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.

     

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.

     

A Bio-Inspired Frequency-Based Approach for Tailorable and Scalable Speckle Pattern Generation

Background

Digital Image Correlation (DIC) is a length scale independent surface pattern matching and tracking algorithm capable of providing full field deformation measurements. The confident registration of this pattern within the imaging system becomes key to the derived results. Practically, conventional speckling methods use non-reliable, non-repeatable patterning methodologies including spray paints and air brushing leading to increased systematic and random errors based on the user’s experience.

Objective

A methodology to develop a speckle pattern tailored to the imaging and experimental conditions of the given system is developed in this paper.

Methods

In this context, a novel bio-inspired speckle pattern development technique is introduced, leveraging spatial imaging parameters in addition to frequency characteristics of speckle patterns, enhancing the results obtained through DIC. This novel technique leverages gradient parameters in the frequency spectrum obtained from patterns fabricated using a bio-templating manufacturing technique.

Results

The analysis presented shows that optimized gradient features alongside tailored spatial characteristics reduce errors while increasing the usefulness of DIC results across the entire region of interest. With this new approach, gradient information is derived from the bio-templated pattern, extracted, optimized and then convolved with spatial properties of a numerically generated 2D point clouds which can then be transferred onto actual specimens. Numerical error analysis shows that the optimized patterns result in significant reduction in root mean square error compared to conventional speckling methods.

Conclusions

Physical experiments show the scalability of this optimized pattern to allow for varying working distances while consistently maintaining a lower error threshold compared to conventional speckling techniques.

     

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.

     

A Review of Speckle Pattern Fabrication and Assessment for Digital Image Correlation

As a carrier of deformation information, the speckle pattern, or more exactly the random intensity distributions, which could be naturally occurred or artificially fabricated onto test samples’ surface, plays an indispensable role in digital image correlation (DIC). It is now well recognized that the accuracy and precision in DIC measurements not only rely on correlation algorithms, but also depend highly on the quality of the speckle pattern. Considering the huge diversity in test materials, spatial scales and experimental conditions, speckle pattern fabrication could be a challenging issue facing DIC practitioners. To obtain good speckle patterns suitable for DIC measurements, some key issues of fabrication methods and quality assessment of speckle patterns must be well addressed. To this end, this review systematically presents the speckle pattern classification and fabrication techniques for various samples and scales, as well as some typical quality assessment metrics.     

数字图像相关方法中散斑图的质量评价研究

在利用数字图像相关方法测量物体表面变形时,被测物体表面必需覆盖有灰度随机分布的散斑场,该散斑场作为试件表面变形信息的载体随试件一起变形。在实际情况下,不同的散斑场会显示出完全不同的灰度分布特征,并对数字图像相关方法的测量结果有着重要影响。因此如何定量评价散斑图的优劣是数字图像相关方法中一个重要的基本问题,也是该方法的使用者非常关心的问题。基于最近数字图像相关方法基本理论研究的进展,本文提出平均灰度梯度这一新参数用于散斑图质量的评价。为证实该参数的有效性,本文对五幅明显不同的散斑图进行了精确平移,并将数字图像相关方法测量的位移与预加的平移量进行比较,分析了位移测量结果的均值误差和标准差。结果显示位移测量结果的均值误差和标准差均与散斑图的平均灰度梯度有关,一个好的散斑图应该具有较大的平均灰度梯度。     

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.

     

Fractal Pattern for Multiscale Digital Image Correlation

Background:

Digital Image Correlation (DIC) is based on the matching, between reference and deformed state images, of features contained in patterns that are deposited on test sample surfaces. These features are often suitable for a single scale, and there is a current lack of multiscale patterns capable of providing reliable displacement measurements over a wide range of scales.

Objective:

Here, we aim to demonstrate that a pattern based on a fractal (self-affine) surface would make a suitable pattern for multiscale DIC.

Methods:

A method to numerically generate patterns directly from a desired auto-correlation function is introduced. It is then enhanced by a Mean Intensity Gradient (MIG) improvement process based on grey level redistribution. Numerical experiments at multiple scales are performed for two different imposed displacement fields and results for one of the patterns generated are compared with those obtained for a random pattern and a Perlin noise one.

Results:

The proposed pattern is shown to lead to DIC errors comparable to those found with the two others for the first scales, but has much greater robustness. More importantly, the pattern generated here exhibits stable errors and robustness with respect to the scale whereas these two outputs become significantly degraded for the other two patterns as the scale increases.

