Grid Method for Microscale Discontinuous Deformation Measurement

The objective of this paper is to explore both grid method and Digital Image Correlation (DIC) technique for microscale and discontinuous displacement measurements, such as those associated with crack tips. First, the principle of the grid method is revisited. The grid method and DIC technique are then applied to computer generated images to calculate the displacement field around crack tips. Finally, the grid method is applied to actual experimental images of fracture tests which are conducted inside a Scanning Electron Microscope (SEM) chamber. A new technique is developed to generate microscale pattern that is suitable for both grid method and DIC technique. The displacement fields calculated from grid method are compared with those from DIC technique to identify the strengths and weaknesses of each technique for the microscale and discontinuous displacement measurements. It has been determined that grid method can obtain data closer to the discontinuity than DIC; however, DIC produces smoother displacement fields at the far field. Using this new pattern generation technique, both grid method and DIC technique can be applied to the fracture test at the microscale to complement with each other to achieve the best experiment results.     

Overview of High-temperature Deformation Measurement Using Digital Image Correlation

Background

Developments in digital image correlation (DIC) in the last decade have made it a practical and effective optical technique for displacement and strain measurement at high temperatures.

Objective

This overview aims to review the research progress, summarize the experience and provide valuable references for the high-temperature deformation measurement using DIC.

Methods

We comprehensively summarize challenges and recent advances in high-temperature DIC techniques.

Results

Fundamental principles of high-temperature DIC and various approaches to generate thermal environment or apply thermal loading are briefly introduced first. Then, the three primary challenges presented in performing high-temperature DIC measurements, i.e., 1). image saturation caused by intensified thermal radiation of heated sample and surrounding heating elements, 2) image contrast reduction due to surface oxidation of the heated sample and speckle pattern debonding, and 3) image distortion due to heat haze between the sample and the heating source, and corresponding countermeasures (i.e., the suppression of thermal radiation, fabrication of high-temperature speckle pattern and mitigation of heat haze) are discussed in detail. Next, typical applications of high-temperature DIC at various spatial scales are briefly described. Finally, remaining unsolved problems and future goals in high-temperature deformation measurements using DIC are also provided. 

Conclusions

We expect this review can guide to build a suitable DIC system for kinematic field measurements at high temperatures and solve the challenging problems that may be encountered during real tests.

     

An Error Criterion in Digital Image Correlation for Unknown Deformation Fields and Its Application of Parameters Selection

Digital image correlation (DIC) is a widely used optical metrology for surface deformation measurement. In DIC, the square root of the mean square error (RMS error) and standard deviation error (SD error) are used as quantitative criteria in order to evaluate the accuracy and robustness of a DIC method\algorithm. However, RMS and SD error criteria are computed from prescribed and measured displacements, which indicates that the prescribed displacement fields must be precisely generated. Therefore, it is difficult to quantitatively evaluate the accuracy and robustness of an algorithm\method in practical DIC measurements because imposed displacements are unknown (that’s why DIC measurements are needed). Moreover, the accuracy of DIC measurements highly relies on parameters selection, especially the selections of subset size and shape function. In practice, the subset size and shape function are usually selected according to experience because there are numerous factors (e.g. the quality of speckle image, local displacement field) and uncertainties (e.g. noise level, out-of-plane motion, illumination lighting fluctuation during image capturing) that affect the parameters selection, which makes it difficult to select optimal parameters based on previous works which mainly focused on theoretical deduction in ideal condition. In this paper, an error criterion for evaluating the accuracy of practical DIC measurements with unknown displacements is proposed. Numerical experiments are used to validate the effectiveness and feasibility of the proposed criterion for accuracy evaluation. It is concluded that the square root of the sum of squared forward and backward displacements difference (SFBD) error has a significant positive linear correlation with the widely used SD error in most practical DIC measurements where the mismatch between the frequently-used first- and second-order shape functions and the actual field is usually small. Also, an application of the proposed criterion is presented by real experiments for subset size and shape function selections, which verifies that the proposed error criterion can be effectively used for DIC parameters selection.     

