Advancements in Optical Methods & Digital Image Correlation in Experimental Mechanics, Volume 3

Shadow moiré technique has been a widely utilized method in industry to determine surface flatness, out-of-plane displacement, and 3D metrology. In this paper, we present a digitized speckle method analogous to the shadow moiré method. A randomly generated speckle pattern is first projected onto a screen and digitally recorded. The same pattern is projected onto a specimen and digitally recorded as well. The two images are then converted into TIFF files to be superimposed and processed using a Fourier transform based algorithm to generate fringes that are similar to shadow moiré fringes. Additionally, a Digital Image Correlation (DIC) software was used to generate fringes that are similar to shadow moiré fringes. The technique is simple and straightforward. We apply the technique to a variety of specimens to demonstrate its applicability.

StereoDIC is employed to quantify wrinkling on 6.35 mm wide and 0.16 mm thick carbon-epoxy tows during advanced fiber placement along straight and circular paths on a planar composite surface. Measurements obtained just after placement provide quantitative deformation fields, including the presence of out-of-plane wrinkles that occur during the placement process. Results show that wrinkles occur at locations where the substrate has defects. Results also show that wrinkles occur at other locations only when the radius of curvature is less than 2540 mm.

This paper is devoted to the experimental verification of a very fundamental concept in the mechanics of materials, the representative volume element (RVE). This concept is a bridge between the theoretical concept of the continuum and the actual discontinuous structure of matter. We begin with reviewing the pertinent concepts of the kinematics of the continuum, the mathematical functions that relate displacement vectorial fields, the recording of these fields by a sensor as scalar fields of gray levels.

The derivative field tensors corresponding to the Eulerian description are then connected to the deformation of the continuum. The differential geometry that provides the deformation of an element of area is introduced. From this differential geometry of an element of area, the Euler-Almansi tensor is extracted. Properties of the Euler-Almansi tensor are derived. The next step is the analysis of the relationship between kinematic and dynamic variables: that is, the connection between strains and stresses in the Eulerian description between the Euler-Almansi tensor with the Cauchy stress tensor.

In the experimental part of the paper, some relationships between components of the Euler-Almansi tensor are verified. An example of an experimental verification of the concept of RVE is given. Finally, the verification for the fact that the Euler-Almansi and Cauchy stress sensor tensors are conjugate tensors in the Hill-Mandel sense is presented.

In this work, the plastic deformation and ductile failure of solid Al 6061-T6 and 304L tube specimens under torsion loading was investigated using a new developed 360° DIC system. The tube specimens of both ductile metals can exhibit very large rotation under torsion loading, which makes it very difficult to experimentally measure the deformation at failure. In our earlier work, 3D DIC system composed of one pair of cameras was applied to investigate the local deformation. The DIC system with one pair of cameras was only able to track the area of interest within a rotation angle of 90° or smaller. However, the specimens failed at rotation angles larger than 240°. The DIC system with one pair of cameras was difficult to obtain the critical strain data at large rotation. In this work, a new 360° DIC system which consists of four pairs of cameras was designed and incorporated into the experiment so that the whole surface can be imaged during the rotation. The new DIC system was able to track the area of interest and measure the deformation till the specimen failure. Shear strain at failure location can be measured and related to the global loading condition.

In this work, we applied the in-situ X-ray Computed Tomography (XCT) mechanical testing method that coupled the in-situ mechanical loading with the XCT imaging to study the damage mechanism of GMBs inside the Sylgard as the material was subject to mechanical loading. We studied Sylgard specimens with different volume fraction of GMBs to understand how they behave differently under compression loading and how the volume fraction of GMBs affect the Sylgard failure.

Both high resolution (1.5 μm/voxel) and low resolution (10 μm/voxel) XCT imaging were performed at different loading levels to visualize the GMB collapse during the compression of Sylgard with different volume fraction of GMBs. Feret shape of GMBs were calculated from the high resolution XCT images to determine whether the GMBs were intact or fractured, as well as the relationship between the size distribution of GMBs and their Feret shapes. Through these quantitative analysis of the high resolution XCT data, we were able to understand how the size and volume fraction of GMBs affect their failure behavior. The Digital volume correlation (DVC) technique was applied to the low resolution XCT images to calculate the local deformation of Sylgard specimen, which enabled us to understand the different failure propagation and failure mechanisms of Sylgard with different volume fraction of GMBs.

Strain measurement is vital in material and mechanical testing. The conventional contact based approaches as strain gauges, extensometers, acoustic emission, seismic waves etc. have limitations like sensitivity to contact areas, susceptible to external noise, vulnerable to breakage, influenced by surrounding environment etc. Recently, development of noncontact based methods has eliminated these challenges. Digital Image Correlation is an optical, noncontact based technique which is being widely used in measuring full-field displacement. The technique is based on acquisition of digital images taken before and during loading and developing a correlation between them with subpixel accuracy. In this paper, the behavior of equivalent coal specimens at varying depth from 92 to 126 m have been evaluated for static loading condition using non-contact based approach i.e. Reliability-guided Digital Image Correlation technique (RG-DIC). There exists a good agreement between the contact (strain gauge) and noncontact based approaches (DIC) for static loading condition. So, Digital Image Correlation (DIC) can also be a reliable strain measuring approach for investigating for earth materials.

