Cross‐Correlation and Differential Technique Combination to Determine Displacement Fields

Abstract: This study presents a method to measure the displacement fields on the surface of planar objects with sub‐pixel resolution, by combining image correlation with a differential technique. First, a coarse approximation of the pixel level displacement is obtained by cross‐correlation (CC). Two consecutive images, taken before and after the application of a given deformation, are recursively split in sub‐images, and the CC coefficient is used as the similarity measure. Secondly, a fine approximation is performed to assess the sub‐pixel displacements by means of an optical flow method based on a differential technique. To validate the effectiveness and robustness of the proposed method, several numerical tests were carried out on computer‐generated images. Moreover, real images from a static test were also processed for estimating the displacement resolution. The results were compared with those obtained by a commercial digital image correlation code. Both methods showed similar and reliable results according to the proposed tests.     

Image correlation technique for strain measurement of polycrystalline microstructures

An image processing technique is proposed to measure the deformation of polycrystalline materials based on correlating the grains in reference and deformed SEM images. The advantage of this technique compared to the conventional subset-based Digital Image Correlation (DIC) is that it can be applied when speckle patterning is not efficient or when studying boundary-related mechanics is the objective. The technique is based on correlating grains by defining their boundaries rather than just subsets of image pixels. It reveals the anisotropy inherent in the polycrystals since it allows the analysis to specify each grain separately without averaging the results. The technique is applied by detecting the approximate grain boundaries edges and then refining their location with high accuracy. The correlation is performed between points calculated from each grain in the reference and deformed images as a Point Set Registration (PSR) problem. Finally, the displacements and strains are calculated from the resulting transformation matrix. A benchmark problem was developed to discuss the error over a strain range of 0.02 to 0.2 and showed that the resulting strains are reasonably accurate. Also, an in situ experiment was conducted to demonstrate the implementation of the technique using a specimen with fine-grained Zirconia polycrystals. The technique successfully revealed the crack tip plastic zone, and strain mismatch between grains.     

Strain Measurement of Nickel Thin Film by a Digital Image Correlation Method

Abstract:  Digital image correlation is a whole-field and non-contact strain-measuring method. It provides deformation information of a specimen by processing two digital images captured before and after the deformation. To search the deformed images, a hybrid genetic algorithm, in which a simulated annealing mutation process and adaptive mechanisms are combined with a real-parameter genetic algorithm, is adopted. This method is used to measure the strain during the microtensile testing of nickel thin film. In addition to the conventional single region, a double region in which the strain is inferred from the distance change of two regions is proposed to calculate the strain by digital image correlation. The results indicate that while the strain values obtained by single-region method are reasonable, those obtained by the double region method are more accurate. Moreover, the mechanical properties of nickel thin film could be obtained.     

应用数字图像相关法测定瓦楞原纸的泊松比

对瓦楞原纸泊松比的测定存在许多困难,传统的接触式方法难以满足测定要求,还没有一种简单高效的方法能解决这个问题。针对传统位移测量方法的不足,提出以数字图像相关法测定瓦楞原纸的泊松比。通过对试样变形前后的图像进行相关性位移分析,将试验所得的实测位移与已标定位移进行对比,所得结果具高度的一致性,相对误差范围为1%～3%。试验测定面纸MD（machine direction）方向和CD（crossmachine direction）方向的泊松比分别为0.175和0.073,芯纸MD方向和CD方向的泊松比分别为0.275和0.119。测试及分析结果表明,应用数字图像相关法测定瓦楞原纸的方法是可行的,具有较佳的应用价值,能为研究纸张的泊松比提供一个新途径。     

An Evaluation of Digital Image Correlation Criteria for Strain Mapping Applications

Abstract:  The performance of four digital image correlation criteria widely used in strain mapping applications has been critically examined using three sets of digital images with various whole-field deformation characteristics. The deformed images in these image sets are digitally modified to simulate the less-than-ideal image acquisition conditions in an actual experiment, such as variable brightness, contrast, uneven local lighting and blurring. The relative robustness, computational cost and reliability of each criterion are assessed for precision strain mapping applications. Recommendations are given for selecting a proper image correlation criterion to efficiently extract reliable deformation data from a given set of digital images.     