Conclusions:

As a result, scale invariance properties of the pattern based on fractal surfaces correspond to scale invariance in DIC errors as well. This is of great interest regarding the use of such patterns in multiscale DIC.

     

Micro- and Nanoscale Deformation Measurement of Surface and Internal Planes via Digital Image Correlation

The digital image correlation (DIC) technique is successfully applied across multiple length scales through the generation of a suitable speckle pattern at each size scale. For microscale measurements, a random speckle pattern of paint is created with a fine point airbrush. Nanoscale displacement resolution is achieved with a speckle pattern formed by solution deposition of fluorescent silica nanoparticles. When excited, the particles fluoresce and form a speckle pattern that can be imaged with an optical microscope. Displacements are measured on the surface and on an interior plane of transparent polymer samples with the different speckle patterns. Rigid body translation calibrations and uniaxial tension experiments establish a surface displacement resolution of 1 μm over a 5×6 mm scale field of view for the airbrushed samples and 17 nm over a 100×100 μm scale field of view for samples with the fluorescent nanoparticle speckle. To demonstrate the capabilities of the method, we characterize the internal deformation fields generated around silica microspheres embedded in an elastomer under tensile loading. The DIC technique enables measurement of complex deformation fields with nanoscale precision over relatively large areas, making it of particular relevance to materials that possess multiple length scales.     

<Emphasis Type="BoldItalic">In-Situ</Emphasis> Mechanical Testing for Characterizing Strain Localization During Deformation at Elevated Temperatures

An experimental methodology has been developed to characterize local strain heterogeneities in alloys via in-situ scanning electron microscope (SEM) based mechanical testing. Quantitative measurements of local strains as a function of grain orientation, morphology and neighborhood are crucial for mechanistic understanding and validation of crystal plasticity models. This study focuses on the technical challenges associated with performing creep tests at elevated temperatures ≤700°C in an SEM. Samples of nickel-based superalloy Rene 104 were used for this study, but the technique is applicable to testing of any metal samples at elevated temperature. Electron beam lithography was employed to produce a suitable surface speckle pattern of hafnium oxide to facilitate full field displacement measurements using a commercial software package. The speckle pattern proved to have good thermal stability and provided excellent contrast for image acquisition using secondary electron imaging at elevated temperature. The speckle pattern and microscope magnification were optimized to obtain the resolution necessary to discern strain localizations within grain interiors and along grain boundaries. Minimum strain resolution due to SEM image distortions was determined prior to tensile testing, and image integration methods were utilized to minimize imaging artifacts. Limitations due to the present specimen heating method and potential solutions to these limitations are also addressed.     

Ceramic-Based Speckles and Enhanced Feature-Detecting Algorithm for Deformation Measurement at High Temperature

The mechanical properties of Ni-base alloys have drawn considerable attention owing to their wide application in the hot components of aircrafts and gas turbines. To accurately measure the deformation of Ni-based alloys at high temperatures, a new type of high-temperature speckles is fabricated on the surface of specimens subjected to long heating durations at temperatures up to 1400 °C. Meanwhile, a novel measurement method based on the scale-invariant feature transform algorithm is developed to measure the deformation and obtain a more accurate result. Both of the above proposed methods are used in a creep test of Inconel 713C at 860 °C. The experimental results indicate that the speckles exhibit excellent performance under heating conditions and adhere well to the substrate at high temperatures. Also, the proposed deformation measurement method exhibits superior image processing even when the speckle quality is imperfect with respect to speckle size.     

Scanning-Digital Image Correlation for Moving and Temporally Deformed Surfaces in Scanning Imaging Mode

Background

Images from scanning electron microscopes, transmission electron microscopes and atomic force microscopes have been widely used in digital image correlation methods to obtain accurate full-field deformation profiles of tested objects and investigate the object’s deformation mechanism. However, because of the raster-scanning imaging mode used in microscopic observation equipment, the images obtained from these instruments can only be used for quasi-static displacement measurements; otherwise, spurious displacements and strains may be introduced into the deformation results if these scanning microscopic images are used directly in general digital image correlation calculations for moving and temporally deformed surfaces.

Objective

Realizing kinematic parameter and dynamic deformation measurements on a scanning electron microscope platform.