This paper discusses fracture from the viewpoint of wave dynamics derived from a recent field theory. Based on a fundamental physical principle, the field theory describes deformation and fracture on the same basis. It characterizes deformation as a wave phenomenon where the spatiotemporal oscillatory behavior of the displacement field initiated by an external load is transferred through the material as a sinusoidal wave carrying the stress energy. Fracture is characterized as the final stage of deformation where the wave becomes solitary representing strain concentration and stops carrying the stress energy. Fracture always occurs along the strain concentration. The transitional behavior of the wave dynamics can be visualized as a change in the optical interferometric fringe pattern generated by the optical technique known as the Electronic Speckle-Pattern interferometry. Finite element analysis has been conducted to explain the experimentally observed behaviors and explore the mechanism of transition from to fracture.

An investigation program has been launched with the objective of presenting combinations of analytical, experimental and numerical methods to predict and monitor fatigue initiation and fatigue damage progression in equipment such as pressure vessels, tanks, piping and pipelines with dents or shape anomalies. The present paper reports initial results from tests where these techniques were applied to a pipeline specimen containing a plain longitudinal dented subjected to hydrostatic cyclic loading. Some of the material’s fatigue properties assessment used validated rapid approaches based on infrared thermography. The monitoring of fatigue initiation and propagation in the actual specimen used nondestructive infrared inspection techniques. Thermoelasticity stress analysis (TSA) and three-dimensional digital image correlation (3D-DIC) were used to determine fatigue hot spots locations as well as strain concentrations. Full field TSA and fiber optic Bragg strain gages (FBSG) were used to determine the overall stress field (TSA) as well hot spot strain evolution (FBSG) along the loading cycles. Strain fields determined from the experimental measurements and from finite element analysis (FEA) were combined with the fatigue Coffin-Manson model to predict fatigue life (Nc). The tested 3 m long tubular specimen was fabricated with API 5L Gr. B 12.75^″ OD with ¼^″ thickness pipes. The excellent agreement among test and predicted results achieved up to now are commented in the paper.

Currently, kinematic field measurements for studying the mechanical behavior of materials and structures use common optical methods, such as mark tracking techniques, grid methods and correlation techniques (Sutton et al., 2009, Image correlation for shape, motion and deformation measurements, Springer, Berlin, https://​doi.​org/​10.​1007/​978-0-387-78747-3). These techniques are used over a region of interest ranging from micro to millimeter scale. However, when studies need to be conducted on even smaller scales such as sub-micrometric scale, the use of more complex means of observation is required. In this case the work can be achieved using the scanning electron microscope SEM, or some specific marking techniques as the Dual-Beam FIB [ANR-11-LABX-0017-01].

For this application, the Digital Image Correlation DIC is chosen to investigate the material behavior. In the present approach, an artificial speckle having the depth of the engraving around (a few hundred nanometers) 200 nm was used. Statistical evaluations such as grayscale histograms, autocorrelations, defocusing effects, and rigid body displacement effects are used to evaluate the error measurement in a field of 100 μm width. Various tests were also performed to ensure the repeatability and reproducibility of the method. The order of the errors is much greater than those obtained in classical optical conditions, but is less than 0.05 pixel.

Based on original analytical concepts by Khalil et al. (International Journal of Fracture 31:37–51, 1986) and subsequently augmented by Ju and Rowlands (Journal of Composite Materials 37:2011–2025, 2003) to study inclined cracks thermoelastically in orthotropic plates, this paper determines the stress intensity factor (SIF) in a double-edge cracked finite orthotropic tensile composite (Fig. 10.1) from a single digital image correlation (DIC) recorded displacement field. The traction-free condition of the crack-face was accounted for using conformal mapping.

In this study, the possible application of plenoptic camera for DIC displacement is explored. A special function, focal-distance change function, of plenoptic camera is first investigated by using 2D DIC method to know how the function would change the images in size and to know the possible pseudo in-plane displacement might introduced. Then the focal-distance change function is applied to generate two images at different focal-length with respect to an image-pair taken before and after object moved, those four images can create six independent in-plane displacement fields by DIC. In this study, four displacement fields are selected out of the six independent ones and used to calculate displacement filed with smaller standard deviation. By properly linearly combining the selected displacement fields, both standard deviation of u- and v-displacement are successfully reduced to 1/3 with respect to the original values and the u- and v-displacement field become flat as compared to the original one but the mean displacement is 10% larger than the nominal displacement determined by a precision linear stage.