Deformation measurements by digital image correlation: Implementation of a second-order displacement gradient

This paper outlines the procedure for refining the digital image correlation (DIC) method by implementing a second-order approximation of the displacement gradients. The second-order approximation allows the DIC method to directly measure both the first- and second-order displacement gradients resulting from nonlinear deformation. Thirteen unknown parameters, consisting of the components of displacement, the first- and second-order displacement gradients and the gray-scale value offset, are determined through optimization of a correlation coefficient. The previous DIC method assumes that the local deformation in a subset of pixels is represented by a first-order Taylor series approximation for the displacement gradient terms, so actual deformations consisting of higher order displacement gradients tend to distort the infinitesimal strain measurements. By refining the method to measure both the first- and second-order displacement gradients, more accurate strain measurements can be achieved in large-deformation situations where second-order deformations are also present. In most cases, the new refinements allow the DIC method to maintain an accuracy of ±0.0002 for the first-order displacement gradients and to reach ±0.0002 per pixel for the second-order displacement gradients.     

A Dedicated DIC Methodology for Characterizing Plastic Deformation in Single Crystals

This paper focuses on the development of an appropriate Digital Image Correlation (DIC) methodology based on Image Registration and dedicated for characterizing the plastic deformation in single crystals. A pure nickel single crystal specimen is plastically deformed in tension and investigated by DIC technique. Based on the measured kinematic fields, the proposed method enables to identify the slip activity on the crystal surface and to locate precisely the slip band interfaces at microscale which behave as kinematic discontinuities. The computed displacement data are projected on a well-defined physical basis containing slip details, then the strain fields can be derived directly from a set of analytical functions. The possible errors in displacement induced by this projection approach are evaluated. Finally, some results of the evaluated strain fields are presented. It demonstrates that the developed DIC methodology allows quantitative characterization of a heterogeneous deformation process and promotes further relationships to be established between slip activity and strain field evolution in single crystals.     

Adaptive Rotated Gaussian Weighted Digital Image Correlation (RGW-DIC) for Heterogeneous Deformation Measurement

Background

Digital image correlation (DIC) has advanced to become a flexible, reliable and fast optical method for the measurement of non-contact and full-field surface deformation. However, the accuracy of existing methods in measuring heterogeneous deformation fields—especially for the high gradient strain field – can be improved.

Objective

In state-of-art local DIC applications, several methods have been put forward to adapt a subset to unknown deformation. Although improvements in performance using these methods are obtained, results are still ungratified for severely heterogeneous deformation such as the Star 2 and Star 5 images from DIC Challenge 2.0.

Methods

In this paper, a rotated Gaussian weighted zero-mean normalized sum of squared difference (RGW-ZNSSD) criterion function is proposed as the basis for RGW-DIC subset size adaptation. RGW-DIC can automatically determine the optimum weight distribution, hence self-adaptivity in subset size and orientation are achieved simultaneously.

Results

The effectiveness of the proposed RGW-DIC is verified using DIC-challenge 2.0 images and simulated sinusoidal deformation images. Results reveal that the adaptively determined subset weight distribution can significantly improve the accuracy of heterogeneous deformation measurement compared with traditional DIC and DIC with isotropic Gaussian weight functions.

Conclusions

The proposed RGW-DIC can be applied to unknown severely heterogeneous deformation measurement.

     

Quantitative Strain Analysis of the Large Deformation at the Scale of Microstructure: Comparison between Digital Image Correlation and Microgrid Techniques

A comparative study has been carried out to assess the accuracy of the Digital Image Correlation (DIC) technique for the quantification of large strains in the microstructure of an Interstitial Free (IF) steel used in automotive applications. A microgrid technique has been used in this study in order to validate independently the strain measurements obtained with DIC. Microgrids with a pitch of 5 microns were printed on the etched microstructure of the IF steel to measure the local in-plane strain distribution during a tensile test carried out in a Scanning Electron Microscope (SEM). The progressive deformation of the microstructure with microgrids has been recorded throughout the test as a sequence of micrographs and subsequently processed using DIC to quantify the distribution of local strain values. Strain maps obtained with the two techniques have been compared in order to assess the accuracy of the DIC measurements obtained using the natural patterns of the revealed microstructure in the SEM micrographs. The results obtained with the two techniques are qualitatively similar and thus, demonstrate the reliability of DIC applied to microstructures, even after large deformations in excess of 0.7. However, an average error of about 16?% was found in the strain values calculated using DIC.     

