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.     

An approach to calculate the J‐integral by digital image correlation displacement field measurement

This paper presents a combined experimental‐numerical technique for the calculation of the J‐integral as an area integral in cracked specimens. The proposed technique is based on full‐field measurement using digital image correlation (DIC) and the finite element method. The J‐integral is probably the most generalised and widely used parameter to quantify the fracture behaviour of both elastic and elastoplastic materials. The proposed technique has the advantage that it does not require crack length measurements nor is it limited to elastic fracture mechanics, provided that only small scale yielding is present. Evaluated are three test geometries; compact tension, three‐point bend and the double torsion beam. Possible errors and their magnitude and the limitations of the method are considered.     

Evaluating the use of digital image correlation for strain measurement in historic tapestries using representative deformation fields

An analysis technique to assess the viability of digital image correlation (DIC) in tracking the full‐field strains across the surface of hanging historic tapestries is presented. Measurement uncertainty related to the use of the inherent tapestry image in tracking displacements is investigated through use of “synthetic” deformation fields. The latter are generated by mapping the details of a given tapestry image into finite element analyses. The combination of self‐weight loading, material non‐linearity, and image specific heterogeneity (related to slit stitching, damage, and patch‐restorations) serve to generate a bespoke deformation field complex enough to assess the reliability of DIC measurements. Accuracy is evaluated by comparing measured results with the original known deformations. The technique demonstrates that the optimum imaging settings and the choice of subset size for DIC analysis are strongly influenced by the tapestry image and the goal of the measurement, they are found using a compromise between conflicting objectives: minimising measurement error while maximising resolution.     

Time‐resolved integrated digital image correlation

This paper discusses a method that provides the direct identification of constitutive model parameters by intimately integrating the finite element method (FEM) with digital image correlation (DIC), namely, directly connecting the experimentally obtained images for all time increments to the unknown material parameters. The problem is formulated as a single minimization problem that incorporates all the experimental data. It allows for precise specification of the unknowns, which can be, but are not limited to, the unknown material properties. The tight integration between FEM and DIC enables for identification while providing necessary regularization of the DIC procedure, making the method robust and noise insensitive. Through this approach, the versatility of the FE method is extended to the experimental realm, enhancing the analyses of existing experiments and opening new experimental opportunities. Copyright © 2015 John Wiley & Sons, Ltd.     

Thermal deformation measurement of flip-chip substrate using digital image correlation method

With the accelerated development of electronic products, flip-chip packaging has become one of the most prominently used and efficient designs in the integrated circuit (IC) industry. In daily application, the IC chip will be subjected to a temperature increase when it is in operation. With the rise in temperature, the chip is liable to a series of deformations which lead to possible malfunction of the IC unit. Therefore, the investigation of thermal deformation of flip-chip substrates is important. In this study, the thermal deformation of flip-chip substrates is measured with dual-camera digital image correlation technology, and with the measured data, a basis is established to predict the warpage conditions and strain tendencies of substrates due to thermal effect. Experiments were carried out with the substrates heated from room temperature to 200°C in a specialized vacuum-sealed oven. The topographic surface profile at higher temperatures can be obtained by adding the measured deformation to the surface profile of the substrates at room temperature. Experimental results show that the center area of the specimen had been warped up around 90?µm from the initial condition and the warpage effect of the substrate is obvious when the temperature increases to 200°C. The related maximum normal and shear strains are also discussed.     

On image gradients in digital image correlation

In digital image correlation (DIC), the unknown displacement field is typically identified by minimizing the linearized form of the brightness conservation equation, while the minimization scheme also involves a linearization, yielding a two‐step linearization with four implicit assumptions. These assumptions become apparent by minimizing the non‐linear brightness conservation equation in a consistent mathematical setting, yielding a one‐step linearization allowing a thorough study of the DIC tangent operator. Through this analysis, eight different image gradient operators are defined, and the impact of these alternative image gradients on the accuracy, efficiency, and initial guess robustness is discussed on the basis of a number of academic examples and representative test cases. The main conclusion is that for most cases, the image gradient most common in literature is recommended, except for cases with: (1) large rotations; (2) initial guess instabilities; and (3) costly iterations due to other reasons (e.g., integrated DIC), where a large deformation corrected mixed gradient is recommended instead. Copyright © 2015 John Wiley & Sons, Ltd.     

