数字图像相关法测量局域变形场中形函数和模板尺寸的影响

数字图像相关法测量均匀变形场已被普遍接受, 其测量结果可与应变片测量结果比较. 然而, 在工程测量中, 针对局域变形场(应变高度集中, 如波特文-勒夏特利埃带、试件缺口附近和裂纹尖端等), 应变片受限于其尺寸, 其测量结果是接触面内的平均应变值. 此时, 采用数字图像相关法能够测量这些局域变形场. 但形函数和模板尺寸等计算参数对计算结果影响很大, 这也导致使用者很难判断计算结果的可靠性. 论文通过对合金拉伸实验获得的不同应变梯度的波特文-勒夏特利埃带和模拟生成的带的计算分析, 发掘了形函数和模板尺寸作用于计算结果的深层机制, 证明了二阶形函数比一阶形函数更适用于高度非均匀的局域变形场. 提出了在局域应变场测量中, 当一阶和二阶形函数计算结果的相对误差小于10% 时, 二阶形函数的结果是可靠的判据.      

Absolute Nodal Coordinates in Digital Image Correlation

A great deal of progress has been made in recent years in the field of global digital image correlation (DIC), where higher-order, element-based approaches were proposed to improve the interpolation performance and to better capture the displacement fields. In this research, another higher-order, element-based DIC procedure is introduced. Instead of the displacements, the elements’ global nodal positions and nodal position-vector gradients, defined according to the absolute nodal coordinate formulation, are used as the searched parameters of the Newton–Raphson iterative procedure. For the finite elements, the planar isoparametric plates with 24 nodal degrees of freedom are employed to ensure the gradients’ continuity among the elements. As such, the presented procedure imposes no linearization on the strain measure, and therefore indicates a natural consistency with the nonlinear continuum theory. To verify the new procedure and to show its advantages, a real large deformation experiment and several numerical tests on the computer-generated images are studied for the standard, low-order, element-based digital image correlation and the presented procedure. The results show that the proposed procedure proves to be accurate and reliable for describing the rigid-body movement and simple deformations, as well as for determining the continuous finite strain field of a real specimen.     

数字图像相关方法中匹配及过匹配形函数的误差分析

基于图像子区的数字图像相关方法需采用合适的形函数来近似目标图像子区的真实变形。由于实际测量时目标子区的局部变形往往是未知的,实际采用的不同阶次(零阶、一阶和二阶)的形函数不可避免地产生误匹配(欠匹配和过匹配)问题,从而引入位移测量的系统或随机误差。尽管由欠匹配形函数引起的系统误差已被充分认识,由过匹配形函数引起的位移误差仍缺少理论解释。本文首先推导出采用一阶和二阶形函数的数字图像相关方法的随机误差理论公式,随后采用一系列数值实验验证了理论公式的准确性。结果显示:过匹配形函数不会引入额外的系统误差,但会增加随机误差,且二阶形函数的随机误差是一阶形函数的二倍。考虑到由欠匹配一阶形函数引入的系统误差往往远大于过匹配二阶形函数的随机误差,因此在未能确知变形的情况下,推荐使用二阶形函数。     

An Error Criterion in Digital Image Correlation for Unknown Deformation Fields and Its Application of Parameters Selection

Digital image correlation (DIC) is a widely used optical metrology for surface deformation measurement. In DIC, the square root of the mean square error (RMS error) and standard deviation error (SD error) are used as quantitative criteria in order to evaluate the accuracy and robustness of a DIC method\algorithm. However, RMS and SD error criteria are computed from prescribed and measured displacements, which indicates that the prescribed displacement fields must be precisely generated. Therefore, it is difficult to quantitatively evaluate the accuracy and robustness of an algorithm\method in practical DIC measurements because imposed displacements are unknown (that’s why DIC measurements are needed). Moreover, the accuracy of DIC measurements highly relies on parameters selection, especially the selections of subset size and shape function. In practice, the subset size and shape function are usually selected according to experience because there are numerous factors (e.g. the quality of speckle image, local displacement field) and uncertainties (e.g. noise level, out-of-plane motion, illumination lighting fluctuation during image capturing) that affect the parameters selection, which makes it difficult to select optimal parameters based on previous works which mainly focused on theoretical deduction in ideal condition. In this paper, an error criterion for evaluating the accuracy of practical DIC measurements with unknown displacements is proposed. Numerical experiments are used to validate the effectiveness and feasibility of the proposed criterion for accuracy evaluation. It is concluded that the square root of the sum of squared forward and backward displacements difference (SFBD) error has a significant positive linear correlation with the widely used SD error in most practical DIC measurements where the mismatch between the frequently-used first- and second-order shape functions and the actual field is usually small. Also, an application of the proposed criterion is presented by real experiments for subset size and shape function selections, which verifies that the proposed error criterion can be effectively used for DIC parameters selection.     

