Two-dimensional Digital Image Correlation Research Articles

Finite element inversion method for interfacial stress analysis of composite single-lap adhesively bonded joint based on full-field deformation

A hybrid inversion method combining the finite element method and full-field displacement data was proposed to analyze the adhesive interface stress at a composite single-lap bonded joint. The displacement field distribution for the outer surface of the overlapped composite plate was measured through the two-dimensional digital image correlation method at different times by performing a tensile test. At the same time, the finite element analysis of the single-lap joint was carried out, which provided the data on structural deformation characteristics. Then, a polynomial interpolation method was used to establish the relation between the internal and external surface displacements. The displacements of the inner surface of the plate can be calculated from the measured displacement data of the outer surface of the plate by using the polynomial function. The displacements of the inner surface of the plate are regarded as the displacement load conditions for the outer and inner surfaces of the plate to establish the finite element model of the adhesive layer. The validity of the hybrid inversion method was proved by FEM analysis and experiments.

Utilizing Digital Image Correlation (DIC) in Asphalt Pavement Testing

Abstract The digital image correlation (DIC) technique as a displacement and strain measurement method is one of the newest measurement technologies employed in asphalt pavement testing. Although DIC was introduced for material testing in the early 1980s; this technology is not yet being used to its highest potential as a reliable and flexible method for measuring displacements and strains and, more importantly, for investigating cracking phenomena and fracture characteristics in asphalt pavement testing. This research aimed to study the requirements for ensuring a reliable and accurate DIC system and to demonstrate areas where the technique could be used to provide an edge over traditional measurement methods. Using proprietary two-dimensional DIC software, the parameters that affect the accuracy of test results were evaluated and the proper analysis configurations for investigating cracked areas were determined. The results showed that the DIC technique, if used properly, is an extremely powerful tool for studying damage progression and fracture characteristics in the fatigue and fracture testing of asphalt concrete.

High-accuracy optical extensometer based on coordinate transform in two-dimensional digital image correlation

In the measurement of plate specimens, traditional two-dimensional (2D) digital image correlation (DIC) is challenged by two aspects: (1) the slant optical axis (misalignment of the optical camera axis and the object surface) and (2) out-of-plane motions (including translations and rotations) of the specimens. There are measurement errors in the results measured by 2D DIC, especially when the out-of-plane motions are big enough. To solve this problem, a novel compensation method has been proposed to correct the unsatisfactory results. The proposed compensation method consists of three main parts: 1) a pre-calibration step is used to determine the intrinsic parameters and lens distortions; 2) a compensation panel (a rigid panel with several markers located at known positions) is mounted to the specimen to track the specimen’s motion so that the relative coordinate transformation between the compensation panel and the 2D DIC setup can be calculated using the coordinate transform algorithm; 3) three-dimensional world coordinates of measuring points on the specimen can be reconstructed via the coordinate transform algorithm and used to calculate deformations. Simulations have been carried out to validate the proposed compensation method. Results come out that when the extensometer length is 400 pixels, the strain accuracy reaches 10 με no matter out-of-plane translations (less than 1/200 of the object distance) nor out-of-plane rotations (rotation angle less than 5°) occur. The proposed compensation method leads to good results even when the out-of-plane translation reaches several percents of the object distance or the out-of-plane rotation angle reaches tens of degrees. The proposed compensation method has been applied in tensile experiments to obtain high-accuracy results as well.

High-accuracy biaxial optical extensometer based on 2D digital image correlation

In two-dimensional digital image correlation (2D-DIC), the optical axis of the camera must be exactly perpendicular to the object surface to avoid the generation of out-of-plane displacement, which leads to low strain accuracy. In this work, we first studied the strain accuracy of a common optical extensometer when the optical axis of the camera is not perpendicular to the specimen surface. Derivation reveals that even a very small oblique angle θ will introduce a considerable strain error and that an opposite oblique angle θ generates an opposite strain error of the same magnitude. Therefore, taking the strain average of these two optical extensometers can almost entirely eliminate such effect of non-perpendicularity, which has the same form as the optical extensometer realized by dual-reflector imaging. Because the transverse strain of a specimen is less than its axial strain, the measurement of transverse strain requires higher strain-measurement accuracy. With the aid of a self-designed right-angled apparatus, we conveniently extend this 1D extensometer to a 2D situation, which is called the biaxial optical extensometer. Uniaxial tensile tests of a stainless-steel specimen are conducted to evaluate the strain accuracy of the biaxial optical extensometer quantitatively. Experimental results show that the transverse and axial strains obtained using the proposed biaxial extensometer are in good agreement with those obtained using strain gauges and that the proposed extensometer achieves higher strain accuracy compared to the 3D-DIC extensometer.

