 milli-radian in

order to generate a plane wave in the sample. A high con-

trast, random and isotropic speckle pattern was applied on

the free surface of the sample to facilitate DIC measurement.

The speckles in all the experiments were about 4 −6 pixels in

size to avoid anti-aliasing due to low sampling of the pixels14.

They were created using a ﬁne tip pen (Pigma Micron, Sakura,

Osaka, Japan) for the experiment on polycarbonate. In other

experiments, black speckles were applied using an airbrush to

obtain higher spatial resolution resulting in smaller speckles

(84-92 µm/pixel). The ﬁeld of view and the images of the

speckle patterns used in the experiments are shown in Fig. 1c.

B. Postprocessing of images

The image sequence acquired using the HPV-X2 high-

speed cameras was analyzed to obtain the displacement ﬁeld

using a widely-used commercial software Vic-3D (Correlated

Solutions Inc., Columbia, SC). To obtain the stereo camera

arrangement calibration parameters, the bundle adjustment al-

gorithm implemented in Vic-3D was used14. This algorithm

yields the extrinsic and intrinsic parameters required for cal-

culating all the displacement components from the speckled

images acquired during impact. Two important parameters

considered during post-processing of the images were the sub-

set size and step size. For a selected subset size, the algorithm

calculates all the displacement components at the center of the

subset, while the step size determines the distance between the

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Threedimensionalfull-eldvelocitymeasurementsinshockcompressionexperimentsusingstereodigitalimagecorrelationSurajRavindran,1,a)VatsaGandhi,2,a)AkshayJoshi,2andGuruswamiRavichandran2,31)AerosapceEngineeringandMechanics,UniversityofMinnesota,Minneapolis,Minnesota55455,USA2)DivisionofEngineeringandAppl...

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Three dimensional full-ﬁeld velocity measurements in shock compression experiments using stereo digital image correlation Suraj Ravindran1aVatsa Gandhi2aAkshay Joshi2and Guruswami Ravichandran2 3

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