图像相关法在高分子材料拉伸性能研究中的应用

本文对聚碳酸酯(PC)和丙烯腈丁二烯苯乙烯(ABS)的合金(PC/ABS)高分子材料不同环境温度下的拉伸性能进行了试验研究。根据图像相关分析法编制了图像法位移测量分析软件,并对该分析软件的适用性进行了分析。系统研究了PC/ABS高分子材料拉伸试验时三个方向的位移场和应变场。根据测得的位移场研究了该高分子材料拉伸过程中应变和应变率的变化以及应力应变变化规律,并对试验结果进行了详细分析。结果表明,文中采用的图像法位移测量系统具有较高的测试精度;拉伸过程中,试件厚度方向的收缩变形大于宽度方向的收缩变形;颈缩过程区具有非常高的应变率,颈缩后的平直颈缩区的应变率快速下降到一个很低的应变率继续缓慢变形;尽管载荷位移曲线出现了较大的载荷下降现象,PC/ABS拉伸时的真应力应变曲线没有明显的应力下降现象出现,因此,载荷下降现象主要由颈缩时的截面减小引起;高分子材料PC/ABS的屈服应力随环境温度的升高而降低。     

Sensitivity of in-Plane Strain Measurement to Calibration Parameter for out-of-Plane Specimen Rotations

In practice, out-of-plane motions usually are not avoidable during experiments. Since 2D–DIC measurements are vulnerable to parasitic deformations due to out-of-plane specimen motions, three-dimensional digital image correlation (StereoDIC or 3D–DIC) oftentimes is employed. The StereoDIC method is known to be capable of accurate deformation measurements for specimens subjected to general three-dimensional motions, including out-of-plane rotations and displacements. As a result, there has been limited study of the deformation measurements obtained when using StereoDIC to measure the displacement and strain fields for a specimen subjected only to out-of-plane rotation. To assess the accuracy of strain measurements obtained using stereovision systems and StereoDIC when a specimen undergoes appreciable out of plane rotation, rigid body out-of-plane rotation experiments are performed in the range ?40⁰?≤?θ?≤?40⁰ using a two-camera stereovision system. Results indicate that (a) for what would normally be considered “small angle” calibration processes, the measured normal strain in the foreshortened specimen direction due to specimen rotation increases in a non-linear manner with rotation angle, with measurement errors exceeding ±1400με and (b) for what would normally be considered “large angle” calibration processes, the magnitude of the errors in the strain are reduced to ±300με. To theoretically assess the effect of calibration parameters on the measurements, two separate analyses are performed. First, theoretical strains due to out-of-plane rigid body rotation are determined using a pinhole camera model to project a series of three-dimensional object points into the image plane using large angle calibration parameters and then re-project the corresponding sensor plane coordinates back into the plane using small angle calibration parameters. Secondly, the entire imaging process is also simulated in order to remove experimental error sources and to further validate the theory. Results from both approaches confirmed the same strain error trends as the experimental strain measurements, providing confidence that the source of the errors is the calibration process. Finally, variance based sensitivity analyses show that inaccuracy in the calibrated stereo angle parameter is the most significant factor affecting the accuracy of the measured strain.     

基于双线性位移模式数字图像相关方法的误差分析及应用

探讨数字图像相关方法测试结果的误差分布规律对提高该方法的测试精度具有重要意义。本文从理论上分析了基于双线性位移模式数字图像相关方法的子区变形场测试误差分布规律,结果表明,当试件的真实变形可由双线性位移模式描述时,变形场最大测试误差通常出现在子区的边界或节点处。因此,若试件发生均匀拉伸等常应变变形,可利用相关系数选取一个最优子区,认为测得最优子区中心应变为试件真实应变。零变形实验验证了该测试方法的可靠性。最后对手机导光板试件在单轴拉伸载荷下的数字图像进行分析,并利用本文方法测试了其弹性常数。     

