Quantification of Three-Dimensional Surface Deformation using Global Digital Image Correlation

A novel method is presented to experimentally quantify evolving surface profiles. The evolution of a surface profile is quantified in terms of in-plane and out-of-plane surface displacements, using a Finite Element based Global Digital Image Correlation procedure. The presented method is applied to a case study, i.e. deformation-induced surface roughening during metal sheet stretching. The surface roughness was captured in-situ using a confocal optical profiler. The Global Digital Image Correlation method with linear triangular finite elements is applied to track the three-dimensional material movement from the measured height profiles. The extracted displacement fields reveal the full-field kinematics accompanying the roughening mechanism. Local deviations from the (average) global displacements are the result of the formation, growth, and stretching of hills and valleys on the surface. The presented method enables a full-field quantitative study of the surface height evolution, i.e. in terms of tracked surface displacements rather than average height values such as Root-Mean-Square or height-height correlation techniques. However, the technique does require that an initial surface profile, i.e. contrast, is present and that the contrast change between two measurements is minimal.     

Recent Progress in Digital Image Correlation

In this paper, we report the following important progress recently made in the basic theory and practical implementation of digital image correlation (DIC) for deformation measurement. First, we answer a basic but confusing question to the users of DIC: what is a good speckle pattern for DIC? We present a simple, easy-to-compute yet effective global parameter, called mean intensity gradient, for quality assessment of the entire speckle pattern. Second, we provide an overview of various correlation criteria used in DIC for evaluating the similarity of the reference and deformed subsets, and demonstrate the equivalence of three robust and most widely used correlation criteria, i.e., a zero-mean normalized cross-correlation (ZNCC) criterion, a zero-mean normalized sum of squared difference (ZNSSD) criterion and a parametric zero-mean normalized sum of squared difference (PSSD_ab) criterion with two additional unknown parameters, which elegantly unifies these correlation criteria for subset-based pattern matching. Third, we describe an iterative least squares (ILS) algorithm for accurate subpixel motion detection, which is proved to be equivalent to the existing Newton–Raphson algorithm, but the principle and implementation of ILS algorithm is more straightforward and easier. Finally, to overcome the two limitations of existing subset-based DIC technique, we introduce a robust and generally applicable reliability-guided DIC technique, in which the calculation path is guided by the ZNCC coefficients of computed points, to determine the genuine full-field deformation of an object with complex shape.     

Combining Image Compression with Digital Image Correlation

Experimental Mechanics - Digital image correlation (DIC) is a powerful experimental technique to determine displacement and strain fields. DIC methods usually require a large number of high...     

Augmented Lagrangian Digital Image Correlation

Experimental Mechanics - Digital image correlation (DIC) is a powerful experimental technique for measuring full-field displacement and strain. The basic idea of the method is to compare images of...     

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.

     

Absolute Nodal Coordinates in Digital Image Correlation

A great deal of progress has been made in recent years in the field of global digital image correlation (DIC), where higher-order, element-based approaches were proposed to improve the interpolation performance and to better capture the displacement fields. In this research, another higher-order, element-based DIC procedure is introduced. Instead of the displacements, the elements’ global nodal positions and nodal position-vector gradients, defined according to the absolute nodal coordinate formulation, are used as the searched parameters of the Newton–Raphson iterative procedure. For the finite elements, the planar isoparametric plates with 24 nodal degrees of freedom are employed to ensure the gradients’ continuity among the elements. As such, the presented procedure imposes no linearization on the strain measure, and therefore indicates a natural consistency with the nonlinear continuum theory. To verify the new procedure and to show its advantages, a real large deformation experiment and several numerical tests on the computer-generated images are studied for the standard, low-order, element-based digital image correlation and the presented procedure. The results show that the proposed procedure proves to be accurate and reliable for describing the rigid-body movement and simple deformations, as well as for determining the continuous finite strain field of a real specimen.     

Digital Image Correlation and Color Cameras

Digital Image Correlation (DIC) is a well-known experimental technique. It works by constructing a (surjective) mapping of pixel intensity from reference to target image, where the mapping parameters are identified using a Least Squares approach. Because it makes use of the luminance component of the image, Digital Image Correlation is usually implemented by assuming monochrome cameras. In this work, we will discuss its implementation when color cameras are used, focusing on pitfalls and potential advantages of this solution. Since most cameras implement color acquisition using a Color Filter Array (CFA), much of the article will focus on this technology. However, we will not limit ourselves to this aspect and will show that Three-CCD cameras can provide significant advantages over both CFA and monochrome cameras.     

Cross Polarization for Improved Digital Image Correlation

Digital image correlation (DIC) is a surface deformation measurement technique for which accuracy and precision are sensitive to image quality. This work presents cross polarization, the use of orthogonal linear polarizers on light source(s) and camera(s), as an effective method for improving optical DIC measurements. The benefits of cross polarization are characterized through quantitative and statistical comparisons from two experiments: rigid body translation of a flat sample and uniaxial tension of a superelastic shape-memory alloy (SMA). In both experiments, cross polarization eliminated saturated pixels that degrade DIC measurements, and increased image contrast, which enabled higher spatial precision by using smaller subsets. Subset sizes are usually optimized for correlation confidence interval (typically with subsets of 21×21 px or larger), but can be decreased to achieve the highest possible spatial precision at the expense of increased correlation confidence intervals. Smaller subset sizes (such as 9×9 px) require better images to maintain correlation within error thresholds. By comparing DIC results from a uniaxial SMA tension test with unpolarized and cross-polarized images, we show that for 9×9 px subsets, the loss of valid DIC data points was reduced almost ten-fold with cross polarization. The only disadvantage we see to cross polarization is the decrease in specimen illumination due to transmission losses through the polarizers, which can easily be accommodated with sufficiently intense light sources. With the installation of relatively inexpensive linear polarizing filters, an optimum optical DIC setup can provide even better DIC measurements by delivering images without saturated pixels and with higher contrast for increased DIC spatial precision.     