An efficient approach for stereo matching of planar objects in stereo-digital image correlation

In many standard mechanical tests and in all two-dimensional digital image correlation (2D-DIC) applications, the surfaces of specimens to be measured are planar. For the special case of planar surfaces, in this paper an efficient approach for stereo matching was proposed to further improve the computation efficiency of stereo-DIC. The proposed stereo matching method utilizes the characteristic of planar objects that the projection transformation functions between left and right images are the same for all matched subsets and can be expressed by eight parameters. In each pair of images, four discrete points were matched to calculate the projection transformation matrix, and then the stereo matching of all other points could be accomplished based on the calculated projection transformation matrix in an easy and efficient way. Both simulations and experimental results demonstrated that the proposed method is feasible and effective and the computational speed is about 20 times faster than that of traditional method. Based on the proposed method, real-time stereo-DIC with a higher frame rate and more points should be achieved.

Damage Monitoring and Analysis of Fiber-Metal Laminates with an Open Hole Using Digital Image Correlation

Notched fiber-mental laminates are susceptible to damage. Nowadays, damage detection mainly depends on visual inspection and C scan. But the two methods are limited to the technical skill of the inspectors, causing missed detection or even fault detection. This paper devotes to exploring the DIC monitoring technique to assess of the damage process taking place in notched (open hole) specimens under uniaxial tensile loading. Two-dimensional (2D) Digital Image Correlation (DIC) techniques are employed to obtain full-field surface strain measurements of GLARE3-3/2 and GLARE6-3/2 laminate with an open circular hole under tensile loading. Failure modes,damage initiation and progression of notched fiber-metal laminates are characterized and discussed.

Material Flow Analysis in Indentation by Two-Dimensional Digital Image Correlation and Finite Elements Method.

The present work shows the material flow analysis in indentation by the numerical two dimensional Finite Elements (FEM) method and the experimental two-dimensional Digital Image Correlation (DIC) method. To achieve deep indentation without cracking, a ductile material, 99% tin, is used. The results obtained from the DIC technique depend predominantly on the pattern conferred to the samples. Due to the absence of a natural pattern, black and white spray painting is used for greater contrast. The stress-strain curve of the material has been obtained and introduced in the Finite Element simulation code used, DEFORM™, allowing for accurate simulations. Two different 2D models have been used: a plain strain model to obtain the load curve and a plain stress model to evaluate the strain maps on the workpiece surface. The indentation displacement load curve has been compared between the FEM and the experimental results, showing a good correlation. Additionally, the strain maps obtained from the material surface with FEM and DIC are compared in order to validate the numerical model. The Von Mises strain results between both of them present a 10–20% difference. The results show that FEM is a good tool for simulating indentation processes, allowing for the evaluation of the maximum forces and deformations involved in the forming process. Additionally, the non-contact DIC technique shows its potential by measuring the superficial strain maps, validating the FEM results.

High-Accuracy, High-Efficiency Compensation Method in Two-Dimensional Digital Image Correlation

The traditional two-dimensional (2D) digital image correlation (DIC) method often leads to results without enough accuracy due to the out-of-plane motions of the specimens in the deformation measurements of plate specimens. To remove the effects of the out-of-plane motions, a compensation method for the 2D DIC method has been developed. The compensation method sharply improves the measuring accuracy of the 2D DIC method. However, the existing compensation method often deduces compensation parameters with strong fluctuations. To solve these problems, an improved compensation method is proposed. The proposed method employs an extra single camera calibration to determine the distortion parameters so that the corresponding coefficient matrix is not affected by the experimental noise. For simplicity, the extensometer line measurement is taken as an example to compare the measuring accuracy of the two compensation methods. Static experiments have been carried out to analyze effects of different measuring parameters. Tensile experiments indicate that the measuring results of the improved compensation method are not only comparative with the results measured by the 3D DIC method but also accord with the results of the strain gage. Besides, a real-time extensometer measuring system with a measurement accuracy of 5 μe at a rate of 28 fps, has been developed.

