Incremental calculation for large deformation measurement using reliability-guided digital image correlation

Conventional digital image correlation (DIC) technique using a fixed reference image provides high-accuracy measurements but normally fails when serious decorrelation effect occurs in the deformed images due to large deformation, serious illumination fluctuations or other reasons. In this paper, an incremental reliability-guided digital image correlation (RG-DIC) technique, by combining the recently developed RG-DIC technique and an automatic reference image updating scheme, is proposed for large deformation measurement. In the incremental RG-DIC technique, a seed point is defined in the original reference image and searched in the deformed images, if the estimated correlation coefficient is larger than a preset threshold, which means no serious decorrelation effect exists in the deformed image, the RG-DIC technique is used to continue correlation analysis to obtain full-field displacements. Otherwise, the image recorded just before the current deformed image is chosen as an updated reference image to proceed with correlation analysis. Afterwards, the incremental displacements extracted by comparing the current deformed image and the updated reference image can be cumulated to determine the overall deformation. The effectiveness of the proposed technique is demonstrated by retrieving the full-field deformation of a foam sample subjected to large compressive deformation.     

数字图像相关中基于位移场局部最小二乘拟合的全场应变测量

为了从含噪声的位移场中计算得到可靠的应变场,提出一种基于位移场局部最小二乘拟合的全场应变求解方法。介绍了数字图像相关方法的原理,阐述了基于位移场局部最小二乘拟合的全场应变求解方法,并讨论了计算区域边界、孔洞及裂纹附近区域等情况下的应变计算。对均匀变形和中心带圆孔的薄铝板拉伸实验的计算结果表明,该方法能有效地从原始位移场数据中提取全场应变信息。在均匀变形情况下应选择大的应变计算窗口,计算结果更逼近真值;在非均匀变形情况下,如果位移场中包含较强的噪声,则应选择较大的应变计算窗口,而位移场精度很高时可选择更小的应变计算窗口。     

Determination of displacement distributions in bolted steel tension elements using digital image techniques

Digital imaging methods have found a great interest in various engineering fields to study stress-deformation characteristics of materials. Recent enhancements in visual instrumentation with the availability of cost-effective hardware and software products make the digital imaging techniques a viable tool to replace direct strain or displacement measurement methods in engineering applications. In this study, deformation characteristics of bolted steel connections are investigated by calculating in-plane displacement distributions using digital image correlation method (DIC). Validation of the method is presented by comparing the strains measured in standard tension specimens using electrical resistance strain gages and the DIC method. Finite element analysis of the connection specimen is also performed to compare the in-plane displacement distributions calculated from both methods. Results from the validation process indicate that the strains obtained from the DIC method compare well with the results of strain gages. The findings also indicate that the displacement distributions calculated from the finite element method may differ from those of the DIC method in terms of distribution pattern, and the location and magnitude of the extreme values of displacements. It is suggested that the proposed method can be used to determine the in-plane displacement distributions for the bolted connections, hence to evaluate their deformation characteristics under loading.     

Accuracy of stress measurement by Laue microdiffraction (Laue‐DIC method): the influence of image noise,calibration errors and spot number

Laue microdiffraction, available at several synchrotron radiation facilities, is well suited for measuring the intragranular stress field in deformed materials thanks to the achievable submicrometer beam size. The traditional method for extracting elastic strain (and hence stress) and lattice orientation from a microdiffraction image relies on fitting each Laue spot with an analytical function to estimate the peak position on the detector screen. The method is thus limited to spots exhibiting ellipsoidal shapes, thereby impeding the study of specimens plastically deformed. To overcome this difficulty, the so‐called Laue‐DIC method introduces digital image correlation (DIC) for the evaluation of the relative positions of spots, which can thus be of any shape. This paper is dedicated to evaluating the accuracy of this Laue‐DIC method. First, a simple image noise model is established and verified on the data acquired at beamline BM32 of the European Synchrotron Radiation Facility. Then, the effect of image noise on errors on spot displacement measured by DIC is evaluated by Monte Carlo simulation. Finally, the combined effect of the image noise, calibration errors and the number of Laue spots used for data treatment is investigated. Results in terms of the uncertainty of stress measurement are provided, and various error regimes are identified.     

Strain measurement of SU-8 photoresist by a digital image correlation method with a hybrid genetic algorithm

Digital image correlation (DIC) is a whole-field and non-contact strain measuring method. It could provide deformation information of a specimen by processing two digital images that are 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 added to the real-parameter genetic algorithm, is proposed in this work. To increase the accuracy and reliability of this method, some key parameters of this method are suggested. Then, this method is used to measure the strain during the micro tensile testing of SU-8 photoresist. In addition to the conventional single region, a double region is proposed to calculate the strain by DIC. The results indicate that while the strains obtained by single region are reasonable, those obtained by double region are accurate. Also the mechanical properties of SU-8 could be accurately obtained.     

