Mode I Fracture at Spot Welds in Dual-Phase Steel: An Application of Reverse Digital Image Correlation

Strain fields in 600 grade dual-phase steel V-notch tensile specimens, both with and without a spot weld, were measured after mode I fracture initiation. Starting with the final image of a fully developed crack, a novel reverse digital image correlation (DIC) analysis was used to determine the path that the crack followed at the onset of fracture as well as the crack tip deformation field. This gave the pixel coordinates of grid points on both sides (i.e. fracture surfaces) of the crack path in the undeformed image. Strain fields that develop in the base material regions surrounding the two fracture surfaces were subsequently measured with forward DIC analysis. Steady state values of the crack tip opening displacement (CTOD) and crack tip opening angle (CTOA), which are important fracture parameters, were measured for the base DP600 metal. Notch tip opening displacement (NTOD) and notch tip opening angle were also measured. It was found that steady state values of the CTOD and CTOA are reached within 2 mm or so of crack growth following completion of the flat-to-slant transition of the fracture surface and stabilization of the crack tunneling effect.     

非连续数字图像相关方法在裂纹重构中的应用

数字图像相关方法作为一种新的非接触式位移测量方法,在力学工程中有广泛的应用前景,然而受限于标准方法对图像变形的连续性要求,这种高效的测量方法在断裂力学领域的推广受到了限制. 为解决这一问题,提出采用引入子区分离数学模型,代替标准方法的连续模型,来对非连续区域进行精确识别和匹配的非连续数字图像相关方法. 研究子区被裂纹等非连续分割后原始像素点的位移情况,并引入裂纹张开向量用以表征被分割子区的主区和副区的位移关系;从而建立子区分离模型的数学表达式,并且为所提出的模型设计相应的图像相关算法;然后将所提出的非连续数字图像相关方法应用于重构平板拉伸试验开裂过程中图像的位移. 研究结果表明,相比于标准的数字图像相关方法,所提出的非连续数字图像相关方法解决了图像相关法在非连续区域失效的问题,提高了数字图像相关方法对位移测量的正确率,特别是能够准确重构裂纹面及附近的位移场,其测量精度能够达到亚像素级别.      

数字图像相关分析法增量位移场测试技术

利用位移场的连续性,对亚像素位移场的算法进行了一些改进,设计了一套分步计算位移场、应变场的测量计算方法,较好地解决了数字图像相关分析法计算精度和效率.采用增量位移场叠加的方法计算大应变位移场,采用局部平面拟合的方法计算应变场.通过对高分子材料拉伸试验位移场的测量和结果标定,说明该方法具有较强的实用性和计算精度.同时,由于避免了对亚像素点的搜索,大大提高了计算效率.     

Determination of the full-field stress and displacement using photoelasticity and sampling moiré method in a 3D-printed model

The quantitative characterization of the full-field stress and displacement is significant for analyzing the failure and instability of engineering materials. Various optical measurement techniques such as photoelasticity, moiré and digital image correlation methods have been developed to achieve this goal. However, these methods are difficult to incorporate to determine the stress and displacement fields simultaneously because the tested models must contain particles and grating for displacement measurement; however, these elements will disturb the light passing through the tested models using photoelasticity. In this study, by combining photoelasticity and the sampling moiré method, we developed a method to determine the stress and displacement fields simultaneously in a three-dimensional (3D)-printed photoelastic model with orthogonal grating. Then, the full-field stress was determined by analyzing 10 photoelastic patterns, and the displacement fields were calculated using the sampling moiré method. The results indicate that the developed method can simultaneously determine the stress and displacement fields.     

基于数字散斑相关实验测量的材料构型力的计算方法

材料构型力学主要研究材料中的缺陷(夹杂、空穴、位错、裂纹、塑性区等)的构型(形状、尺寸和位置)改变时,所引起的系统自由能的变化。本研究将基于数字散斑相关技术,实验测量材料试件的位移场分布,随后通过材料构型力的定义式,计算求得弹塑性材料中缺陷构型力的分布。其方法概括如下:位移场通过数字图像相关技术测得;应变及位移梯度场利用三次样条拟合获得;线弹性材料应力通过简单线弹性本构方程获取,而塑性材料的表面应力场通过Ramberg-Osgood本构方程计算求得;弹塑性应变能密度分布则由应力-应变曲线数值积分获得。该方法对普通弹性材料或者弹塑性材料均适用,可以用于各种不同的缺陷及缺陷群的材料构型力测量。     