A Projected Finite Element Update Method for Inverse Identification of Material Constitutive Parameters in transversely Isotropic Laminates

In this paper, a novel application of Finite Element Update Method (FEUM) is proposed for the inverse identification of material constitutive parameters in transversely isotropic laminates. Two-dimensional Digital Image Correlation (2D–DIC) is used for full-field measurements which is required for the identification process. Instead of measuring the in-plane displacements, which is a well-known application of 2D–DIC, we seek to measure the pseudo-displacements resulting from out-of-plane (towards camera) deflection of plate under a point load. These pseudo-displacements are basically the perspective projection of the three dimensional displacement fields on the image-plane of the image acquisition system. The cost function in this method is defined in terms of these projections instead of the true displacements – and hence the name Projected Finite Element Update Method (PFEUM). In this article, identification of in-plane elastic moduli of Carbon Fiber Reinforced Plastic (CFRP) plate has been performed using plate bending experiments which show pre-dominantly out-of-plane deflection with little contribution from the in-plane displacements. Identification results are validated by direct experimental measurements of the unknown elastic constants as well as theoretical estimates based on volume ratio of constituents. The results show good conformance between estimated and target values for at least three material parameters namely E1, E2 and G12. Effects of experimental noise on parameter estimates has also been evaluated to explain the observed deviation in estimated parameters with current test configuration.

Analysis of the ductility dip cracking in the nickel-base alloy 617mod

While testing steam leading power plant components made of the nickel-base alloy A617mod at elevated temperatures (700 °C), ductility dip cracking (DDC) was observed in welding seams and their surroundings. In order to clarify the mechanism of crack formation, investigations were carried out on welded specimens made of A617mod. Interrupted tensile tests were performed on tensile specimens taken from the area of the welding seam. To simulate the conditions, the tensile tests were conducted at a temperature of 700 °C and with a low strain rate. Local strain fields at grain boundaries and inside single grains were determined at different deformation states by means of two-dimensional digital image correlation (DIC). Besides the strain fields, local hardnesses (nanoindentation), energy dispersive X-Ray spectroscopy (EDX), and electron backscatter diffraction (EBSD) measurements were performed. Besides information concerning the grain orientation, the EBSD measurement provides information on the coincidence site lattice (CSL) at grain boundaries as well as the Schmid factor of single grains. All results of the analysis methods mentioned above were correlated and compared to each other and related to the crack formation. Among other things, correlations between strain fields and Schmid factors were determined. The investigations show that the following influences affect the crack formation: orientation of the grain boundaries to the direction of the loading, the orientation of the grains to each other (CSL), and grain boundary sliding.

Contribution of the Imaging System Components in the Overall Error of the Two-Dimensional Digital Image Correlation Technique

Abstract Digital image correlation (DIC) is one of the most widely used non-invasive methods for measuring full-field surface strains in a wide variety of applications. The DIC method has been used by numerous researchers for measuring strains during the plastic range of deformation where the strains are relatively large. The estimation of the amount of background strain error in the measurements is of prime importance for determining the applicability of this method for measuring small strains (such as the elastic strains in metals, ceramics, bone samples, etc.). In this study, the strain errors in 2D-DIC measurements associated with different types of imaging systems were investigated. In-plane rigid-body-translation, experiments were used to estimate the overall amount of error in DIC displacement and strain measurements. Different types of cameras having different types of sensors and different spatial resolutions were used in the study. Also, for the same type of camera, different types of lenses were used. Results show that the DIC measurement accuracy depends on the magnitude of image displacement and that different error estimation parameters can be used for quantifying the accuracy of the measurements. Also, the effect of the lens on measurement accuracy is more pronounced than that of the camera. Furthermore, imaging conditions such as image sharpness and camera gain also affect the accuracy. Further still, the measurement accuracy was found to be influenced by the direction of translation. The results indicate that measurement error can be reduced by orienting the camera such that the major displacement direction is parallel to the width direction of the image. The experimental approach used in this study can be used for quantitatively assessing the quality of the different types of cameras and lenses and to determine their suitability for use in experimental techniques that depend on image analysis such as DIC and particle image velocimetry (PIV).

