Quantitative Study of Residual Strain and Geometrically Necessary Dislocation Density Using HR-EBSD Method

Background

Optical metrology is widely used to measure materials’ deformation and mechanical properties but current fundamental research requires more precise measurement of microstructure and deformation in internal materials. Electron backscattered diffraction (EBSD) technique measures crystal orientation in individual grain and high resolution EBSD (HR-EBSD) method provides information about residual strain and GND density.

Objective

Deformation of two stainless steels Nitronic 60 and Tristelle 5183 with different proportions of ferrite and carbides are characterised.

Methods

Push-release bend testing was used to provide progressive increasing bending stress in two iron-based material samples. HR-EBSD and high resolution digital image correlation (HR-DIC) methods characterised residual strain, GND density and plastic strain distributions in each sample.

Results

Nitronic 60 and Tristelle 5183 were deformed and obtained 3.8% and 0.9% plastic strain ?xx. High GND densities distributed neighbouring grain boundaries in Nitronic 60 while high GND densities distributed around carbides, especially intragranular carbides in Tristelle 5183.

Conclusions

HR-EBSD and HR-DIC quantitative characterised deformation in two iron-based alloys, grain/twin boundaries and carbides resulted in GND density increase, promoted work hardening and accumulated high residual elastic strain. Heterogeneous grain/carbide size distribution leaded to stress concentration and cause carbide decohesion and brittle fracture of sample.

     

Coupling Self-Adaptive Meshing-Based Regularization and Global Image Correlation for Spatially Heterogeneous Deformation Characterization

Background

Image-based global correlation involves a class of ill-posed inverse problems associated with speckle quality and deformation gradients on specimen surfaces. However, the method used to simultaneously integrate the prior information related to images and deformations and effectively regularize these inverse problems still faces severe challenges, especially when complex heterogeneous deformation gradients exist over sample surfaces with locally degraded speckle patterns.

Objective

We propose a novel self-adaptive meshing-based regularization for global image correlation to determine spatially complex heterogeneous deformations.

Methods

A virtual truss system with a linearly elastic constitutive relationship is employed to self-adaptively implement surface meshing by numerically balancing the exerted virtual forces under the constraints of the local speckle image quality and deformation gradients. The 2-norm-based condition number of the local stiffness matrix is introduced to ensure numerical stability during meshing.

Results

The algorithms can behave as a smart regularization procedure integrating all the prior information during numerical calculations, consequently achieving an accurate, precise and robust characterization of heterogeneous deformations, as demonstrated by virtual simulations and actual experiments.

Conclusions

The regularization strategy coupled to image-based correlation is also promising for automatic quantification of complex heterogeneous deformations, particularly from images with locally degraded speckle patterns.

     

光绘:自由开源的数字散斑图像生成和评价软件

生成数字散斑图像以及对应的变形图像是数字图像相关研究的基础,然而至今仍然缺乏功能齐全、操作简单、界面友好的专业散斑生成和分析软件;研究者需要自行实现相关算法,不仅费时耗力,也增加了出错的可能性。本文发布了一款自由开源的数字散斑图像生成和评价软件:《光绘》。该软件具有散斑图生成、变形图生成、散斑质量评价和散斑图案推荐等功能:可以生成椭圆、多边形和高斯散斑;可以渲染平移、拉伸/压缩、旋转、正弦、高斯和剪切带等变形模式的变形图;可以计算散斑占空比、散斑尺寸、系统误差和随机误差等关键散斑质量评价参数;可以根据工况生成矢量格式的推荐散斑图案。本文提出向后映射初值快速估计算法和散斑图预渲染技术实现了变形图的实时渲染显示,并使用积分图像技术大幅提升了灰度梯度平方和的计算效率。该软件不仅可用于数字图像相关的学术研究和工程应用,也可服务于实验力学的教学工作,具有广阔的应用前景。     

Adaptive Rotated Gaussian Weighted Digital Image Correlation (RGW-DIC) for Heterogeneous Deformation Measurement

Background

Digital image correlation (DIC) has advanced to become a flexible, reliable and fast optical method for the measurement of non-contact and full-field surface deformation. However, the accuracy of existing methods in measuring heterogeneous deformation fields—especially for the high gradient strain field – can be improved.