Measurement of Local Thermal Deformations in Heterogeneous Microstructures via SEM Imaging with Digital Image Correlation

It is challenging to measure accurately and with high spatial resolution the local thermal strains in heterogeneous microstructures due of the complex nature of the thermal deformations and local boundary conditions. In the enclosed study, a digital image correlation (DIC) based, thermal strain mapping technique is described that is able to probe thermal deformations with sub-micron spatial resolution and sub-nanometer displacement accuracy for both homogeneous and heterogeneous materials, including cross-sections of IC packages. The full-field thermal deformation maps of different materials within a nanostructured IC chip cross-section are established from room temperature up to 160 °C, uncovering the heterogeneous nature of the specimen while accurately measuring the highly non-uniform displacement and strain fields across the multiple material constituents. As described in this work, the DIC-enabled technique is capable of high resolution mapping of local thermo-mechanical deformations in heterogeneous materials, providing a methodology that can improve our understanding of complex material systems under controlled thermal-environmental conditions.     

A Robust Finite Element-based Filter for Digital Image and Volume Correlation Displacement Data

Background

Digital Image and Volume Correlation (DIC and DVC) are non-contact measurement techniques that are used during mechanical testing for quantitative mapping of full-field displacements. The relatively high noise floor of DIC and DVC, which is exasperated when differentiated to obtain strain fields, often requires some form of filtering. Techniques such as median filters or least-squares fitting perform poorly over high displacement gradients, such as the strain localisation near a crack tip, discontinuities across crack flanks or large pores. As such, filtering does not always effectively remove outliers in the displacement field.

Objective

This work proposes a robust finite element-based filter that detects and replaces outliers in the displacement data using a finite element method-based approximation.

Methods

A method is formulated for surface (2D and Stereo DIC) and volumetric (DVC) measurements. Its validity is demonstrated using analytical and experimental displacement data around cracks, obtained from surface and full volume measurements.

Results

It is shown that the displacement data can be filtered in such a way that outliers are identified and replaced. Moreover, data can be smoothed whilst maintaining the nature of the underlying displacement field such as steep displacement gradients or discontinuities.

Conclusions

The method can be used as a post-processing tool for DIC and DVC data and will support the use of the finite element method as an experimental–numerical technique.

     

A q-Factor-Based Digital Image Correlation Algorithm (qDIC) for Resolving Finite Deformations with Degenerate Speckle Patterns

Digital image correlation (DIC) has become a widely utilized non-contact, full-field displacement measurement technique for obtaining accurate material kinematics. Despite the significant advances made to date, high resolution reconstruction of finite deformations for images with intrinsically low quality speckle patterns or poor signal-to-noise content has not been fully addressed. In particular, large image distortions imposed by materials undergoing finite deformations create significant challenges for most classical DIC approaches. To address this issue, this paper describes a new open source DIC algorithm (qDIC) that incorporates cross-correlation quality factors (q-factors), which are specifically designed to assess the quality of the reconstructed displacement estimate during the motion reconstruction process. A q-factor provides a robust assessment of the uniqueness and sharpness of the cross-correlation peak, and thus a quantitative estimate of the subset-based displacement measure per given image subset and level of applied deformation. We show that the incorporation of energy- and entropy-based q-factor metrics leads to substantially improved displacement predictions, lower noise floor, and reduced decorrelation even at significant levels of image distortion or poor speckle quality. Furthermore, we show that q-factors can be utilized as a quantitative metric for constructing a hybrid incremental-cumulative displacement correlation scheme for accurately resolving very large homogeneous and inhomogeneous deformations, even in the presence of significant image data loss.     

Quantitative Strain Analysis of the Large Deformation at the Scale of Microstructure: Comparison between Digital Image Correlation and Microgrid Techniques

A comparative study has been carried out to assess the accuracy of the Digital Image Correlation (DIC) technique for the quantification of large strains in the microstructure of an Interstitial Free (IF) steel used in automotive applications. A microgrid technique has been used in this study in order to validate independently the strain measurements obtained with DIC. Microgrids with a pitch of 5 microns were printed on the etched microstructure of the IF steel to measure the local in-plane strain distribution during a tensile test carried out in a Scanning Electron Microscope (SEM). The progressive deformation of the microstructure with microgrids has been recorded throughout the test as a sequence of micrographs and subsequently processed using DIC to quantify the distribution of local strain values. Strain maps obtained with the two techniques have been compared in order to assess the accuracy of the DIC measurements obtained using the natural patterns of the revealed microstructure in the SEM micrographs. The results obtained with the two techniques are qualitatively similar and thus, demonstrate the reliability of DIC applied to microstructures, even after large deformations in excess of 0.7. However, an average error of about 16?% was found in the strain values calculated using DIC.     