Sub-Grain Scale Digital Image Correlation by Electron Microscopy for Polycrystalline Materials during Elastic and Plastic Deformation

Damage during loading of polycrystalline metallic alloys is localized at or below the scale of individual grains. Quantitative assessment of the heterogeneous strain fields at the grain scale is necessary to understand the relationship between microstructure and elastic and plastic deformation. In the present study, digital image correlation (DIC) is used to measure the strains at the sub-grain level in a polycrystalline nickel-base superalloy where plasticity is localized into physical slip bands. Parameters to minimize noise given a set speckle pattern (introduced by chemical etching) when performing DIC in a scanning electron microscope (SEM) were adapted for measurements in both plastic and elastic regimes. A methodology for the optimization of the SEM and DIC parameters necessary for the minimization of the variability in strain measurements at high spatial resolutions is presented. The implications for detecting the early stages of damage development are discussed.     

Measurement of Creep Deformation across Welds in 316H Stainless Steel Using Digital Image Correlation

Spatially resolved measurement of creep deformation across weldments at high temperature cannot be achieved using standard extensometry approaches. In this investigation, a Digital Image Correlation (DIC) based system has been developed for long-term high-temperature creep strain measurement in order to characterise the material deformation behaviour of separate regions of a multi-pass weld. The optical system was sufficiently stable to allow a sequence of photographs to be taken suitable for DIC analysis of creep specimens tested at a temperature of 545 °C for over 2000 h. The images were analysed to produce local creep deformation curves from two cross-weld samples cut from contrasting regions of a multi-pass V-groove weld joining thick-section AISI Type 316H austenitic stainless steel. It is shown that for this weld, the root pass is the weakest region of the structure in creep, most likely due to the large number of thermal cycles it has experienced during the fabrication process. The DIC based measurement method offers improved spatial resolution over conventional methods and greatly reduces the amount of material required for creep characterisation of weldments.     

Full-Field Deformation Measurements in Liquid-like-Solid Granular Microgel Using Digital Image Correlation

This paper presents the experimental characterization of the in-plane deformation field at any depth within a granular support medium (GSM) called Carbomer 940 using digital image correlation (DIC) and particle image velocimetry (PIV). A method was developed to produce a 2D plane of randomly shaped speckles within the GSM for DIC. Four different needle diameters and four different speeds were used as test specimens representative of those utilized for 3D printing of soft matter in the GSM. The results can be used to determine dimensional tolerances and assessing interactions between multiple injection needles and acceptable spacing. The displacements in the direction of needle motion (u) and transverse (v) were obtained. Subsequently, the magnitudes were determined as a function of distance from the needle path and time history. Results show that near the needle there is a region of yielded/fluidized material and away from the needle path the material acts like a viscoelastic solid. Permanent deformation decreases with increased distance from the path and recovery is enhanced by reversing back through the path.     

Diffraction Assisted Image Correlation: A Novel Method for Measuring Three-Dimensional Deformation using Two-Dimensional Digital Image Correlation

Digital Image Correlation (DIC) provides a full-field non-contact optical method for accurate deformation measurement of materials, devices and structures. The measurement of three-dimensional (3D) deformation using DIC in general requires imaging with two cameras and a 3D-DIC code. In the present work, a new experimental technique, namely, Diffraction Assisted Image Correlation (DAIC) for 3D displacement measurement using a single camera and 2D-DIC algorithm is presented. A transmission diffraction grating is placed between the specimen and the camera, resulting in multiple images which are then used to obtain apparent in-plane displacements using 2D-DIC. The true in-plane and out-of-plane displacements of the specimen are obtained from the apparent in-plane displacements and the diffraction angle of the grating. The validity and accuracy of the DAIC method are demonstrated through 3D displacement measurement of a small thin membrane. This technique provides new avenues for performing 3D deformation measurements at small length scales and/or dynamic loading conditions.     