Objective

In state-of-art local DIC applications, several methods have been put forward to adapt a subset to unknown deformation. Although improvements in performance using these methods are obtained, results are still ungratified for severely heterogeneous deformation such as the Star 2 and Star 5 images from DIC Challenge 2.0.

Methods

In this paper, a rotated Gaussian weighted zero-mean normalized sum of squared difference (RGW-ZNSSD) criterion function is proposed as the basis for RGW-DIC subset size adaptation. RGW-DIC can automatically determine the optimum weight distribution, hence self-adaptivity in subset size and orientation are achieved simultaneously.

Results

The effectiveness of the proposed RGW-DIC is verified using DIC-challenge 2.0 images and simulated sinusoidal deformation images. Results reveal that the adaptively determined subset weight distribution can significantly improve the accuracy of heterogeneous deformation measurement compared with traditional DIC and DIC with isotropic Gaussian weight functions.

Conclusions

The proposed RGW-DIC can be applied to unknown severely heterogeneous deformation measurement.

     

Full-field speckle pattern image correlation with B-Spline deformation function

A full-field speckle pattern image correlation method is presented that will determine directly the complete, two-dimensional deformation field during the image correlation process on digital images obtained using computer vision systems. In this work, a B-Spline function is used to represent the object deformation field throughout the entire image area. This is an improvement over subset-based image correlation methods by implicitly maintaining position and derivative continuity constraints among subsets up to a specified order. The control point variables within the B-Spline deformation function are optimized iteratively with the Levenberg-Marquardt method to achieve minimum disparity between the predicted and actual deformed images. Results have shown that the proposed method is computationally efficient, accurate and robust. The general framework of this method can be applied ton-dimensional image correlation systems that solve for multi-dimension vector fields.     

A study of localisation in dual-phase high-strength steels under dynamic loading using digital image correlation and FE analysis

Tensile tests were conducted on dual-phase high-strength steel in a Split-Hopkinson Tension Bar at a strain-rate in the range of 150–600/s and in a servo-hydraulic testing machine at a strain-rate between 10^?3 and 10⁰/s. A novel specimen design was utilized for the Hopkinson bar tests of this sheet material. Digital image correlation was used together with high-speed photography to study strain localisation in the tensile specimens at high rates of strain. By using digital image correlation, it is possible to obtain in-plane displacement and strain fields during non-uniform deformation of the gauge section, and accordingly the strains associated with diffuse and localised necking may be determined. The full-field measurements in high strain-rate tests reveal that strain localisation started even before the maximum load was attained in the specimen. An elasto-viscoplastic constitutive model is used to predict the observed stress–strain behaviour and strain localisation for the dual-phase steel. Numerical simulations of dynamic tensile tests were performed using the non-linear explicit FE code LS-DYNA. Simulations were done with shell (plane stress) and brick elements. Good correlation between experiments and numerical predictions was achieved, in terms of engineering stress–strain behaviour, deformed geometry and strain fields. However, mesh density plays a role in the localisation of deformation in numerical simulations, particularly for the shell element analysis.     

Overview of High-temperature Deformation Measurement Using Digital Image Correlation

Background

Developments in digital image correlation (DIC) in the last decade have made it a practical and effective optical technique for displacement and strain measurement at high temperatures.

Objective

This overview aims to review the research progress, summarize the experience and provide valuable references for the high-temperature deformation measurement using DIC.

Methods

We comprehensively summarize challenges and recent advances in high-temperature DIC techniques.

Results

Fundamental principles of high-temperature DIC and various approaches to generate thermal environment or apply thermal loading are briefly introduced first. Then, the three primary challenges presented in performing high-temperature DIC measurements, i.e., 1). image saturation caused by intensified thermal radiation of heated sample and surrounding heating elements, 2) image contrast reduction due to surface oxidation of the heated sample and speckle pattern debonding, and 3) image distortion due to heat haze between the sample and the heating source, and corresponding countermeasures (i.e., the suppression of thermal radiation, fabrication of high-temperature speckle pattern and mitigation of heat haze) are discussed in detail. Next, typical applications of high-temperature DIC at various spatial scales are briefly described. Finally, remaining unsolved problems and future goals in high-temperature deformation measurements using DIC are also provided. 