A novel speckle pattern—Adaptive digital image correlation approach with robust strain calculation

Digital image correlation (DIC) has seen widespread acceptance and usage as a non-contact method for the determination of full-field displacements and strains in experimental mechanics. The advances of imaging hardware in the last decades led to high resolution and speed cameras being more affordable than in the past making large amounts of data image available for typical DIC experimental scenarios. The work presented in this paper is aimed at maximizing both the accuracy and speed of DIC methods when employed with such images. A low-level framework for speckle image partitioning which replaces regularly shaped blocks with image-adaptive cells in the displacement calculation is introduced. The Newton-Raphson DIC method is modified to use the image pixels of the cells and to perform adaptive regularization to increase the spatial consistency of the displacements. Furthermore, a novel robust framework for strain calculation based also on the Newton-Raphson algorithm is introduced. The proposed methods are evaluated in five experimental scenarios, out of which four use numerically deformed images and one uses real experimental data. Results indicate that, as the desired strain density increases, significant computational gains can be obtained while maintaining or improving accuracy and rigid-body rotation sensitivity.     

Strain field denoising for digital image correlation using a regularized cost-function

In digital image correlation (DIC), the widely used forward-additive Newton–Raphson (FA-NR) algorithm and the recently introduced equivalent but more efficient inverse-compositional Gauss–Newton (IC-GN) algorithm are capable of providing both displacements and displacement gradients (strains) for each calculation point. However, the obtained displacement gradients are seriously corrupted by various noises, and for this reason these directly computed strains are usually considered as useless information and therefore discarded. To extract strain distributions more accurately, much research efforts have been dedicated to how to smooth and differentiate the noisy displacement fields using appropriate numerical approaches. In this contribution, contrary to these existing strain estimation approaches, a novel and alternative strain estimation approach, based on denoising the noisy strain fields obtained by FA-NR or IC-GN algorithm using a regularized cost-function, is proposed. The effectiveness and practicality of the proposed strain estimation technique is carefully examined using both computer-simulated images with imposed homogeneous and inhomogeneous deformation, and experimentally obtained images. Experimental results reveal that the strains obtained by the proposed method are comparable to those determined by post-processing of the displacement fields using conventional pointwise least squares strain estimation approach.     

Optical strain gauge vs. traditional strain gauges for concrete elasticity modulus determination

In the field of Civil Engineering, the evaluation of concrete elasticity modulus relies heavily on traditional strain gauges like electric resistance strain gauge, demec mechanical strain and compressometer. These strain gauges work pretty well but the sample surface preparation and the strain gauge adhesion are tedious and time-consuming. On the other hand, convenient non-destructive testing methods like rebound hammer and ultrasonic pulse velocity have the disadvantage of large data scattering and low reliability. In this paper, we aim to develop a handy, reliable and cost-effective method for concrete property evaluation based on an optical technique called automatic digital image correlation (ADIC), which acts as an optical strain gauge. By incorporating an automatic searching approach, the proposed ADIC greatly expands the convergence range of normal digital image correlation (DIC) algorithms and is able to automatically determine concrete strain in real time without human interaction. After the optical strain gauge is set up, the axial concrete strain as well as the stress-strain curve is plotted in real time when the concrete sample under testing is loaded. The concrete elasticity modulus is then determined from the curve. A series of experiments have been conducted to evaluate the performance of the proposed optical strain gauge. Comparisons are also carried out between the proposed optical strain gauge and traditional strain gauges such as electronic strain gauge, compressometer and demec mechanical strain gauge, which further confirm the accuracy, convenience and reliability of the proposed technique.     

Accurate kinematic measurement at interfaces between dissimilar materials using conforming finite-element-based digital image correlation

Digital image correlation (DIC) is now an extensively applied full-field measurement technique with subpixel accuracy. A systematic drawback of this technique, however, is the smoothening of the kinematic field (e.g., displacement and strains) across interfaces between dissimilar materials, where the deformation gradient is known to be large. This can become an issue when a high level of accuracy is needed, for example, in the interfacial region of composites or joints. In this work, we described the application of global conforming finite-element-based DIC technique to obtain precise kinematic fields at interfaces between dissimilar materials. Speckle images from both numerical and actual experiments processed by the described global DIC technique better captured sharp strain gradient at the interface than local subset-based DIC.     