Evolution of strain field in an over-matching welded joint under tension estimated using digital image correlation

Two-dimensional digital image correlation (2D-DIC) is a computer-based, non-contacting, surface deformation measurement. Using this method, the strain field was measured in the welded joint under tension. Due to the different mechanical properties, the strains are inhomogeneous in the different parts of the welded joint. Their differences were revealed, and the strain evolution in each part of the welded joint was estimated.

Novel projector calibration method for monocular structured light system based on digital image correlation

Monocular structured light system, which consists of one camera and one digital light processing (DLP) projector, is a simple and effective tool to acquire accurate three-dimensional (3D) shapes. But such high precision is only possible if the projector is accurately calibrated. Many of the existing projector calibration methods have complicated procedures or low calibration precision. In this paper, an accurate speckle-based feature points matching method is proposed to estimate the image coordinates of feature points in projection chip (digital micro-mirror device or DMD) plane. The method relies on an uncalibrated camera and makes use of affine transformation theory and two-dimensional digital image correlation (2D-DIC) method to reach sub-pixel matching precision. Considering the skew of the projection chip, a full-parameter calibration model is presented to describe the projector. A novel system is developed and series of validation tests were carried out to demonstrate the performance of the proposed method.

Self-calibration single-lens 3D video extensometer for high-accuracy and real-time strain measurement.

The accuracy of strain measurement using a common optical extensometer with two-dimensional (2D) digital image correlation (DIC) is not sufficient for experimental applications due to the effect of out-of-plane motion. Although three-dimensional (3D) DIC can measure all three components of displacement without introducing in-plane displacement errors, 3D-DIC requires the stringent synchronization between two digital cameras and requires complicated system calibration of binocular stereovision, which makes the measurement rather inconvenient. To solve the problems described above, this paper proposes a self-calibration single-lens 3D video extensometer for non-contact, non-destructive and high-accuracy strain measurement. In the established video extensometer, a single-lens 3D imaging system with a prism and two mirrors is constructed to acquire stereo images of the test sample surface, so the problems of synchronization and out-of-plane displacement can be solved easily. Moreover, a speckle-based self-calibration method which calibrates the single-lens stereo system using the reference speckle image of the specimen instead of the calibration targets is proposed, which will make the system more convenient to be used without complicated calibration. Furthermore, an efficient and robust inverse compositional Gauss-Newton algorithm combined with a robust stereo matching stage is employed to achieve high-accuracy and real-time subset-based stereo matching. Tensile tests of an Al-alloy specimen were performed to demonstrate the feasibility and effectiveness of the proposed self-calibration single-lens 3D video extensometer.

Deformation measurement using digital image correlation by adaptively adjusting the parameters

As a contactless full-field displacement and strain measurement technique, two-dimensional digital image correlation (DIC) has been increasingly employed to reconstruct in-plane deformation in the field of experimental mechanics. In practical application, it has been demonstrated that the selection of subset size and search zone size exerts a critical influence on measurement results of DIC, especially when decorrelation occurs between the reference image and the deformed image due to large deformation over the search zone involved. Correlation coefficient is an important parameter in DIC, and it also makes the most direct connection between subset size and search zone. A self-adaptive correlation parameter adjustment method based on correlation coefficient threshold to realize measurement efficiently by adjusting the size of the subset and search zone in a self-adaptive approach is proposed. The feasibility and effectiveness of the proposed method are verified through a set of experiments, which indicates that the presented algorithm is able to significantly reduce the cumbersome trial calculation as compared with the traditional DIC, in which the initial correlation parameters needed to be manually selected in advance based on practical experience.

Self-correction method of out-of-plane motions in two-dimensional digital image correlation

Strain monitoring is very important in the manufacturing, assembling, installation and servicing processes in both mechanical and civil engineering fields. Two-dimensional digital image correlation is a simple, efficient strain monitoring method, but one major bottleneck is the unacceptable error due to the unavoidable out-of-plane motions of the object in practice. We propose a “self-correction” method: employing the originally extracted strain values in different directions to correct the errors due to out-of-plane motions. It is applicable to many engineering applications with known relationship of strains in different directions. A uniaxial tension test was conducted to demonstrate the effectiveness and practicality of this self-correction method. Compared with other correction methods, this method is not only simpler but also more efficient in correcting errors due to the lens distortion caused by self-heating. Both the experiment and theoretical analyses demonstrate that this self-correction method maintains the high accuracy of the digital image correlation method.

