Uncertainty quantification in DIC with Kriging regression

A Kriging regression model is developed as a post-processing technique for the treatment of measurement uncertainty in classical subset-based Digital Image Correlation (DIC). Regression is achieved by regularising the sample-point correlation matrix using a local, subset-based, assessment of the measurement error with assumed statistical normality and based on the Sum of Squared Differences (SSD) criterion. This leads to a Kriging-regression model in the form of a Gaussian process representing uncertainty on the Kriging estimate of the measured displacement field. The method is demonstrated using numerical and experimental examples. Kriging estimates of displacement fields are shown to be in excellent agreement with ‘true’ values for the numerical cases and in the experimental example uncertainty quantification is carried out using the Gaussian random process that forms part of the Kriging model. The root mean square error (RMSE) on the estimated displacements is produced and standard deviations on local strain estimates are determined.     

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.     

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.     

Path-independent digital image correlation with high accuracy,speed and robustness

The initial guess transferring mechanism is widely used in iterative DIC algorithms and leads to path-dependence. Using the known deformation at a processed point to estimate the initial guess at its neighboring points could save considerable computation time, and a cogitatively-selected processing path contributes to the improved robustness. In this work, our experimental study demonstrates that a path-independent DIC method is capable to achieve high accuracy, efficiency and robustness in full-field measurement of deformation, by combining an inverse compositional Gauss–Newton (IC-GN) algorithm for sub-pixel registration with a fast Fourier transform-based cross correlation (FFT-CC) algorithm to estimate the initial guess. In the proposed DIC method, the determination of initial guess accelerated by well developed software library can be a negligible burden of computation. The path-independence also endows the DIC method with the ability to handle the images containing large discontinuity of deformation without manual intervention. Furthermore, the possible performance of the proposed path-independent DIC method on parallel computing device is estimated, which shows the feasibility of the development of real-time DIC with high-accuracy.     

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。     

Comparison of subset-based local and FE-based global digital image correlation: Theoretical error analysis and validation

Subset-based local and finite-element-based (FE-based) global digital image correlation (DIC) approaches are the two primary image matching algorithms widely used for full-field displacement mapping. Very recently, the performances of these different DIC approaches have been experimentally investigated using numerical and real-world experimental tests. The results have shown that in typical cases, where the subset (element) size is no less than a few pixels and the local deformation within a subset (element) can be well approximated by the adopted shape functions, the subset-based local DIC outperforms FE-based global DIC approaches because the former provides slightly smaller root-mean-square errors and offers much higher computation efficiency. Here we investigate the theoretical origin and lay a solid theoretical basis for the previous comparison. We assume that systematic errors due to imperfect intensity interpolation and undermatched shape functions are negligibly small, and perform a theoretical analysis of the random errors or standard deviation (SD) errors in the displacements measured by two local DIC approaches (i.e., a subset-based local DIC and an element-based local DIC) and two FE-based global DIC approaches (i.e., Q4-DIC and Q8-DIC). The equations that govern the random errors in the displacements measured by these local and global DIC approaches are theoretically derived. The correctness of the theoretically predicted SD errors is validated through numerical translation tests under various noise levels. We demonstrate that the SD errors induced by the Q4-element-based local DIC, the global Q4-DIC and the global Q8-DIC are 4, 1.8–2.2 and 1.2–1.6 times greater, respectively, than that associated with the subset-based local DIC, which is consistent with our conclusions from previous work.     

Quality assessment of speckle patterns for digital image correlation

Digital image correlation (DIC) is an optical–numerical full-field displacement measuring technique, which is nowadays widely used in the domain of experimental mechanics. The technique is based on a comparison between pictures taken during loading of an object. For an optimal use of the method, the object of interest has to be covered with painted speckles. In the present paper, a comparison is made between three different speckle patterns originated by the same reference speckle pattern. A method is presented for the determination of the speckle size distribution of the speckle patterns, using image morphology. The images of the speckle patterns are numerically deformed based on a finite element simulation. Subsequently, the displacements are measured with DIC-software and compared to the imposed ones. It is shown that the size of the speckles combined with the size of the used pixel subset clearly influences the accuracy of the measured displacements.     

Mesoscopic strain fields in woven composites: Experiments vs. finite element modeling

Detailed determination of strain in woven composite materials is fundamental for understanding their mechanics and for validating sophisticated computational models. The digital image correlation technique is briefly presented and applied to the full-field strain determination in a twill-weave carbon-fiber-reinforced-plastic (CFRP) composite under in-plane loading. The experimental results are used to assess companion results obtained with an ad hoc finite element-based model. The DIC vs. FEM comparison is carried out at the mesoscopic scale.     

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.     