Mechanoluminescent powders are new materials that can be considered as intelligent, active or responsive because they have the property of emitting light when they are mechanically deformed. They open perspectives for the measurement of stresses in mechanical parts. The present study focused on the stress concentrations in granular materials. Granular systems are defined as a collection of particles whose macroscopic behavior depends on the contact forces at the local scale. Some techniques are available for measurements in the bulk, such as X-ray tomography combined with volumetric digital image correlation. An extensive literature also deals with two-dimensional approaches: optical photography combined with digital image correlation, photoelasticimetry, infrared thermography. Mechanoluminescent materials offer new possibilities for revealing contact force networks in granular materials. Epoxy resin and mechanoluminescent powder were mixed to prepare dumbbell-like specimens and cylinders. Dumbbell-like specimens were used for preliminary uniaxial tensile tests. Cylinders were used to prepare granular systems for confined compression tests. Homogeneous light emission was obtained in the former case, while light concentrations were evidenced in the latter case.

This paper illustrate the use of deflectometry in the infrared spectrum to measure surface slopes on a plate deformed in bending.

For accurate measurement, phase-shifting technique is usually adopted to the shadow moiré measurement system. Accurately introducing the amount of phase shift is required in order to extract the phase properly. However, the specimen or system may be moved during the time of image capture, and not suitable for real-time measurement. In order to overcome this drawback and make an in-line measurement, a shadow moiré system consisted of two light source of different colors and a color CCD camera is proposed. The phase shift is introduced by using two light sources illuminate the grating from different position simultaneously. The two moiré fringe patterns are captured by the color CCD camera, and are processed by a fringe analysis scheme using spiral phase transform (SPT) and optical flow techniques. The proposed fringe analysis scheme was applied to a simulated surface and a real specimen. The test results are reported and the validity of the scheme is investigated.

The use of intra-operative images with a magnetic resonance imager (MRI) can enable more precise surgical procedures when treating deep brain tumors. The constrained space inside the imager creates the need for robotic assistive devices. However, the strong static magnetic fields, fast changing magnetic gradients and sensitivity to electrical noise create challenges that can be partly addressed by a novel class of MRI compatible resonant piezoelectric motors to actuate the robots. These motors consist of a stator that is mechanically excited by a bonded piezoelectric ring and a frictionally coupled rotor. Steady-state excitation at certain frequencies leads to specific mode shapes with surface waves having both in- and out-of-plane displacement components. The interaction between the surface waves of the stator with the rotor results in the rotor spinning. Optimal operation of these motors depends on the stator’s mode shapes generating waves that result in maximizing torquing of the rotor while reducing tangential force components. We present a finite element multi-physics model of the stator using COMSOL in frequency and time-domain. We combine the FEM with stroboscopic and time averaged, high-speed digital holography to create a validated model useful for optimizing motor design and performance. The methodology is used in the study of 30 mm diameter 40–60 kHz driven motor that have been demonstrated in an in-bore MRI compatible surgical robot.

Digital volume correlation consists in registering series of 3D images of experiments to yield 4D displacement fields. These 4D analyses have been conducted for the last two decades. Some achievements and current challenges are reviewed herein.

A feature quantity type whole-space tabulation method (F-WSTM) was proposed by authors to make 3D shape measurement devices robust for vibrating. This method makes possible a camera calibration-free 3D shape measurement. Three phase information obtained with three projectors are used to obtain 3D coordinates without any camera parameters. That is, change of lens position does not cause the systematic error. In this method, focusing, zooming, pan and tilt are available anytime. In this paper, a prototype of a 3D shape measurement device using the F-WSTM was developed. The evaluation of the device was performed with an experiment of a shape measurement of a step object.

We are developing a High-speed Digital Holographic (HDH) system capable of performing near-simultaneous measurements of nanometer-scale displacement and micrometer-scale shape within a fraction of a second during uncontrolled environmental and physiological disturbances, suitable for industrial and life science applications. However, for some applications where time-dependent variations introduce geometrical discontinuities, optical phase measurements become a challenge. In this paper, we present methodologies that overcome these geometrical discontinuities while enabling different levels of measuring resolution. The HDH shape measurements are based on Multiple Wavelength Holographic Interferometry (MWHI). In MWHI the wavelength of the laser is rapidly varied between a series of exposures resulting in micro to millimeter scale synthetic wavelengths. In the holographic recording step, during a single laser tuning ramp, tens of rapid optical phase samplings are acquired, each describing the phase of the object with slightly varied illumination wavelengths (i.e., <0.1 nm). In the holographic reconstruction step, a database consisting of hundreds of phase maps with different synthetic wavelengths is constructed by recovering the shape from any two non-repeated combinations of the phase samplings. A custom temporal phase unwrapping method is developed that resolves and unwraps the depth uncertainties of high-resolution phase maps using the collection of low-fringe density wrapped phase maps from the database that are immune to surface discontinuities. Measurements on National Institute of Standard and Technology (NIST) traceable gauges and discontinuous samples demonstrate the performance of the method. A use of the method in a specific biomedical application is presented.

A recently developed Projection-based Digital Image Correlation (P-DVC) method is here extended to 4D (space and time) displacement field measurement and mechanical identification based on a single radiograph per loading step instead of volumes as in standard DVC methods. Two levels of data reductions are exploited, namely, reduction of the data acquisition (and time) by a factor of 1000 and reduction of the solution space by exploiting model reduction techniques. The analysis of a complete tensile elastoplastic test composed of 127 loading steps performed in 6 min is presented. The 4D displacement field as well as the elastoplastic constitutive law are identified.