A Review of Surface Deformation and Strain Measurement Using Two-Dimensional Digital Image Correlation

AbstractAmong the full-field optical measurement methods, the Digital Image Correlation (DIC) is one of the techniques which has been given particular attention. Technically, the DIC technique refers to a non-contact strain measurement method that mathematically compares the grey intensity changes of the images captured at two different states: before and after deformation. The measurement can be performed by numerically calculating the displacement of speckles which are deposited on the top of object’s surface. In this paper, the Two-Dimensional Digital Image Correlation (2D-DIC) is presented and its fundamental concepts are discussed. Next, the development of the 2D-DIC algorithms in the past 33 years is reviewed systematically. The improvement of 2DDIC algorithms is presented with respect to two distinct aspects: their computation efficiency and measurement accuracy. Furthermore, analysis of the 2D-DIC accuracy is included, followed by a review of the DIC applications for two-dimensional measurements.

Integration of fringe projection and two-dimensional digital image correlation for three-dimensional displacements measurements

A low-cost approach for three-dimensional (3-D) full-field displacement measurement is applied for the analysis of large displacements involved in two different mechanical events. The method is based on a combination of fringe projection and two-dimensional digital image correlation (DIC) techniques. The two techniques have been employed simultaneously using an RGB camera and a color encoding method; therefore, it is possible to measure in-plane and out-of-plane displacements at the same time with only one camera even at high speed rates. The potential of the proposed methodology has been employed for the analysis of large displacements during contact experiments in a soft material block. Displacement results have been successfully compared with those obtained using a 3D-DIC commercial system. Moreover, the analysis of displacements during an impact test on a metal plate was performed to emphasize the application of the methodology for dynamics events. Results show a good level of agreement, highlighting the potential of FP + 2D DIC as low-cost alternative for the analysis of large deformations problems.

Exploiting measurement-based validation for a high-fidelity model of dynamic indentation of a hyperelastic material

The high-speed (up to 1m/s) loading and unloading of a rubber block by a rigid wedge has been simulated using a finite element model. The model has been refined and validated using measured data obtained from combined fringe projection and two-dimensional digital image correlation during the real-time loading and unloading of a rubber block by an aluminium wedge. Comprehensive data was obtained from the experiment in the spatial and temporal domains at resolutions of 0.075mm and 0.00125s respectively. Image decomposition techniques were used to represent the predicted and measured displacement fields in order to allow a number of quantitative measures to be employed to assess the fidelity of the model. It was demonstrated that it was essential to refine the Mooney–Rivlin material model to provide an accurate representation of the material behaviour for the speeds of the loading and unloading. The refined model was validated using the European Committee for Standardization (CEN) procedure and found to exhibit differences relative to the experiment of less than 5%. Together the predicted and measured data fields probably represent the best description yet of a soft material being deformed by a rigid indenter.

Fracture-based forming limit criteria for anisotropic materials in sheet metal forming

This paper is concerned with modeling of fracture-based forming limit criteria for anisotropic materials in sheet metal forming to predict the sudden fracture in complicated forming processes. The Lou–Huh ductile fracture criterion is modified using the Hill's 48 anisotropic yield function instead of the von Mises isotropic yield function to take account of the influence of anisotropy on the equivalent plastic strain at the onset of fracture. For the derivation of an anisotropic ductile fracture criterion, the principal stresses (σ1,σ2,σ3) are expressed in terms of the stress triaxiality, the Lode parameter, and the equivalent stress (ηH,LP,σ¯H) based on the Hill's 48 yield function. Three different kinds of fracture-based forming limit criteria are suggested and investigated with an assumption that the stress state is under the plane stress condition with proportional loading. To determine the parameters of the model proposed, the two-dimensional digital image correlation (2D-DIC) method is utilized to measure the strain histories on the surface of three different types of specimens during deformation and the measurement results are investigated to identify the anisotropy effect on the equivalent plastic strain at the onset of fracture. This paper also discusses about a scaling method for a strain-based fracture forming limit criterion in order to capture the onset of fracture using a single forming limit curve for an anisotropic material. From the comparison of various forming limit criteria suggested, it is concluded that a polar effective plastic strain-based (PEPS) fracture forming limit diagram (FFLD) is suitable for prediction of the sudden fracture in AHSS sheets in complicated sheet metal forming processes on the basis of its path independence and simplicity of measuring strains in real forming processes.