3D strain mapping in rocks using digital volumetric speckle photography technique

Speckle photography technique is a versatile displacement/deformation mapping technique that can be applied to almost any material. It has its genesis in the laser speckle interferometry technique whereby the natural speckles created by illuminating an optically rough surface using a coherent laser beam are used as displacement gauging elements. It evolves into the white light speckle photography technique whereby a random pattern of any type is used as a displacement measurement transducer. With the advent of digital cameras and ubiquitous usage of computers, the digital version of the technique is developed. Up to now, the technique is essentially limited to 2D applications. Recently, we extended the technique into the 3D domain by using the volumetric imaging capabilities of CT or MRI. In this paper, we apply this technique to measuring the internal deformation of rocks. It so happens that certain rocks have natural density variation at various places such that when imaged by CT these impurities can be treated as 3D speckles. The elements of volumetric speckle photography technique are as follows. A reference volumetric image of the rock is recorded by a micro-CT scan and stored as a reference. Under load, the deformed CT image of the rock is also recorded. Both volume images are divided into subsets of certain voxel arrays. Each corresponding pair of the subsets is “compared” via a two-step 3D Fourier transform analysis. The result is a 3D map of displacement vectors representing the collective displacement experienced by all the speckles within the subset of voxels. The strain distribution of the entire rock specimen can then be calculated using appropriate displacement strain relations. The application of this technique to strain mapping of red sandstone and argillite rocks is presented.     

Computer-aided speckle pattern interferometry

An on-line computer system for measuring the deformation of a diffuse object with a speckle interferometer is presented. Methods for evaluating a speckle interferogram using digital image processing techniques are also discussed. The system consists of an interferometric optical setup and a computer-TV image processing facility. A speckle interferogram is generated arithmetically between two digitized speckle patterns before and after deformation of the object. The information about the deformation is extracted by two procedures in analyzing the interferogram: (a) automatic analysis using digital image processing techniques such as gray scale modification, linear spatial filtering, thresholding, and skeletoning; (b) man-machine interactive method for simple high-speed processing of the interferogram using a light pen. The determined fringe order numbers are interpolated and differentiated spatially to give strain, slope, and bending moment of the deformed object. Some examples of processed patterns are presented.     

Basic principle of digital image correlation for in-plane displacement and strain measurement

The basic principle and the algorithm of a digital image correlation method, and the procedure for obtaining displacements and strains are described. In order to describe the basic principle precisely, only in-plane displacement and strain measurement of a planar object are explained. Gray levels between integer pixels of a digital image after deformation are interpolated to obtain displacements with subpixel resolution. Displacements are then determined by solving nonlinear simultaneous equations taking the deformation of a subset into consideration. Strains are obtainable by differentiating the measured displacements. In addition to the basic principle of digital image correlation, the example of the measurement and its results are shown.     

Measurement of transient deformations using digital image correlation method and high-speed photography: application to dynamic fracture

The digital image correlation method is extended to the study of transient deformations such as the one associated with a rapid growth of cracks in materials. A newly introduced rotating mirror type, multichannel digital high-speed camera is used in the investigation. Details of calibrating the imaging system are first described, and the methodology to estimate and correct inherent misalignments in the optical channels are outlined. A series of benchmark experiments are used to determined the accuracy of the measured displacements. A 2%-6% pixel accuracy in displacement measurements is achieved. Subsequently, the method is used to study crack growth in edge cracked beams subjected to impact loading. Decorated speckle patterns in the crack tip vicinity at rates of 225,000 frames per second are registered. Two sets of images are recorded, one before the impact and another after the impact. Using the image correlation algorithms developed for this work, the entire crack tip deformation history, from the time of impact to complete fracture, is mapped. The crack opening displacements are then analyzed to obtain the history of failure characterization parameter, namely, the dynamic stress intensity factor. The measurements are independently verified successfully by a complementary numerical analysis of the problem.     

Application of digital-image-correlation techniques in analysing cracked cylindrical pipes

Cracks induced by external excitation on a material that has defects may generate the stress concentration phenomenon. The stress concentration behaviour causes local buckling, which will induce the damage of the members made of this material. Thus, developing techniques to monitor the strain variation of a cracked member is an important study. The traditional technique (such as strain gauge) can only measure the average strain of a region. The strain variation within this region cannot be determined. Therefore, it cannot sufficiently reflect the mechanical behaviour surrounding the crack. The Digital image correlation technique recently developed is an image identification technique to be applied for measuring the object deformation. This technique is capable of correlating the digital images of an object before and after deformation and further determining the displacement and strain field of an object based on the corresponding position on the image. In this work, this technique is applied to analyse the mechanics of a cylindrical pipe experiencing crack destruction. The fixing device is used to avoid shaking the specimen during the pressurizing process. The image capture instruments are fixed on the stable frame to measure the deformation of specimen accurately. Through the cylindrical pipe cracking test, the capacity of the digital image correlation technique for surveying the strain variation in a tiny region is validated. Then, the experimental results obtained using the digital image correlation analysis is used to demonstrate the crack development tendency in defect materials and the stress concentration zone.     