Digital Volume Correlation: Review of Progress and Challenges

3D imaging has become popular for analyzing material microstructures. When time lapse series of 3D pictures are acquired during a single experiment, it is possible to measure displacement fields via digital volume correlation (DVC), thereby leading to 4D results. Such 4D analyses have been performed for almost two decades. The present paper aims at reviewing the achievements of and challenges faced by such measurement technique. Ex-situ and in-situ experiments are discussed. A general and unified DVC framework is introduced. Various sources of measurement bias and uncertainties are analyzed. The current challenges are studied and some propositions are given to address them.     

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.     

An Improved Error Evaluation in One-Dimensional Deformation Measurements by Linear Digital Image Correlation

Simple analytical error formulas were derived for one-dimensional deformation parameter estimation by an image correlation analysis with linear subpixel interpolation. A two-parameter deformation function was used in the analysis to account for both rigid-body translation and constant displacement gradient in an image subset. Errors in parameter estimation were found to explicitly relate to the image grayscale error consisting of subpixel approximation, image noise (including quantization error), and subset deformation mismatch at each point of the subset. A power-law dependence of the standard deviation of errors in deformation parameter estimation on the subset size was established when random image noise was dominant and it was confirmed by the numerical results of both nonlinear and linear image correlation analyses of synthetic image pairs. The power-law relationship can be used to guide the selection of suitable image quality, subpixel approximation, subset size, and subset deformation function for the desired measurement precision of deformation parameters.     

Identification of Local Viscoplastic Properties in P91 Welds from Full Field Measurements at Room Temperature and 625 °C

A methodology to obtain visco-plastic laws in heterogeneous materials with digital image correlation (DIC) is proposed based on tensile and tensile-relaxation tests conducted at room temperature and at 625 °C. Tested samples are manufactured from a P91 weld in which a microstructural heterogeneity translates into graded mechanical properties. To simplify the problem, a classical decomposition of the weld into five different domains is considered. Strain field in each domain is obtained by means of digital image correlation applied to high magnification pictures recorded with an optical long distance microscope. The conducted identifications exhibit key features in the behaviour of each domain in terms of yield stress, ultimate tensile stress and hardening at both room temperature and 625 °C. Experimental fields are compared to the fields provided by finite element simulations. Eventually, the benefit of accounting for transverse strains in the identification procedure is examined, and the robustness of the procedure with addition of noise (representative of experimental conditions) in the measurement is characterized.     

Displacement fields denoising and strains extraction by finite element method

Optical full-field measurement methods are now widely applied in various domains. In general, the displacement fields can be directly obtained from the measurement, however in mechanical analysis strain fields are preferred. To extract strain fields from noisy displacement fields is always a challenging topic. In this study, a finite element method for smoothing displacement fields and calculating strain fields is proposed. An experimental test case on a holed aluminum specimen under tension is applied to validate this method. The heterogeneous displacement fields are measured by digital image correlation (DIC). By this proposed method, the result shows that the measuring noise on experimental displacement fields can be successfully removed, and strain fields can be reconstructed in the arbitrary area.     

Full-field Thermal Deformation Measurements in a Scanning Electron Microscope by 2D Digital Image Correlation

Using recently developed methods for application of a nano-scale random pattern having high contrast during SEM imaging, baseline full-field thermal deformation experiments have been performed successfully in an FEI Quanta SEM using 2D-DIC methods. Employing a specially redesigned commercial heating plate and control system, with modified specimen attachment procedures to minimize unwanted image motions, recently developed distortion correction procedures were shown to be effective in removing both drift and spatial distortion fields under thermal heating. 2D-DIC results from heating experiments up to 125°C on an aluminum specimen indicate that (a) the fully corrected displacement components have nearly random variability and a standard deviation of 0.02 pixels (≈25 nm at 200× and ≈0.5 nm at 10,000×) in each displacement component and (b) the unbiased measured strain fields have a standard deviation ≈150 × 10⁻⁶ and a mean value that is in good agreement with independent measurements, confirming that the SEM-DIC based method can be used for both micro-scale and nano-scale thermal strain measurements.