Fractal Pattern for Multiscale Digital Image Correlation

Background:

Digital Image Correlation (DIC) is based on the matching, between reference and deformed state images, of features contained in patterns that are deposited on test sample surfaces. These features are often suitable for a single scale, and there is a current lack of multiscale patterns capable of providing reliable displacement measurements over a wide range of scales.

Objective:

Here, we aim to demonstrate that a pattern based on a fractal (self-affine) surface would make a suitable pattern for multiscale DIC.

Methods:

A method to numerically generate patterns directly from a desired auto-correlation function is introduced. It is then enhanced by a Mean Intensity Gradient (MIG) improvement process based on grey level redistribution. Numerical experiments at multiple scales are performed for two different imposed displacement fields and results for one of the patterns generated are compared with those obtained for a random pattern and a Perlin noise one.

Results:

The proposed pattern is shown to lead to DIC errors comparable to those found with the two others for the first scales, but has much greater robustness. More importantly, the pattern generated here exhibits stable errors and robustness with respect to the scale whereas these two outputs become significantly degraded for the other two patterns as the scale increases.

Conclusions:

As a result, scale invariance properties of the pattern based on fractal surfaces correspond to scale invariance in DIC errors as well. This is of great interest regarding the use of such patterns in multiscale DIC.

     

Digital Image Correlation Using Stochastic Parallel-Gradient-Descent Algorithm

This article proposes a digital image correlation (DIC) method based on the stochastic parallel gradient descent (SPGD) algorithm. Stochastic parallel perturbations are imposed on deformation parameters to make the correlation coefficients converge to a global extremum; thus, this allows the final measured values of the deformation parameters to be obtained and the DIC measurement to be made. Both simulated and real data processing, including rigid body and strain deformation, show that the proposed method can achieve nearly the same accuracy as the Newton–Raphson (NR) method in most cases and higher accuracy in some cases, such as the simulated experiments of rigid body translation with and without noise. It also has a good noise-robustness. Furthermore, a series of experiments have been designed to evaluate the convergence characteristics of the proposed method, and it has been proved able to process large displacement and have a stable convergence process, good robustness, and a high convergence speed when bilinear interpolation is adopted.     

Digital Image Correlation with Self-Adaptive Gaussian Windows

A novel subpixel registration algorithm with Gaussian windows is put forward for accurate deformation measurement in digital image correlation technique. Based on speckle image quality and potential deformation states, this algorithm can automatically minimize the influence of subset sizes by self-adaptively tuning the Gaussian window shapes with the aid of a so-called weighted sum-of-squared difference correlation criterion. Numerical results of synthetic speckle images undergoing in-plane sinusoidal displacement fields demonstrate that the proposed algorithm can significantly improve displacement and strain measurement accuracy especially in the case with relatively large deformation.     

On the Implementation of the Integral Method for Residual Stress Measurement by Integrated Digital Image Correlation

Experimental Mechanics - The Integrated Digital Image Correlation method (iDIC) is a simple and effective approach for residual stress measurement. iDIC differs from Digital Image Correlation...     

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.

     

关于数字图像相关中曲面拟合法的几点讨论

曲面拟合法求解亚像素位移是数字图像相关亚像素位移定位中的一种重要方法,它具有抗噪声能力较强、精度高、计算效率高等优点,在实际应用中多被采用.本文就该算法中影响亚像素位移定位精度的各要素进行了详细讨论,并用计算机生成的模拟散斑图和金属试件的刚体平移实验进行了验证,结果表明,整像素搜索时选取不同的计算窗口对计算结果的影响最大,而文中所列的几种相关函数的选取对计算结果的影响则可以忽略.     

Digital Image Correlation Based Internal Friction Characterization in Granular Materials

Experimental Mechanics - Based on the realization that Newtonian fluids have the unique property to redirect the forces applied to them in a perpendicular direction, a new apparatus, called the...     

Mirror-assisted Multi-view Digital Image Correlation with Improved Spatial Resolution

Experimental Mechanics - Accurate measurements of panoramic/dual-surface kinematic fields are essential to elastoplastic mechanics for the determination of true stress-strain curves,...     

Smart Digital Image Correlation Patterns via 3D Printing

Experimental Mechanics - Digital Image Correlation (DIC) is a popular experimental technique for measuring full-field deformations in materials. Accurate motion and displacement field...     

Digital Image Correlation for Specimens with Multiple Growing Cracks

Measuring the surface displacements of specimens having multiple, growing cracks is difficult with most implementations of the digital image correlation (DIC) method. This difficulty arises from the need to exclude the cracked area from the analysis, a process that oftentimes requires significant and time-consuming user input to achieve successful results. This work presents a set of modifications to the Newton–Raphson based DIC process that allows the method to automatically analyze specimens with multiple growing cracks. The modifications combine a relatively simple crack identification process that takes advantage of the consistency of quasi-regular speckle patterns with a method to reestablish the analysis in areas segregated by the crack growth. The use of a regular dot pattern does, however, introduce a greater chance for registration error in the correlation process. A method to minimize possible registration problems is also presented. Finally, the effectiveness of the method is demonstrated using images of concrete specimens with a complex and growing crack pattern.     

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.