The centrally cracked Brazilian disc: closed solutions for stresses and displacements for cracks under opening mode

Closed-form solutions for the stress and displacement fields in a centrally cracked Brazilian disc are obtained. The disc is subjected to uniformly distributed radial pressure along two finite symmetric arcs on its perimeter. The solution is based on the complex potentials method introduced by Kolosov and Muskhelisvili, and advantage is taken of a recently introduced closed-form solution for the intact Brazilian disc. Special attention is paid to the displacements of the crack lips, since they dictate whether the lips are in an opening or closing mode. The solutions obtained are valid for configurations for which the crack lips are in an opening loading mode, where there are no contact forces along the crack flanks. As well as stresses and displacements, the stress intensity factors are also determined in closed form and are found to be in good agreement with the respective values obtained from existing approximate solutions. Preliminary experimental data obtained using the digital image correlation technique support the analytically deduced conclusions for the deformation and rotation of the crack flanks.     

Full-Field Displacement Measurement of a Speckle Grid by using a Mesh-Free Deformation Function

Abstract:  In the present study, a combined experimental–numerical technique for the determination of the displacement and strain fields in the surface of a deformable body is described. The experimental part of this technique is based on the recording of the pair of images of the surface before and after deformation of the body, by means of a digital camera. This is done after spraying the surface with a random field of speckles (dots). Then the dots (having finite dimensions) of the second image are identified and uniquely paired with the dots of the first image. This permits the experimental determination of the deformation field in the surface. Then, by means of a mesh-free numerical method, a smoothed deformation field can be constructed. For that, the moving least square method is applied. The deformation field being available, the corresponding strain field can easily be obtained. Numerical simulation of this technique in three simple examples indicates that promising applications are expected.     

Virtually calibrated projection moire interferometry

Projection moire interferometry (PMI) is an out-of-plane displacement measurement technique that consists of differencing reference and deformed images of a grid pattern projected onto the test object. In conventional PMI, a tedious process of computing the fringe sensitivity coefficient (FSC), which requires moving the test object or the reference plane to known displacements, is used. We present a new technique for computing the FSC values that is called virtually calibrated projection moire interferometry (VCPMI). VCPMI is based on computer simulations of the conventional PMI process and does not require moving the actual test object or reference plane. We validate the VCPMI approach by comparing results for a flat plate and an airfoil with those made by use of other measurement methods.     

Internal microstructure evolution of aluminum foams under compression

In this paper, the internal microstructure deformation of open-cell and closed-cell aluminum foams under compression was investigated by using synchrotron radiation X-ray computed tomography (SR-CT) technique and digital image analysis method. The reconstructed images were obtained by using filtered back projection algorithm based on the original images taken from SR-CT experiments. Several important parameters including cross-section porosity, total porosity and cross-section deformation were computed from the reconstructed images. The variation of these parameters provided useful evolution information of internal microstructure of aluminum foams under compression.     

Application of Elastic Image Registration and Refraction Correction for Non‐Contact Underwater Strain Measurement

Abstract: The refraction‐induced image distortion introduces large errors in the deformation measurement of fluid submerged specimens using digital image correlation (DIC). This study provides a review of the nature of the refraction‐induced image distortion, assesses experimental conditions that interact with refraction and proposes an elastic image registration technique to correct the refraction distortion of underwater images. In the elastic image registration technique, control points are selected on reference and refracted images of a template object and locally sensitive transformation functions that overlay the two images are obtained. The transformation functions so obtained are then used to reconstruct undistorted images from underwater images and the former are used as input to a DIC system. The proposed approach has shown to improve the refraction error in the order of 5–8% for typical material test samples undergoing deformation inside a water‐filled glass chamber.     

A dual domain decomposition method for finite element digital image correlation

The computational burden associated to finite element based digital image correlation methods is mostly due to the inversion of finite element systems and to image interpolations. A non‐overlapping dual domain decomposition method is here proposed to rationalise the computational cost of high resolution finite element digital image correlation measurements when dealing with large images. It consists in splitting the global mesh into submeshes and the reference and deformed states images into subset images. Classic finite element digital image correlation formulations are first written in each subdomain independently. The displacement continuity at the interfaces is enforced by introducing a set of Lagrange multipliers. The problem is then condensed on the interface and solved by a conjugate gradient algorithm. Three different preconditioners are proposed to accelerate its convergence. The proposed domain decomposition method is here exemplified with real high resolution images. It is shown to combine the metrological performances of finite element based digital image correlation and the parallelisation ability of subset based methods. Copyright © 2015 John Wiley & Sons, Ltd.     