基于退相关DIC的疲劳裂纹全局动态测量方法

工程材料和结构在反复荷载长期作用下容易发生疲劳开裂, 疲劳裂纹测量对于开展科学试验研究和工程问题分析都至关重要, 但现有方法无法实现高精度的疲劳裂纹全局动态测量. 本文基于数字图像相关(digital image correlation, DIC)技术, 合理利用DIC的退相关效应, 提出一种疲劳裂纹全局动态测量及可视化方法. 该方法首先在相机采集得到的裂纹图像内, 建立具备拓扑关系的目标点云结构, 并运用DIC亚像素算法得到裂纹区域位移场, 再基于零均值归一化互相关(zero-mean normalized cross correlation, ZNCC)计算结果剔除退相关的DIC目标点(灭点). 进一步通过“三生点”算法提取得到裂纹离散边界, 并采用最小二乘法将离散边界拟合为连续裂纹边界, 实现裂纹形态的几何重构, 最终自动计算得到裂纹长度和宽度的动态变化过程. 该方法原理清晰、理论简单, 易于实现. 开展数值模拟和钢节点疲劳试验, 对相关算法和图像采集参数进行了验证, 结果表明本文方法对疲劳裂纹边界的数字化重构误差在0.5个像素内, 基于重构结果计算得到的裂纹长度和宽度误差分别为0.46像素和0.08像素(类同于0.06 mm和0.01 mm), 并成功实现了对疲劳试验裂纹扩展形态的精细化动态测量及可视化. 研究成果证明了DIC技术用于疲劳裂纹全局动态测量及可视化的有效性, 并在测量精度、效率、成本等方面具有显著优势, 可在实验室测量和工程现场测试中推广应用.      

利用分形相关法测量股骨头剖开面的面内位移

由于股骨头内松质骨结构的复杂性,对股骨头内骨小梁的应力和变形的分析与测试十分困难。在已经开展的这一方面的研究工作中主要是进行松质骨试样的宏观力学性能测试。随着计算机和图像技术的发展,图像及图像相关方法开始被用来进行松质骨的生物力学研究,这是非接触的测量方法,可以用来测量松质骨的表面位移场。本文利用图像相关方法在宏观尺度下测量了股骨头受外力作用时冠状面的面内的位移分布,作为进一步探索的开端。尽管松质骨表面的凹凸不平性对测量精度有影响,但是,还是可以分析出面内位移的分布特点。     

A generalized processing technique in digital particle image velocimetry with direct estimation of velocity gradients

A technique is proposed for the processing of digital particle image velocimetry (PIV) images, in one single step providing direct estimates of fluid velocity, out-of-plane vorticity and in-plane shear rate tensor. The method is based on a generalization of the standard PIV cross-correlation technique and substitutes the usual discrete cross-correlation of image pairs with a correlation of interpolated two-dimensional image intensity functions, being subject to affine transformations. The correlation is implemented by using collocation points, on which image intensity values are interpolated. The resulting six-dimensional correlation function is maximized using a general purpose optimization algorithm. The use of the method is demonstrated by application to different types of synthetically generated image pairs constructed with known particle displacement functions. The resulting errors are assessed and compared with those of a representative standard PIV method as well as with those of the present technique using no differential quantities in the search of the peak location. The examples demonstrate that significant improvements in accuracy can be obtained for flow fields with regions containing strong velocity gradients.     

Submicron deformation field measurements: Part 2. Improved digital image correlation

This is the second paper in a series of three devoted to the application of scanning tunneling microscopy (STM) to mechanics problems. In this paper, improvements to the digital image correlation method are outlined, a technique that compares digital images of a specimen surface before and after deformation to deduce its two-dimensional surface displacement field and strains. The necessity of using the framework of large deformation theory for accurately addressing rigid body rotations to reduce associated errors in the strain components is pointed out. In addition, the algorithm is extended to compute the three-dimensional surface displacement field from STM data; also, significant improvements are achieved in the rate as well as the robustness of the convergence. For (STM) topographs, the resolution yields 4.8 nm for the in-plane and 1.5 nm for the out-of-plane displacement components spanning an area of 10 m×10m.     