A fast digital image correlation method for deformation measurement

Fast and high-accuracy deformation analysis using digital image correlation (DIC) has been increasingly important and highly demanded in recent years. In literature, the DIC method using the Newton-Rapshon (NR) algorithm has been considered as a gold standard for accurate sub-pixel displacement tracking, as it is insensitive to the relative deformation and rotation of the target subset and thus provides highest sub-pixel registration accuracy and widest applicability. A significant drawback of conventional NR-algorithm-based DIC method, however, is its extremely huge computational expense. In this paper, a fast DIC method is proposed deformation measurement by effectively eliminating the repeating redundant calculations involved in the conventional NR-algorithm-based DIC method. Specifically, a reliability-guided displacement scanning strategy is employed to avoid time-consuming integer-pixel displacement searching for each calculation point, and a pre-computed global interpolation coefficient look-up table is utilized to entirely eliminate repetitive interpolation calculation at sub-pixel locations. With these two approaches, the proposed fast DIC method substantially increases the calculation efficiency of the traditional NR-algorithm-based DIC method. The performance of proposed fast DIC method is carefully tested on real experimental images using various calculation parameters. Results reveal that the computational speed of the present fast DIC is about 120-200 times faster than that of the traditional method, without any loss of its measurement accuracy     

Large deformation measurement scheme for 3D digital image correlation method

Difficulties often arise for digital image correlation (DIC) technique when serious de-correlation occurs between the reference image and the deformed image due to large deformation. An updating reference image scheme could be employed to deal with large deformation situation, however that will introduce accumulated errors. A large deformation measurement scheme, combining improved coarse search method and updating reference image scheme, is proposed in this paper. For a series of deformation images, the correlation calculation begins with a seed point and spreads out. An improved coarse search method is developed to calculate the initial correlation parameters for the seed point, which guarantees that the correlation calculation can be carried out successfully even in large deformation situation. Only for extremely large deformation, the reference image is updated. Using this method, not only extremely large deformation can be measured successfully but also the accumulated error could be controlled. A polymer material tensile test and a foam compression test are used to verify the proposed scheme. Experimental results show that up to 450% tensile deformation and 83% compression deformation can be measured successfully.     

Study of optimal subset size in digital image correlation of speckle pattern images

This paper investigates the effect of subset size, associated with image pattern quality and subset displacement functions, on the accuracy of deformation measurements by digital image correlation(DIC). A concept of subset entropy is introduced in this work to quantify the subset image pattern quality for DIC analysis and its effectiveness was demonstrated by experimental studies. By employing white-light images with almost uniform subset entropy and first-order displacement functions, the effect of subset size on DIC analysis was investigated for the deformation cases of translation, uniform deformation, and simulated quadratic deformation, respectively. The results show that the chosen subset size must be large enough for precise displacement measurements when subset displacement functions match underlying actual deformation. On the other hand, optimal subset size in DIC for nonhomgeneous deformation measurements appears as a result of a tradeoff between the influence of random errors and systematic errors.     

On the use of the digital image correlation method for heterogeneous deformation measurement of porous solids

In this paper, several crucial issues arising from the application of the digital image correlation (DIC) method to the measurement of heterogeneous deformation of porous solids are discussed. To handle samples with complex geometry, the performance of the two commonly employed DIC methods, namely the subset-based DIC and the finite-element based DIC methods are first evaluated and compared. A combined DIC approach and an adaptive DIC approach suitable for samples with discontinuities/holes are then proposed. Aluminum plates with circular holes subject to compressive loading are employed to evaluate the accuracy of the proposed methods. It has been found that in addition to other factors such as the number of pixels and speckle size, the orientation of the camera lens also plays an important role on the measurement accuracy. A calibration method for the adjustment of camera orientation is proposed, which leads to a good agreement between the experimentally measured displacements and finite element simulation results. Another finding of the presented work is that for relatively stiff specimens, the deformation of the loading system itself must be considered in order to obtain an accurate displacement.     

A novel 2nd-order shape function based digital image correlation method for large deformation measurements

Compared with the traditional forward compositional matching strategy, the inverse compositional matching strategy has almost the same accuracy, but has an obviously higher efficiency than the former in digital image correlation (DIC) algorithms. Based on the inverse compositional matching strategy and the auxiliary displacement functions, a more accurate inverse compositional Gauss-Newton (IC-GN2) algorithm with a new second-order shape operator is proposed for nonuniform and large deformation measurements. A theoretical deduction showed that the new proposed second-order shape operator is invertible and can steadily attain second-order precision. The result of the numerical simulation showed that the matching accuracy of the new IC-GN2 algorithm is the same as that of the forward compositional Gauss-Newton (FC-GN2) algorithm and is relatively better than in IC-GN2 algorithm. Finally, a rubber tension experiment with a large deformation of 27% was performed to validate the feasibility of the proposed algorithm.     