采用数字图像相关方法的莫来石纤维增强气凝胶复合材料力学试验

基于V型缺口试样双轨剪切法设计了面内剪切试验方案,开展了莫来石纤维增强气凝胶复合材料的室温面内剪切和弯曲性能试验,采用数字图像相关方法对试样表面的位移场和应变场进行测量,并分析了力学行为和破坏模式。结果表明:设计的试验方案可以在测试区域获得均匀的剪切应变场,适用于莫来石纤维增强气凝胶复合材料的面内剪切性能测试。试验获得的面内剪切模量和强度分别为248 MPa和0.95 MPa,弯曲模量和强度分别为294 MPa和2.08 MPa。面内剪切载荷下,试样的裂纹萌生于缺口尖端附近,并沿两缺口连线方向扩展。根据弯曲正应变场的分布特点,发现试样中性层与几何对称面不重合,验证了该材料拉压模量不同的性质。采用数字图像相关方法获得的中性层位置和理论计算值比较接近,相对误差在10%左右。     

Low-cost digital image correlation and strain measurement for geotechnical applications

Particle image velocimetry (PIV), or digital image correlation (DIC), is a widely used technique to measure soil displacements and strains in small-scale geotechnical models. Arrays of single-board computers (SBCs) produced by Raspberry Pi, and their associated 8-MP cameras, are being used at the University of Cambridge to capture the images required for DIC analysis. This alternative to more expensive camera set-ups has numerous advantages. A single expensive and large camera can be replaced—at low cost—by multiple cameras, adding flexibility and affordability to any experimental set-up. Traditionally, the alignment of multiple cameras to each other and the referencing to a known coordinate system required painted or machined markers to be located on the observation windows through which the experiments are viewed. This can obstruct localised soil grain displacement measurements in those areas of the model where such markers are placed. To complement the Raspberry Pi camera system, a markerless calibration method was used during image acquisition. This paper outlines the set-up of four of these small computers and associated cameras, provides an overview of the use of the markerless referencing system and reviews two different experimental apparatus used to measure soil displacement and strain. When the cost of additional cabling, connectors and mounting hardware is considered for this system, the total cost to implement was approximately $125 USD per camera plus one-time costs of $175 USD for system peripherals, which represents outstanding value and enables practically all geotechnical laboratories to develop similar capabilities.     

Extended digital image correlation with crack shape optimization

The methodology of eXtended finite element method is applied to the measurement of displacements through digital image correlation. An algorithm, initially based on a finite element decomposition of displacement fields, is extended to benefit from discontinuity and singular enrichments over a suited subset of elements. This allows one to measure irregular displacements encountered, say, in cracked solids, as demonstrated both in artificial examples and experimental case studies. Moreover, an optimization strategy for the support of the discontinuity enables one to adjust the crack path configuration to reduce the residual mismatch, and hence to be tailored automatically to a wavy or irregular crack path. Copyright © 2007 John Wiley & Sons, Ltd.     

Subpixel precision of crack lip movements by Heaviside-based digital image correlation for a mixed-mode fracture

This study reports on the Heaviside-based digital image correlation (H-DIC) procedure and its application in fracture analysis. This improved DIC procedure was proposed to solve the uncertainty problems at the vicinity of the crack and to evaluate the opening and shear movements of crack lips and the orientations of cracks in the subset. Some tests were conducted to demonstrate the performance of the H-DIC algorithm. An application on argillaceous rock mass exhibiting multiple mixed-mode fractures is shown to validate the efficiency and robustness of the proposed method. This application consisted in processing images acquired from an experimental investigation performed in a gallery front submitted to climatic seasonal variations. The results illustrated how the H-DIC procedure enables to localise and to quantify the opening, shearing and orientation of subpixel cracks. A sensibility study performed on the opening and shear components demonstrated that the precision of crack aperture by H-DIC procedure is close to 0.14 pixel and the spatial resolution is equal to one pixel. Moreover, the crack area was calculated from local apertures on a monitoring duration of 1 year, and a maximum value of 595.8 mm² in winter was obtained.     