Micro- and Nanoscale Deformation Measurement of Surface and Internal Planes via Digital Image Correlation

The digital image correlation (DIC) technique is successfully applied across multiple length scales through the generation of a suitable speckle pattern at each size scale. For microscale measurements, a random speckle pattern of paint is created with a fine point airbrush. Nanoscale displacement resolution is achieved with a speckle pattern formed by solution deposition of fluorescent silica nanoparticles. When excited, the particles fluoresce and form a speckle pattern that can be imaged with an optical microscope. Displacements are measured on the surface and on an interior plane of transparent polymer samples with the different speckle patterns. Rigid body translation calibrations and uniaxial tension experiments establish a surface displacement resolution of 1 μm over a 5×6 mm scale field of view for the airbrushed samples and 17 nm over a 100×100 μm scale field of view for samples with the fluorescent nanoparticle speckle. To demonstrate the capabilities of the method, we characterize the internal deformation fields generated around silica microspheres embedded in an elastomer under tensile loading. The DIC technique enables measurement of complex deformation fields with nanoscale precision over relatively large areas, making it of particular relevance to materials that possess multiple length scales.     

Error Assessment in Stereo-based Deformation Measurements

Increasing interest in the use of digital image correlation (DIC) for full-field surface shape and deformation measurements has led to an on-going need for both the development of theoretical formulae capable of providing quantitative confidence margins and controlled experiments for validation of the theoretical predictions. In the enclosed work, a series of stereo vision experiments are performed in a manner that provides sufficient information for direct comparison with theoretical predictions using formulae developed in Part I. Specifically, experiments are performed to obtain appropriate optimal estimates and the uncertainty margins for the image locations/displacements, 3-D locations/displacements and strains when using the method of subset-based digital image correlation for image matching. The uncertainty of locating the 3-D space points using subset-based pattern matching is estimated by using theoretical formulae developed in Part I and the experimentally defined confidence margins for image locations. Finally, the uncertainty in strains is predicted using formulae that involves both the variance and covariance of intermediate variables during the strain calculation process. Results from both theoretical predictions and the experimental work show the feasibility and accuracy of the predictive formulae for estimating the uncertainty in the stereo-based deformation measurements.     

Parallax Correction for a Digital Array High-Speed Imaging System for Dynamic Deformation Measurements

In this paper, a parallax correction method for a digital array high-speed imaging system in dynamic deformation measurement is proposed based on the digital image correlation (DIC) technique. First, a new type of digital array high-speed imaging system is designed and the optical parallax of this system is analyzed. Second, a parallax correction method based on the sub-pixel shift concept is employed to eliminate the optical parallax. Finally, the corrected dynamic deformation fields of three-point bending specimen under low-speed impact are obtained using the parallax correction method. The numerical results of the dynamic deformation are in good agreement with the corrected results, which verifies the effectiveness of the proposed parallax correction method.     

Subset-based local vs.finite element-based global digital image correlation:A comparison study

Being the two primary approaches for full-field kinematics measurements,both subset-based local digital image correlation(DIC) and finite element-based global DIC have been extensively studied.Nowadays,most commercial DIC systems employ local DIC algorithm because of its advantages of straight forward principle and higher efficiency.However,several researchers argue that global DIC can provide better displacement results due to the displacement continuity constraint among adjacent elements.As such,thoroughly examining the performance of these two different DIC methods seems to be highly necessary.Here,the random errors associated with local DIC and two global DIC methods are theoretically analyzed at first.Subsequently,based on the same algorithmic details and parameters during analyses of numerical and real experiments,the performance of the different DIC approaches is fairly compared.Theoretical and experimental results reveal that local DIC outperforms its global counterpart in terms of both displacement results and computational efficiency when element(subset) size is no less than 11 pixels.     

Elastic Constants Determination and Deformation Observation Using Brazilian Disk Geometry

Brazilian disk compression has been proposed as an alternative for measuring elastic constants of brittle solids with very low tensile strength (Hondros, Aust J Appl Sci 10:243–268, 1959). Subsequently however, the Brazilian disk geometry was mainly used for measuring fracture toughness and tensile strength of brittle materials, like rocks and concretes. In this study, we revisit the Brazilian disk specimen as a tool for determining elastic constants and for observing the deformation process up to failure. We used the optical digital image correlation (DIC) technique to obtain the displacement field on the specimen surface and proposed a scheme for determining the elastic constants from the measured displacement field and the applied load. Details of the elastic constant determination of a homogeneous material, epoxy resin, were presented. Comparison of the elastic constant measured using Brazilian disk with those obtained through more conventional means was carried out. We also present observations of the deformation evolution of the epoxy resin disk subjected to large nonlinear deformation up to failure and subjected to compressive loading and unloading.     