A Novel “Subset Splitting” Procedure for Digital Image Correlation on Discontinuous Displacement Fields

Digital Image Correlation (DIC) is an easy to use yet powerful approach to measure displacement and strain fields. While the method is robust and accurate for a variety of applications, standard DIC returns large error and poor correlation quality near displacement discontinuities such as cracks or shear bands. This occurs because the subsets used for correlation can only capture continuous deformations from the reference to the deformed image. As a result the regions around discontinuities are typically removed from the area of interest, before or after analysis. Here, a novel approach is proposed which enables the subset to split in two sections when a discontinuity is detected. This method enables the measurement of “displacement jumps”, and also of displacements and strains right by the discontinuity (for example a crack profile or residual strains in the wake). The method is validated on digitally created images based on mode I and mode II asymptotic displacement fields, for both sub-pixel and super-pixel crack opening displacements. Finally, an actual fracture experiment on a high density polyethylene (HDPE) specimen demonstrates the robustness of the method on actual images. Compared to other methods capable of handling discontinuities, this novel “subset-splitting” procedure offers the advantage of being a direct extension of the now popular standard DIC, and can therefore be implemented as an “upgrade” to that method.     

Optimization of Digital Image Correlation for High-Resolution Strain Mapping of Ceramic Composites

Digital image correlation (DIC) is assessed as a tool for measuring strains with high spatial resolution in woven-fiber ceramic matrix composites. Using results of mechanical tests on aluminum alloy specimens in various geometric configurations, guidelines are provided for selecting DIC test parameters to maximize the extent of correlation and to minimize errors in displacements and strains. The latter error is shown to be exacerbated by the presence of strain gradients. In a case study, the resulting guidelines are applied to the measurement of strain fields in a SiC/SiC composite comprising 2-D woven fiber. Sub-fiber tow resolution of strain and low strain error are achieved. The fiber weave architecture is seen to exert a significant influence over strain heterogeneity within the composite. Moreover, strain concentrations at tow crossovers lead to the formation of macroscopic cracks in adjacent longitudinal tows. Such cracks initially grow stably, subject to increasing app lied stress, but ultimately lead to composite rupture. Once cracking is evident, the composite response is couched in terms of displacements, since the computed strains lack physical meaning in the vicinity of cracks. DIC is used to identify the locations of these cracks (via displacement discontinuities) and to measure the crack opening displacement profiles as a function of applied stress.     

旋转悬臂梁的刚柔耦合动力学建模与频率分析

对固结于转动刚体上外接柔性梁的刚柔耦合动力学建模和频率特性进行了研究,在精确描述柔性梁非线性变形的基础上,利用Hamilton变分原理和假设模态法,在计入柔性梁由于横向变形而引起的轴向变形二阶耦合量的条件下,推导出考虑"动力刚化"项的一次近似耦合模型。首先忽略柔性梁纵向变形的影响,给出一次近似简化模型,引入无量纲变量,对简化模型做无量纲化处理,分析梁固有频率对模态截断数的依赖性;其次研究在一次近似简化模型和零次近似简化模型下,调谐角速度与共振现象的关系;最后分析一次近似耦合模型的动力特性。研究发现,为保证计算的精度,模态截断数应随无量纲角速度的增大而增加,合理的模态截断数具有收敛值;一次近似简化模型下悬臂梁横向弯曲振动不存在共振调谐角速度,一次耦合模型下柔性梁并没有出现屈曲失稳现象。现有典型文献的相关结论是值得商榷的。     

On the finite displacement problem of a hollow sphere under internal and external pressures

Taking advantage of successive approximations the present boundary-value problemis solved.We find the first-order and second-order solutions,and there fore we obtain theformulae in the second approximatior for the displacement,strain,and stress fields.     