NiCr/ZrO2功能梯度复合材料中混合型准静态裂纹启裂的数字散斑相关方法实验研究

采用粉末冶金方法制备出NiCr/ZrO₂功能梯度材料FGMs。通过2种断裂试件研究了材料梯度对混合型断裂行为的影响(FGM-A试件,裂纹位于试件的弹性模量较大一侧;FGM-B试件,裂纹位于试件的弹性模量较小一侧)。对2种断裂试件在非对称载荷下进行准静态断裂实验,并利用数字散斑相关方法测得Ⅰ、Ⅱ型应力强度因子。结果表明：FGM-A的裂纹的开裂角小于FGM-B的开裂角;FGM-A的弹性梯度对静态裂纹有保护作用;弹性模量的梯度变化和裂尖局部材料的断裂韧性会影响混合型裂纹的启裂。     

Improvement of the digital image correlation close to the borders of an object

The measurement error of the finite-element-based Digital Image Correlation is reduced along the borders of an object by using the precise measurement, obtained by Virtual Image Correlation (VIC). The proposed method is called Virtual and Digital Image Correlation (VDIC). The boundary, identified by the VIC with a subpixel precision, is used firstly to create an adapted mesh and secondly to create a pixel mask. Futhermore, the VDIC also uses the VIC measurement of the boundary in the deformed state as a constraint on the radial displacement field along the border. The optimal values of the parameters of the VDIC are discussed throughout a sensitivity analysis. The compared performances of the constrained and unconstrained VDIC are obtained thanks to a synthetic test of a plate with a hole in tension. Finally, the method is checked on a sample geometry which includes holes and a U-shaped notch.     

基于数字图像相关方法的气凝胶复合材料各向异性热变形测量

在热防护材料及结构高温力学性能研究中,测量其在热载荷与机械载荷作用下产生的变形是重要且基础的工作。基于数字图像相关方法,建立了可实现800℃变形测量的非接触式测量系统。针对陶瓷纤维增强SiO_2气凝胶复合材料,从面外和面内两个材料方向,以25℃为参考温度,试验测量了材料加热至300~800℃范围内不同温度时产生的热变形。研究结果表明,在此试验系统基础上的变形测量方法可用来测量此类热防护材料的高温变形。陶瓷纤维增强SiO2气凝胶复合材料的高温热变形具有明显的各向异性,面外方向上表现为"收缩",面内方向上表现为"膨胀"。SiO_2气凝胶基体中的颗粒团聚以及增强纤维在面内方向上的铺层分布是导致热变形各向异性的主要原因。     

Measurement of large,discontinuous displacement from digital images

One main limitation of conventional digital image correlation (DIC) methods is their incapacity to treat with large, discontinuous displacements. This paper seeks to resolve this issue using a variational method. Specifically, the objective function is written in a form of L¹-norm instead of L²-norm for discontinuity preservation. This convex, non-differentiable objective function is resolved by a proximal gradient method. Then, the entire correlation process is embedded into a multi-level image pyramid, enabling large displacements to be measured accurately. The proposed method is first validated on images with prescribed small displacements; its performance to treat with discontinuous, large displacements is then examined. The results show that the proposed method exhibits an acceptable performance when measuring some extreme displacements up to 16.5 pixels in a 500 × 500 pixels resolution image. Concerning subpixel accuracy, the errors can be lessened to a very low level with optimised parameters even for a dense correlation at each pixel. Good performance is also demonstrated in forms of noise proof and illumination fluctuation tolerance. Finally, an application is conducted on an experiment concerned with cracking in desiccated soils, in which the proposed method succeeds in tracking the nucleation and propagation processes of multiple cracks.     

Displacement field denoising for high-temperature digital image correlation using principal component analysis

Principal component analysis (PCA) was extended to minimize the noise effect in digital image correlation (DIC) measurement under a high-temperature atmosphere environment. First, the principle of PCA was introduced, and the singular vectors and singular values for each component of the displacement fields from DIC were obtained. Then, the simulated high-temperature speckle images were developed to investigate the influences of noise on the DIC method under a high-temperature environment. Finally, the displacement fields of several special conditions were extracted from the simulated speckle images and experimental images; the effects of noise on the PCA were also analyzed.     

Nylon-230T/TPU织物蒙皮撕裂性能的数值模拟和试验研究

针对每平方厘米由230根尼龙纱平纹编织并复合热塑性聚氨酯（Nylon-230T/TPU）的织物蒙皮,通过数值模拟和撕裂试验研究了预制裂纹对其撕裂性能的影响,主要包括裂纹长度、裂纹倾斜角度和裂纹位置对蒙皮撕裂强度的影响,通过数字图像相关技术（DIC）获取蒙皮撕裂过程中的应变场,研究了撕裂过程中蒙皮应变场变化规律;分别利用扩展有限元法（XFEM）、内聚力单元法（CZM）及虚拟裂纹闭合技术（VCCT）对预制裂纹Nylon-230T/TPU织物蒙皮的裂纹扩展过程和路径进行了数值模拟,模拟结果与试验结果吻合较好。研究结果表明：Nylon-230T/TPU织物蒙皮的撕裂强度与预制裂纹长度、裂纹倾斜角度及裂纹位置都密切相关;裂纹极大地影响了蒙皮的应变场分布;本文数值模拟方法能够准确预测织物蒙皮裂纹的扩展过程和路径。     