Conclusions

We expect this review can guide to build a suitable DIC system for kinematic field measurements at high temperatures and solve the challenging problems that may be encountered during real tests.

     

Obtaining a Wide-Strain-Range True Stress–Strain Curve Using the Measurement-In-Neck-Section Method

Background

Measuring true stress–strain curve over a large-strain-range is essential to understand mechanical behavior and simulate non-linear plastic deformation. The digital image correlation (DIC) technique, a non-contact full-field optical measurement technique, is a promising candidate to obtain a long-range true stress–strain curve experimentally.

Objective

This paper proposes a method for measuring true stress–strain curves over a large-strain-range during tensile testing using DIC.

Methods

The wide-strain-range true stress–strain curves of dual-phase and low carbon steels were extracted on the transverse direction in the neck region. The axial strain on the neck section was estimated by averaging the inhomogeneous deformation on the cross-section of the tensile specimen. The true stress was calculated from the engineering stress and the cross-sectional area of the neck.

Results

The validity of the proposed method was assessed by comparing the experimental load–displacement responses during tensile testing with the finite element method (FEM) simulation results. The stress and strain on the neck section estimated using the FEM and DIC, respectively, were proven to satisfy the uniaxial condition and successfully obtained.

Conclusions

The experimental results agree well with the FEM results. The proposed concept can be applied to various deformation modes for accurately measuring long-range true stress–strain curves.

     

Videometrics Measurement for Dynamic Topography of Large Flexible Cable Net Based on Tiny Light Spot Markers

Background:

Traditional videometric method can not be used in the measurement of large flexible cable-net structure for its large overall size and small partial size.

Objective

A videometrics technique was proposed in this work to measure the topography and deformation of a large cable net structure.

Methods

Tiny spots with high brightness (and large gray gradient) are used to mark the cable net nodes. By arranging the imaging light path properly, the light spot markers can be enlarged and accurately identified in the captured images.

Results

The relationship between the imaging parameters and the gray distribution of the light spot markers were derived and verified. And a topographical measurement experiment of a cable net structure was carried out with the proposed videometrics technique.

Conclusions

The topography/deformation of the cable net can be measured with tiny-light spot markers, and the effectiveness and robustness of the technique on topography and deformation measurement of large cable-net structures are demonstrated.

     

Plastic Strain Mapping with Sub-micron Resolution Using Digital Image Correlation

Digital image correlation (DIC) of images obtained using scanning electron microscopy has been used to study, quantitatively, the plastic deformation of stainless steel at the microstructural scale. An artificial speckle pattern was generated by the remodelling of a deposited gold layer. A new experimental setup was shown to accelerate the remodelling process and promote the formation of finer nano-scale speckles with sizes ranging 30 nm to 150 nm and of similar spacing. The effects of surface preparation on speckle morphology are discussed. The high density of speckles enabled displacement mapping with resolution of one displacement vector each 0.2?×?0.2 μm² of surface area. It is shown that sub-micron resolution is necessary to capture the plastic deformation associated with the formation of slip bands in stainless steel, which are an important component of the deformation of these materials at the microscale. Electron backscatter diffraction (EBSD) was used to reconstruct the surface grain boundaries and enabled these deformation features to be linked to the microstructure.     

Assessment of High Speed Imaging Systems for 2D and 3D Deformation Measurements: Methodology Development and Validation

Ultra high-speed and moderate speed image acquisition platforms have been characterized, with special emphasis on the variability and accuracy of the measurements obtained when employed in either 2D or 3D computer vision systems for deformation and shape measurements. Specifically, the type of image distortions present in both single channel cameras (HS-CMOS) and multi-channel image intensified cameras (UHS-ICCD) are quantified as part of the overall study, and their effect on the accuracy of experimental measurements obtained using digital image correlation have been determined. Results indicate that established methods for noise suppression and recently developed models for distortion correction can be used effectively in situations where the primary intensity noise components are characterized by minimal cross-talk and stationary spatial distortions. Baseline uniaxial tension experiments demonstrate that image correlation measurements using high speed imaging systems are unbiased and consistent with independent deformation measurements over the same length scale, with point-to-point strain variations that are similar to results obtained from translation experiments. In this study, the point-to-point variability in strain using the image intensified system is on the order of 0.001, whereas the non-intensified system had variability of 0.0001. Results confirm that high speed imaging systems can be utilized for full field two and three-dimensional measurements using digital image correlation methods.