Systematic errors in digital image correlation due to undermatched subset shape functions

Digital image correlation techniques are commonly used to measure specimen displacements by finding correspondences between an image of the specimen in an undeformed or reference configuration and a second image under load. To establish correspondences between the two images, numerical techniques are used to locate an initially square image subset in a reference image within an image taken under load. During this process, shape functions of varying order can be applied to the initially square subset. Zero order shape functions permit the subset to translate rigidly, while first-order shape functions represent an affine transform of the subset that permits a combination of translation, rotation, shear and normal strains. In this article, the systematic errors that arise from the use of undermatched shape function, i.e., shape functions of lower order than the actual displacement field, are analyzed. It is shown that, under certain conditions, the shape functions used can be approximated by a Savitzky-Golay low-pass filter applied to the displacement functions, permitting a convenient error analysis. Furthermore, this analysis is not limited to the displacements, but naturally extends to the higher-order terms included in the shape functions. This permits a direct analysis of the systematic strain errors associated with an undermatched shape function. Detailed numerical studies are presented for the case of a second-order displacement field and first- and second-order shape functions. Finally, the relation of this work to previously published studies is discussed.     

橡胶材料弹性模量数字图像相关测定法

利用数字图像相关方法测量了小应变下柔性橡胶的弹性模量.用CCD相机记录单轴压缩实验中圆柱体橡胶试样表面人工散斑图像,作为数字图像相关测量技术中的变形信息载体.分析了镜头畸变对位移测量的影响,运用数字图像相关法得出小应变范围内像胶的应力应变曲线,计算出橡胶的弹性模量.并与采用千分表所得到的结果进行了比较,两者符合较好.实...     

数字图像相关中的亚像素位移定位算法进展

数字图像相关方法 (DIC) 已经作为一种常用的光学计量有效手段应用于实验力学及其它科学研究和工程应用领域中. 经过 20 多年的发展, 该方法日渐成熟和完善. 作为提高测量精度的亚像素位移定位算法被认为是该方法的关键技术之一. 本文对二维数字图像相关的基本原理及其中为提高测量精度而提出的各种亚像素位移定位算法做了概括性的介绍. 在总结已有研究成果的基础上, 分析了各种方法优缺点. 并对数字图像相关方法的最新进展作了简要介绍, 随着算法精度、效率以及硬件设备性能的提高, 该方法必将会获得更广泛的应用.      

Sub-Grain Scale Digital Image Correlation by Electron Microscopy for Polycrystalline Materials during Elastic and Plastic Deformation

Damage during loading of polycrystalline metallic alloys is localized at or below the scale of individual grains. Quantitative assessment of the heterogeneous strain fields at the grain scale is necessary to understand the relationship between microstructure and elastic and plastic deformation. In the present study, digital image correlation (DIC) is used to measure the strains at the sub-grain level in a polycrystalline nickel-base superalloy where plasticity is localized into physical slip bands. Parameters to minimize noise given a set speckle pattern (introduced by chemical etching) when performing DIC in a scanning electron microscope (SEM) were adapted for measurements in both plastic and elastic regimes. A methodology for the optimization of the SEM and DIC parameters necessary for the minimization of the variability in strain measurements at high spatial resolutions is presented. The implications for detecting the early stages of damage development are discussed.     

Use of 3-D Digital Image Correlation to Characterize the Mechanical Behavior of a Fiber Reinforced Refractory Castable

Refractory castables exhibit very low fracture strain levels when subjected to tension or bending. The main objective of this work is to show that 3-D digital image correlation (3-D DIC) allows such low strain levels to be measured. Compared to mechanical extensometer measurements, 3-D DIC makes it possible to reach similar strain resolution levels and to avoid the problem of position dependance related to the heterogeneous nature of the strain and to strain localization phenomena. First, the 3-D DIC method and the experimental set-up are presented. Secondly, an analysis of the 3-D DIC method is performed in order to evaluate the resolution, the standard uncertainty and the spatial resolution for both displacement and strain measurements. An optimized compromise between strain spatial resolution and standard uncertainty is reached for the configuration of the experimental bending test. Finally, the macroscopic mechanical behavior of a fiber reinforced refractory castable (FRRC) is studied using mechanical extensometry and 3-D DIC in the case of tensile and four-point bending tests. It is shown that similar results are obtained with both methods. Furthermore, in the case of bending tests on damaged castable, 3-D DIC results demonstrate the ability to determine Young’s modulus from heterogeneous strain fields better than by using classical beam deflection measurements.