DIC Challenge: Developing Images and Guidelines for Evaluating Accuracy and Resolution of 2D Analyses

With the rapid spread in use of Digital Image Correlation (DIC) globally, it is important there be some standard methods of verifying and validating DIC codes. To this end, the DIC Challenge board was formed and is maintained under the auspices of the Society for Experimental Mechanics (SEM) and the international DIC society (iDICs). The goal of the DIC Board and the 2D–DIC Challenge is to supply a set of well-vetted sample images and a set of analysis guidelines for standardized reporting of 2D–DIC results from these sample images, as well as for comparing the inherent accuracy of different approaches and for providing users with a means of assessing their proper implementation. This document will outline the goals of the challenge, describe the image sets that are available, and give a comparison between 12 commercial and academic 2D–DIC codes using two of the challenge image sets.     

Combined Temperature and Deformation Measurement During Glass Forming in a Real Scale Setup

An experimental setup has been built and instrumented with non intrusive measurement methods aiming at measuring temperature fields and deformations of a soda-lime-silica glass piece during thermoforming process. A real scale furnace has been used and a realistic thermal load case applied. Infrared measurements based on the Christiansen effect have been performed on the present glass sample, providing the temperature distribution on the sample surface through IR images at 7.8 μm. Piece deformation has been registered simultaneously, using a DIC (Digital Image Correlation) technique combined with a fringe projection method. Results have been analysed in a combined manner, showing a non symmetrical deformation despite a quite homogeneous thermal field, which could be explained by mould/glass contact problems. The non intrusive measurement technique has been proven to be relevant for a possible control of the thermal environment of the piece during the thermoforming process. Further tests should be carried out on a wide range of shapes and glass types.     

Multi-scale Measurement of (Amorphous) Polymer Deformation: Simultaneous X-ray Scattering,Digital Image Correlation and In-situ Loading

This paper presents a method to investigate the behaviour of polymers on different scales during deformation using simultaneously collected synchrotron X-ray scattering, digital image correlation (DIC) and tensile loading. The method is demonstrated through experiments made on specimens of amorphous polycarbonate. Deformation is measured in-situ, simultaneously across different scales from the macroscopic deformation, measured using sensors on the tensile machine, to the full-field mesoscopic deformation, measured using DIC, down to the deformation of the nano-scale structure, studied using small and wide angle X-ray scattering (SAXS/WAXS). The DIC reveals highly inhomogeneous deformations that render conventional techniques for measuring deformation, such as extensiometers, virtually useless. The X-ray scattering is measured in several spatial points during continuous loading giving the evolution of the microstructure with respect to both spatial location and load level. The spatial mapping of the scattering reveals characters that would not be observed when only measuring at the centre point or measuring on a large area of the specimen, e.g. wide beam SAXS/WAXS or small angle neutron scattering (SANS). With these data, the macroscopic and the mesoscopic deformation can be correlated to the behaviour of the microstructure providing relevant information when developing micro-mechanical based constitutive models. The experimental results shown here indicate a direct correlation between the major principal strain direction and the maximum anisotropy direction of the SAXS patterns. The current approach can be extended to any kind of polymeric materials or polymer-based nano-composites.     

Development of Optimal Multiscale Patterns for Digital Image Correlation via Local Grayscale Variation

In many applications of digital image correlation (DIC), it is advantageous to have measurements at multiple scales. Because it is rare to have natural features that can be used for DIC at multiple magnifications, an appropriately multiscale DIC pattern is needed. This work develops a multiscale DIC pattern that (1) contains features appropriate for both high and low magnification, (2) does not need to know the location of high magnification a priori, and (3) does not require specialized DIC equipment beyond what is necessary to achieve the two magnifications. The pattern is developed based on an optimization framework that minimizes expected DIC error while constraining sub-regions of the pattern to biased average grayscale values. The inclusion of local grayscale biases in the pattern has the effect of introducing resolvable features at a length scale much larger than the speckles of which the pattern is composed. Numerical and physical experiments were performed to illustrate the functionality and utility of the designed patterns. Notable among the findings is the trade off between DIC accuracy at the two scales and how it is controlled by grayscale bias.