Digital image correlation measurement of near‐tip fatigue crack displacement fields: constant amplitude loading and load history effects

Recent work by de Matos and colleagues employed digital image correlation to measure near tip displacement fields for fatigue cracks in 6082 T6 aluminium alloy. The main focus of this work was to directly measure fatigue crack closure, but the measurements can also be used to examine conditions at and ahead of the crack tip. In this paper, the results are re‐analysed and compared to two crack‐tip deformation models. The first assumes simple elastic deformation (according the Westergaard solution). This allows the history of crack‐tip stress intensity to be examined. Reasonable agreement with the elastic model is obtained, although there is a residual stress intensity caused by the plastic wake, which gives rise to crack closure. The second model examined is a simple elastic–plastic assumption, proposed by Pommier and colleagues. This can be applied to constant amplitude loading, although the results obtained here are very similar to the elastic case. A slightly more complex load case (a single overload in an otherwise constant amplitude variation of load) gives a much more complicated crack‐tip history. Here, the importance of crack‐tip plastic displacement, represented by the second term in Pommier's model becomes much clearer. Load history effects are captured by the residual value of this term and its associated displacement fields as well as by stress intensity factor. The implications for further modelling and experimental work are discussed.     

数字图像技术在航空铝合金形变测量中的应用

利用DIC(Digital image correlation)非接触全场应变测量系统分析2024铝合金板材静态拉伸应变场。对散斑质量参数、图像采集系统参数进行正交试验优化。优化结果表明,影响散斑质量的主次因素及最优结果分别为:散斑半径0.02in,散斑密度50%,散斑分布随机性69%;影响图像采集系统的主次因素及最优结果分别为:子集大小59个像素,步长值12个像素,相机间的角度20~25°,光圈值5.6~8。采用该优化参数测量无孔及不同开孔尺寸铝合金板材静态拉伸应变场。首先,对无孔试样裂纹两侧取点,研究裂纹扩展趋势,判定裂纹源及相应载荷。其次,研究长短轴之比及开孔面积对力学性能的影响,并沿孔径方向取点,分析局部应变情况。研究表明,越靠近开孔位置,应变越集中。减小开孔面积,降低开孔的长短轴之比,可以有效降低试样的应变集中系数,延长使用寿命。最后,对比分析非接触测量方法、引伸计法及Patran建模仿真方法试验结果。     

Digital image correlation analysis of vertical strain for corrugated fiberboard box panel in compression

This work was aimed at examining the overall contributions to displacement of panels of compressed boxes, such as panel compression strain and flap and crease displacements. 3D digital image correlation (DIC) was used to analyse motion of side panels of corrugated fiberboard regular slotted containers. The vertical displacement and the vertical component of strain of the panel face during box compression test were examined. Measuring displacements of the whole compressed box with DIC enables measurement of the in‐plane compression of a panel in isolation from the horizontal fold or crease zone displacement, without having to test tube sections of the box to infer or extract the in‐plane panel compression behaviour. Detailed study of two box designs in three representative test cases was presented, which in future could be extended to other box designs. At peak load, the in‐plane compression of the panels, calculated from the average vertical component of the strain along the right edge of the long panel of the box, was 3% to 6% of total crosshead displacement for the test cases. At peak load, the portion of the box compression associated with bottom box flaps or crease zone crushing was 48% to 59% of total crosshead displacement for the different cases. The analysis showed that the majority of the vertical displacement of the box occurred in the top and bottom creased folds and that these folds are responsible for the low apparent in‐plane stiffness of a box.     

Use of digital image correlation to measure strain recovery in particle toughened thermoset resins

A methodology for finding the yield point of epoxy resins, both neat and particulate toughened, is described. Trends of the effect that particulate filling has on the time dependent response of these materials were constructed from observations made with stereo‐based digital image correlation (3D–DIC), namely, creep and stress relaxation at constant load. The use of 3D–DIC also enabled the observation of differences in deformation mechanisms resulting from the particle addition. The focus is put on the technique's potential to characterise materials and produce clear relationships between composition and mechanical strain response. The methodology proposed herein allows the observation and study of multiple deformation mechanisms from a single test, and thus can potentially minimise the number of specimens needed for a comprehensive test campaign.