Methods

Establishing a scanning imaging model of moving and temporally deformed objects that contains motion and deformation equations, a scanning equation and an intensity invariance assumption for small deformations. Then proposing a scanning-digital image correlation (S-DIC) method based on combing the characteristics of the scanning imaging mode with digital image correlation.

Results

Quantitatively investigating the effects of the spurious displacements and strains introduced when using scanning images to represent moving and temporally deformed surfaces in the measurement results. Numerical simulations verify that the accuracy of the S-DIC method is 10^?2pix for the displacement, 10^?4 for the strain, 10^?4pix/s for the velocity and 10^?6s^?1 for the strain rate. Experiments also show that the proposed S-DIC method is effective. Conclusions: The results of this work demonstrate the utility of S-DIC on the field of microscopic dynamic measurement.

     

Drone-Based StereoDIC: System Development,Experimental Validation and Infrastructure Application

Background

Digital Image Correlation (DIC) is widely used for remote and non-destructive structural health evaluation of infrastructure. Current DIC applications are limited to relatively small areas of structures and require the use of stationary stereo vision camera systems that are not easy to transfer and deploy in remote areas.

Objective

The enclosed work describes the development and validation of an Unmanned Aircraft System (UAS, commonly known as drone) with an onboard stereo-vision system capable of acquiring, storing and transmitting images for analysis to obtain full-field, three-dimensional displacement and strain measurements.

Methods

The UAS equipped with a StereoDIC system has been developed and tested in the lab. The drone system, named DroneDIC, autonomously hovers in front of a prestressed railroad tie under pressure and DIC data are collected. A stationary DIC system is used in parallel to collect data for the railroad tie. We compare the data to validate the readings from the DroneDIC system.

Results

We present the analysis of the results obtained by both systems. Our study shows that the results we obtain from the DroneDIC system are similar to the ones gathered from the stationary DIC system.

Conclusions

This work serves as a proof of concept for the successful integration of DIC and drone technologies into the DroneDIC system. DroneDIC combines the high accuracy inspection capabilities of traditional stationary DIC systems with the mobility offered by drone platforms. This is a major step towards autonomous DIC inspection in portions of a structure where access is difficult via conventional methods.

     

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.

     

DIC-Based Surface Motion Correction for ESPI Measurements

Electronic Speckle Pattern Interferometry (ESPI) provides a sensitive technique for measuring surface deformations. The technique involves comparison of the speckle phase angles within surface images measured before and after material deformation. This phase angle comparison requires that the speckle positions be consistent in all images. A lateral shift between image sets of just one pixel substantially degrades ESPI measurements, while a shift of two or more pixels typically causes complete decorrelation and compromises the measurement entirely. To prevent such rigid body motions, the specimen and the optical system must be rigidly fixed. This requirement typically impedes use of the ESPI method in applications outside laboratories or where it is necessary to remove the specimen from the optical setup between ESPI measurements. Here, Digital Image Correlation (DIC) is used to track speckle motion caused by specimen displacement between ESPI phase stepped image sets. The measured image set can then be mathematically shifted to restore the original speckle locations, thereby recorrelating the ESPI measurement. Examples are presented where ESPI measurements are successfully made with specimen shifts over 60 pixels.     

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 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.

     

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.     

Mechanically Regularized FE DIC for Heterogeneous Materials

In situ tensile tests in a scanning electron microscope (SEM) have been conducted on a 8-layer 5-harness satin carbon fibre and epoxy matrix composite to observe the first stages of damage at the scale of fibres and matrix. A speckle pattern based on a suspension of alumina particles was applied onto the surface of the specimen to facilitate the use of digital image correlation (DIC). Local and finite element (FE) DIC are compared on pictures acquired during the tensile tests, with and without a speckle pattern. FE DIC with mechanical regularization was found to be the only approach able to measure displacement fields at a fine enough resolution in both cases. This method, initially created for homogeneous materials, was then adapted to heterogeneous materials. First, a microstructure consistent mesh was created and used for correlation purposes. Second, the difference between the mechanical properties of the constituents is taken into account in the mechanical regularization. Last, the accuracy of the method is analysed. The adaptation presented herein was proved to be able to measure displacement fields in the matrix between fibres with an error of 10 nm (a fifth of a pixel) and to detect the initiation of the first damage mechanisms by means of the mechanical residuals.

     

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.