Dynamic Subsurface Deformation and Strain of Soft Hydrogel Interfaces Using an Embedded Speckle Pattern With 2D Digital Image Correlation

Background

Subsurface mechanisms can greatly affect the mechanical behavior of biological materials, but observation of these mechanisms has remained elusive primarily due to unfavorable optical characteristics. Researchers attempt to overcome these limitations by performing experiments in biological mimics like hydrogels, but measurements are generally restricted due to the spatio-temporal limitations of current methods.

Objective

Utilization of contemporary 3D printing techniques into soft, transparent, aqueous yield-stress materials have opened new avenues of approach to overcoming these roadblocks. By incorporating digital image correlation with such 3D printing techniques, a method is shown here that can acquire full-field deformation of a hydrogel subsurface in real-time.

Methods

Briefly, the method replaces the solvent of a transparent and low polymer concentration yield-stress material with an aqueous hydrogel precursor solution, then a DIC speckle plane is 3D printed into it. This complex is then polymerized using photoinitiation thereby locking the speckle plane in place.

Results

Full-field deformation measurements are made in real-time as the embedded speckle plane (ESP) responds with the bulk to the applied load. Example results of deformation and strain fields associated with indentation, relaxation, and sliding contact experiments are shown.

Conclusions

This method has successfully observed the subsurface mechanical response in the bulk of a hydrogel and has the potential to answer fundamental questions regarding biological material mechanical behaviors.

     

Relating inhomogeneous deformation to local texture in zirconium through grain-scale digital image correlation strain mapping experiments

The effect of local texture on inhomogeneous plastic deformation is studied in zirconium subjected to uniaxial compression. Cross-rolled commercially pure Zr 702 plate that had a strong basal (0 0 0 1) texture through the plate thickness, and a non-basal texture in cross-section, was obtained. At a compressive strain rate of 1 s^?1, samples loaded either in the through-thickness or in-plane directions exhibited significant differences in yield strength, hardening response and failure mechanisms. These macroscopic differences are related to microstructural features by combining information from electron backscattered diffraction with real time in situ imaging and subsequent full-field strain measurements obtained using digital image correlation. Experimental results indicate that the through-thickness loaded zirconium samples, which show a strong basal-texture in the loading direction, do not deform homogeneously – implying the lack of a representative volume element. The detailed surface deformation fields provided by digital image correlation allow for a qualitative and quantitative analysis of the relationship between grain orientation and patterns of deformation bands that form as the precursors to development of an adiabatic shear band in the through-thickness loaded sample. For the in-plane loaded samples, inhomogeneities still exist at the microscale, but the collective behavior of several grains leads to a homogeneous response at the macroscale. It is observed that local texture for hcp polycrystals, which are significantly slip restricted, can directly affect both local and global response, even at low to moderate plastic strains.     

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.      

In-situ Strain Field Measurement and Mechano-electro-chemical Analysis of Graphite Electrodes Via Fluorescence Digital Image Correlation

Background

Mechano-electro-chemical coupling during the ion diffusion process is a core factor to determine the electrochemical performance of electrodes. However, relationship between the mechanics and the electrochemistry has not been clarified by experiments.

Objective

In this work, we conduct an in situ, visual, comprehensive characterization of strain field and Li concentration distribution to further explore the mechano-electro-chemical relationship.

Methods

The digital image correlation characterized by fluorescent speckle and active optical imaging is developed. Combined with electrochromic-based Li concentration detection, the spatiotemporal evolution of in-plane strain and Li concentration of a graphite electrode during the lithiation and delithiation processes are measured and displayed visually via a dual optical path acquisition system.