数字图像相关曲面拟合法相关系数修正算法的实验研究

为了提高数字图像相关曲面拟合法亚像素定位精度,经研究发现,在实际应用中,曲面拟合法在亚像素位移为0.5像素左右时会发生较大的波动,与实际亚像素位移发生一定偏离,导致此位置位移的不连续。本文通过分析曲面拟合法亚像素位移偏离真实位移的原因,给出了具体修正方法,用模拟平移实验讨论了修正系数k和子区大小对修正结果的影响,用三点弯曲实验验证了修正方法在复杂变形情况下的有效性,提高了曲面拟合法在实际应用中的测量精度。     

Scanning Electron Microscopy for Quantitative Small and Large Deformation Measurements Part II: Experimental Validation for Magnifications from 200 to 10,000

A combination of drift distortion removal and spatial distortion removal are performed to correct Scanning Electron Microscope (SEM) images at both ×200 and ×10,000 magnification. Using multiple, time-spaced images and in-plane rigid body motions to extract the relative displacement field throughout the imaging process, results from numerical simulations clearly demonstrate that the correction procedures successfully remove both drift and spatial distortions with errors on the order of ±0.02 pixels. A series of 2D translation and tensile loading experiments are performed in an SEM for magnifications at ×200 and ×10,000, where both the drift and spatial distortion removal methods described above are applied to correct the digital images and improve the accuracy of measurements obtained using 2D-DIC. Results from translation and loading experiments indicate that (a) the fully corrected displacement components have nearly random variability with standard deviation of 0.02 pixels (≈25 nm at ×200 and ≈0.5 nm at ×10,000) in each displacement component and (b) the measured strain fields are unbiased and in excellent agreement with expected results, with a spatial resolution of 43 pixels (≈54 μm at ×200 and ≈1.1 μm at ×10,000) and a standard deviation on the order of 6 × 10⁻⁵ for each component.

Digital Image Correlation with Self-Adaptive Gaussian Windows

A novel subpixel registration algorithm with Gaussian windows is put forward for accurate deformation measurement in digital image correlation technique. Based on speckle image quality and potential deformation states, this algorithm can automatically minimize the influence of subset sizes by self-adaptively tuning the Gaussian window shapes with the aid of a so-called weighted sum-of-squared difference correlation criterion. Numerical results of synthetic speckle images undergoing in-plane sinusoidal displacement fields demonstrate that the proposed algorithm can significantly improve displacement and strain measurement accuracy especially in the case with relatively large deformation.     

Full-field representation of discretely sampled surface deformation for displacement and strain analysis

A detailed evaluation of the feasibility of determining displacements and displacement gradients from measured surface displacement fields is presented. An improved methodology for both the estimation and elimination of noise is proposed. The methodology is used to analyze the gradients for three tests: (1) uniform rotation, (2) uniform strain, and (3) crack-tip displacement fields. Results of the study indicate that the proposed methodology can be used to extract the underlying two-dimensional displacements and their corresponding gradients from the noisy data with reasonable accuracy. Specifically, it is shown that (a) the digital correlation method for acquiring displacement fields has an error in strain of approximately 150 strain at each point, (b) the average strain in a region of uniform strain has much less error, typically on the order of 20 strain, (c) the displacement nolse present in digital correlation is very small, approximately 0.01 pixels, (d) the proposed methodology for reducing noise in the data is essential to the accurate evaluation of displacement gradients and (e) the successful evaluation of displacement and displacement gradients for all three cases indicates that the proposed methodology can be used both to quantify the displacement fields and to reasonably estimate the overall gradient trends.     

Towards High Performance Digital Volume Correlation

We develop speed and efficiency improvements to a three-dimensional (3D) digital volume correlation (DVC) algorithm, which measures displacement and strain fields throughout the interior of a material. Our goal is to perform DVC with resolution comparable to that achieved in 2D digital image correlation, in time that is commensurate with the image acquisition time. This would represent a significant improvement over the current state-of-the-art available in the literature. Using an X-ray micro-CT scanner, we can resolve features at the 5 micron scale, generating 3D images with up to 36 billion voxels. We compute twelve degrees-of-freedom at each correlation point and utilize tricubic spline interpolation to achieve high accuracy. We improve the algorithm’s speed and robustness through an improved coarse search, efficient implementation of spline interpolation, and using smoothing splines to address noisy image data. For DVC, the volume of data, number of correlation points, and work to solve each correlation point grow cubically. We therefore employ parallel computing to handle this tremendous increase in computational and memory requirements. We demonstrate the application of DVC using simulated deformations of 3D micro-CT scans of polymer samples with embedded particles forming an internal pattern.