Dynamic displacement field reconstruction through a limited set of measurements: Application to plates

The paper presents a procedure for the identification of the full-field dynamic response of a structure from a limited set of experimental measurements. An iterative technique based on modal decomposition maps the displacement field of the vibrating structure by using experimental data in conjunction with the numerical model of the considered structure. Algebraic relationships between experimental measurements and equivalent modal loads allow the identification of the full-field dynamic response from few experimental data. This procedure is detailed for a plate structure subjected to a harmonic concentrated load.     

Determining the tensile response of materials at high temperature using DIC and the Virtual Fields Method

An experimental approach based on Digital Image Correlation (DIC) is successfully applied to predict the uniaxial stress-strain response of 304 stainless steel specimens subjected to nominally uniform temperatures ranging from room temperature to 900 °C. A portable induction heating device equipped with custom made water-cooled copper coils is used to heat the specimen. The induction heater is used in conjunction with a conventional tensile frame to enable high temperature tension experiments. A stereovision camera system equipped with appropriate band pass filters is employed to facilitate the study of full-field deformation response of the material at elevated temperatures. Using the temperature and load histories along with the full-field strain data, a Virtual Fields Method (VFM) based approach is implemented to identify constitutive parameters governing the plastic deformation of the material at high temperature conditions. Results from these experiments confirm that the proposed method can be used to measure the full field deformation of materials subjected to thermo-mechanical loading.     

Single-element objective lens for soft x-ray differential interference contrast microscopy

High-resolution soft x-ray differential interference contrast (DIC) imaging was demonstrated through the use of a single-element objective, the XOR pattern, in a full-field soft x-ray microscope. DIC images of the magnetic domains in a 59 nm thick amorphous Gd25Fe75 layer were obtained and magnetic phase contributions were directly imaged. With its elemental, chemical, and magnetic specificity, compatibility with various sample environments, and ease of implementation, we expect this soft x-ray DIC technique to become one of the standard modes of operation for existing full-field soft x-ray microscopes.     

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     

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.     

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.     

Mechanical characterization of polytetrafluoroethylene polymer using full-field displacement method

The aim of this work is to estimate two important material properties of the polytetrafluoroethylene (PTFE) polymer by means of a single experimental test. The displacement fields around a crack tip are used for estimating the modulus of elasticity (or, Young's modulus) and Poisson's ratio. These parameters are evaluated by fitting linear fracture mechanic expression of displacement fields in the vicinity of the crack, for mode I, to the experimental data. Measurements of these displacements are carried out using digital image correlation (DIC) method. In this way, the experimental procedure is conducted by loading a double-edge-cracked plate specimen. In order to validate the results, two available experimental tests have been performed. The modulus of elasticity is determined by means of the tensile test, using a standard test machine. Moreover, the Poisson's ratio is obtained by measuring lateral compressive and longitudinal extensional strain using DIC method.     

High accuracy digital image correlation powered by GPU-based parallel computing

A sub-pixel digital image correlation (DIC) method with a path-independent displacement tracking strategy has been implemented on NVIDIA compute unified device architecture (CUDA) for graphics processing unit (GPU) devices. Powered by parallel computing technology, this parallel DIC (paDIC) method, combining an inverse compositional Gauss–Newton (IC-GN) algorithm for sub-pixel registration with a fast Fourier transform-based cross correlation (FFT-CC) algorithm for integer-pixel initial guess estimation, achieves a superior computation efficiency over the DIC method purely running on CPU. In the experiments using simulated and real speckle images, the paDIC reaches a computation speed of 1.66×10⁵ POI/s (points of interest per second) and 1.13×10⁵ POI/s respectively, 57–76 times faster than its sequential counterpart, without the sacrifice of accuracy and precision. To the best of our knowledge, it is the fastest computation speed of a sub-pixel DIC method reported heretofore.     

3-D computer vision in experimental mechanics

Optical methods that give displacement or strain fields are now widely used in experimental mechanics. Some of the methods can only measure in-plane displacements/strains on planar specimens and some of them can give both in-plane and out-of-plane displacement/strain fields on any kind of specimen (planar or not). In the present paper, the stereovision technique that uses two cameras to measure 3-D displacement/strain fields on any 3-D object is presented. Additionally, a quite inclusive list of references on applications of stereovision (and 3-D DIC) to experimental mechanics is given at the end of the paper.     

Optical extensometer and elimination of the effect of out-of-plane motions

A novel optical extensometer is developed to estimate the local uniform strain on planar surface accurately. The proposed system consists of a shared large format lens and two image sensors, which acquire pairs of images of two isolated small regions on the object surface simultaneously. Digital image correlation (DIC) algorithm is applied to determine the relative displacement between gauge points designated on recorded pairs of images. Then local strain can be extracted after dividing the relative displacement by the scale distance. Moreover, a special experimental setup called “correction sheet” is used to eliminate the virtual strain induced by out-of-plane motions. Uni-axial tensile experiments are performed to validate the reliability and resolution of the optical extensometer, and the measurement results demonstrate that the resolution of the optical extensometer achieves 2–3 με.