Measurement of Fracture Parameters for a Mixed-Mode Crack Driven by Stress Waves using Image Correlation Technique and High-Speed Digital Photography

Abstract:  Measurement of fracture parameters for a rapidly growing crack in syntactic foam sheets using image correlation technique and high-speed photography is presented. The performance of a rotating mirror-type multi-channel high-speed digital camera to measure transient deformations is assessed by conducting benchmark tests on image intensity variability, rigid translation and rigid rotation. Edge-cracked foam samples are subjected to eccentric impact loading relative to the initial crack plane to produce mixed-mode loading conditions in a three-point bend configuration. High-speed photography is used to record decorated random speckles in the vicinity of the crack tip at a rate of 200 000 frames per second. Two sets of images are recorded, the first set before impact and the second after impact. Using image correlation methodology, crack-tip displacement field histories and dominant strains from the time of impact up to complete fracture are mapped. Over-deterministic least-squares analyses of crack-tip radial and tangential displacements are used to obtain mixed-mode fracture parameters. The measurements are compared with complementary finite element results. The fracture parameters determined from radial displacements seem more robust even when fewer number of higher order terms in the crack-tip asymptotic expansion are used.     

Investigation of the Uncertainty of DIC Under Heterogeneous Strain States with Numerical Tests

Abstract: In this research, numerical 2D digital image correlation (DIC) tests are carried out to assess the uncertainty of DIC under heterogeneous strain states. DIC is implemented to measure the deformation of the numerically deformed images with respect to the undeformed counterparts, which are taken from the real tensile specimens. The tensile specimens are made of three materials, that is, steel DC06, steel DX54D+Z and aluminium alloy Al6016 and cut into three different geometries, namely one standard design and two complex designs. The specimens are all painted manually with random speckle patterns. The original images are deformed by imposed displacement fields, which are obtained by simulating uni‐axial tensile tests of the specimens with finite element analysis (FEA). In this way, the errors sourcing from the hardware of the image system are excluded. According to the geometries of the specimens, homogeneous and heterogeneous strain states are achieved by FEA. The optimum mesh sizes of the models are identified to minimise theirs influence on the imposed fields. The impacts of subset sizes, step sizes and strain window sizes are studied for an optimum correlation. Finally, the influence of the strain state is investigated. It is found that the DIC accuracy and precision decrease under highly heterogeneous strain states.     

DVC‐based image subtraction to detect microcracking in lightweight concrete

This paper presents an image subtraction technique based on digital volume correlation to detect and extract the complex network of microcracks that progressively developed in a lightweight concrete sample submitted in situ to uniaxial compression and imaged by X‐ray computed tomography. From local digital volume correlation measurements, performed only on positions with sufficient image contrast, the mechanical transformation is estimated at all voxels within the whole sample using an adjusted interpolation procedure that computes an affine approximation of the local transformation. The deformed image (containing cracks) is thus transformed back to the same frame as the reference image (without cracks) to compute the difference between both images, taking into account possible brightness and contrast adjustments. The resulting subtracted image reveals the path of cracks, which is clearly visible without the underlying heterogeneous microstructure of the concrete. The detection accuracy is here estimated to one tenth of a voxel, allowing early‐age cracks to be detected while they would barely have been noticed on the X‐ray computed tomography images. Segmentation of the crack network is also made much easier. To overcome a low signal‐to‐noise ratio for the tiniest cracks, a Hessian‐based filter is used to extract the complex crack network. The cracks can be directly located in the microstructure segmented in the reference image and compared for all loading steps to characterise their initiation and propagation.     

Response of spray-deposited,stirred-cast and conventional cast Pb-Sn alloys to deformation in the semi-solid state

Pb-35 wt% Sn alloys were deformed in the semi-solid state. The effects of the initial microstructures, deformation temperatures and deformation rates on the microstructures and the formability of the alloy were studied. A physical phenomenological model is proposed to explain the different behaviours of the stress-strain curves of semi-solid forming of various materials under various conditions. Three different processes, spray deposition (S/D), semi-solid synthesizing (SSS) and conventional casting (CC) were used to produce the Pb-35 wt% Sn alloys with different initial microstructures. Two strain rates, (0.083 and 0.00083 s^–1) and two deformation temperatures, (190 and 200°C) were used in this study. There is no significant variation in particle size and in sphericity during semi-solid forming of Pb-35wt% Sn alloys. The deformation stress increases monotonically as strain increases during semi-solid deformation of S/D materials, which consist of smaller solid particles. However, for SSS and CC materials, which consist of larger solid particles, the deformation stress increases in the beginning to a local maximum, then decreases to a minimum before it starts to increase again as strain increases. This phenomenon is more noticeable at lower deformation temperatures and higher strain rates. The deformation stresses required for deformation at higher deformation rates and at lower deformation temperatures are larger than those at lower deformation rates and at higher deformation temperatures, respectively.