Results

The visual results show that in-plane strain and Li concentration possess a spatially non-uniform gradient distribution along the radial direction (i.e., diffusion path) with large values outside and small values inside, and that both present obvious temporal segmentation. And mechano-electro-chemical coupling analysis reveals that the in-plane strain is not always linearly related to the concentration and infers that a high strain limits the diffusion and lithiation. The strain–concentration evolution exhibits obvious asymmetric differences between lithiation and delithiation, wherein three equations are fitted to approximately represent the evolution process between in-plane strain and concentration during the lithiation and delithiation processes

Conclusions

This work overcomes the difficulties of fine strain measurements and collaborative concentration characterization during the electrochemical process, and provides an effective experimental method and data support for further exploration of mechano-electro-chemical coupling.

     

Analysis of interpolation schemes for image deformation methods in PIV: effect of noise on the accuracy and spatial resolution

As testified by a previous article (Astarita and Cardone in Exp Fluids 38:233–243, 2005), a critical point that can influence significantly the accuracy of image deformation methods (IDM) for particle image velocimetry (PIV) is the interpolation scheme (IS) used in the reconstruction of deformed images. In the cited paper the effect of noise has been neglected and for this reason in this follow-up paper the influence of the IS, in the presence of noise, on both accuracy and spatial resolution is studied. Performance assessment is conducted using synthetic images with particles of Gaussian shape and with constant and sinusoidal displacement fields. Both the local and the top hat moving average approaches are investigated and the modulation transfer function, the total and bias errors have been used to evaluate the performances of IDMs for PIV applications. The results show that, when a high noise level is present in the images, the influence of the IS is less relevant than what was shown by Astarita and Cardone (Exp Fluids 38:233–243, 2005).     

Digital Image Correlation Study of Plastic Deformation and Fracture in Fully Martensitic Steels

Plastic deformation and fracture of two grades of fully martensitic steel are investigated with a miniature tensile stage, a custom image acquisition algorithm and digital image correlation. The image acquisition algorithm controls the camera framing rate according to user defined load, displacement and timing thresholds. This provides a greater number of images captured during periods of rapid load change over small displacements. True stress–true strain curves reveal substantial differences in material ductility and failure behavior. Fracture surfaces are examined using scanning electron microscopy and energy dispersive spectroscopy to provide insight into differences in the tensile behaviors observed for these steels.     

基于体视显微镜的测量系统标定研究

微观三维变形测量系统在工程上有广泛的应用。本文构建了体视显微镜双相机微观图像采集与测量系统,可以实现对微小物体形貌、位移、变形的全场测量。微观三维变形的测量精度与成像系统的畸变模型存在密切的关系。本文采用了考虑多种不确定情况的畸变模型,能很好地表达体视显微镜测量系统的成像误差,并设计了点阵式标定模板和精密的平动平台,实现了基于Tsai标定的自动标定算法。实验表明,体视显微镜测量系统可以在各种放大倍数下稳定工作,标定的精度得到很大的提高,并给出了在不同放大倍数下对规则圆柱体的形貌和直径的测量结果。     

Template matching for improved accuracy in molecular tagging velocimetry

In 2D molecular tagging velocimetry (MTV), tags are written into a fluid flow with a laser grid and imaged at discrete times. These images are analyzed to calculate Lagrangian displacement vectors, often by direct cross correlation. The cross correlation method is inherited from particle imaging velocimetry, where the correlated images contain a random pattern of particles. A template matching method is presented here which takes advantage of the known geometry of laser written tag grids in MTV to achieve better accuracy. Grid intersections are explicitly located in each image by correlation with a template with several linear and rotational degrees of freedom. The template is a continuous mathematical function, so the correlation may be optimized at arbitrary sub-pixel resolution. The template is smooth at the spatial scale of the image noise, so random error is substantially suppressed. Under typical experimental conditions at low imaging resolution, displacement uncertainty is reduced by a factor of 5 compared to the direct cross correlation method. Due to the rotational degrees of freedom, displacement uncertainty is insensitive to highly deformed grids, thus permitting longer delay times and increasing the relative accuracy and dynamic range of the measurement. In addition, measured rotational displacements yield velocity gradients which improve the fidelity of interpolated velocity maps.