Experimental determination of Representative Volume Element (RVE) size in woven composites

A systematic approach is proposed to estimate the length scales of the representative volume element (RVE) in orthogonal plain woven composites. The approach is based on experimental full-field deformation measurements at mesoscopic scales. Stereovision digital image correlation (DIC) is conducted to determine the full-field strain distribution in on- and off-axis specimens loaded axially in tension. A sensitivity analysis is carried out to optimize the image correlation parameters. Using the optimized set of image correlation parameters, full-field strains are measured and used in conjunction with a simple strain averaging algorithm to identify the length scales at which globally applied and spatially-averaged local strains converge in values. The size of a virtual window containing local strain data, the average of which has the same value as the global strain, is identified as the RVE dimensions for the examined material. The smallest RVE sizes found in this work are shown to be both strain and angle dependent. The largest RVE dimension obtained is reported as a unique, strain and orientation insensitive RVE size for the woven composite examined.     

A linear least squares approach for evaluation of crack tip stress field parameters using DIC

In the present work, an experimental study is carried out to estimate the mixed-mode stress intensity factors (SIF) for different cracked specimen configurations using digital image correlation (DIC) technique. For the estimation of mixed-mode SIF׳s using DIC, a new algorithm is proposed for the extraction of crack tip location and coefficients in the multi-parameter displacement field equations. From those estimated coefficients, SIF could be extracted. The required displacement data surrounding the crack tip has been obtained using 2D-DIC technique. An open source 2D DIC software Ncorr is used for the displacement field extraction. The presented methodology has been used to extract mixed-mode SIF׳s for specimen configurations like single edge notch (SEN) specimen and centre slant crack (CSC) specimens made out of Al 2014-T6 alloy. The experimental results have been compared with the analytical values and they are found to be in good agreement, thereby confirming the accuracy of the algorithm being proposed.     

面内位移测量的基于梯度的数字图像相关方法

将整像素位移搜索和基于微区统计性质的亚像素位移梯度算法相结合的数字图像相关方法具有计算简单、求解效率高等优点。该方法的基本假设是变形前后的子区做刚体平移,这则与有位移梯度存在的实际情况相矛盾。首先分析了该基本假设的理论误差,在基于梯度的数字图像相关方法中,得出变形子区做刚体平移的假设和在Newton-Rapshon方法中子区均匀变形的假设所获得的变形子区中心位移在理论上为相同的结论。然后用四组实验来验证该方法在实际实验条件下的计算精度和稳定性,并在铝板试件的单向拉伸实验中,将该方法与N-R方法在有应变存在情况下的计算结果作比较,结果表明该方法计算的位移和理论位移符合得很好,但其计算速度和效率要远优越于N-R方法。     

Deformation field interaction in sequential circular indentation of a strain hardening material

An experimental study was made to characterise and model the deformation field in sequential circular indentation of a model strain hardening material. Digital image correlation was used to measure the evolving subsurface deformation field in terms of displacement, strain rate and strain as a function of indentation spacing and depth. These measurements were used to validate a finite element model for complementary simulations. The results identify relationships between sequential indentation parameters and overlap of subsurface strain distributions, maximum subsurface strains and indentation loads. Maximum strain and the degree of strain field overlap in the deformed subsurface were maximised when the ratio of indentation spacing (S) to projected indentation contact length (L) was approximately S/L?=?[1.1, 1.2]. Also discussed are the implications for understanding process-scale considerations for indentation-based mechanical surface treatments, including energy dissipation and relationship of surface coverage measures to subsurface strain overlap. Relative differences in energy expended were found for conditions that produce similar levels of subsurface plastic strain and strain field overlap. Finally, the role of sequential indentation parameters on strain path changes and path reversals in the deformed subsurface is investigated and discussed in the context of heterogeneous mechanics and corresponding effects on subsurface microstructure evolution.     

Experimental study on the micromechanical behavior of a PBX simulant using SEM and digital image correlation method

The micro-scale mechanical behavior of a polymer-bonded explosive (PBX) simulant was experimentally studied using a scanning electron microscope (SEM) imaging system and digital image correlation (DIC) method. The semi-circular bend (SCB) test was chosen for the study. During the testing, a series of SEM images of the specimen was acquired in situ. The natural micro-structural features of the specimen were used as random speckle pattern for DIC analysis. The displacement and strain fields at the area of interest were obtained by DIC. The deformation and damage of PBX were analyzed. Heterogeneous strain fields demonstrated the damage evolution underneath the specimen surface and predicted possible micro-crack growth. Based on the contour plots of the correlation coefficient, the formation and extension of microscopic cracks were quantitatively analyzed.     

物体内部三维位移场分析的数字图像相关方法

提出了物体内部三维位移场的数字图像相关分析方法，对物体变形前后，或连续变形的两个相邻状态的内部三维结构的数字图像，通过相关运算获得三维位移场.文中给出了三维相关法的体搜索窗口、相关函数及亚像素运算的相关系数拟合函数.数字模拟结果证明了三维相关法的正确性及可靠性.位移计算精度为0.02像素. 关键词： 数字图像相关 三维相关 亚像素