Towards Criteria Characterizing the Metrological Performance of Full-field Measurement Techniques

Users of full-field measurement methods like Digital Image Correlation (DIC) often aim to perform measurements with the best trade-off between spatial resolution, bias and measurement resolution. Whenever two full-field methods are compared, it is essential that these criteria are taken into consideration. Recently a metrological efficiency indicator for full-field measurements has been proposed and discussed. This indicator combines measurement resolution and spatial resolution. It has been shown to be invariant to the subset size in the case of Local DIC. The goal of this article is to discuss a method, which determines both the spatial and the measurement resolutions for a given bias for two different DIC methods, in order to obtain the metrological efficiency indicator for each of these methods. The benefit of this indicator is that it does not depend on setting parameters such as the subset size, which are chosen by the user. As such, it can be considered as intrinsic to each technique, thus enabling fair comparison. Local DIC and triangular finite element based Global DIC will be the subject of this investigation. With this setting, their respective subset and triangular element sizes will be related to the spatial resolution of both methods for a given acceptable bias. By using the metrological efficiency indicator, the performance of the two methods will be compared and discussed to a new level of detail. Generally speaking, the indicator shows that the metrological performance of both methods is similar, confirming their popularity. However, it will be shown that, depending on the choice of what an acceptable bias is, one of the method may be preferred to another. The results show that for the specific DIC versions used in the study, for cases for which a significant bias is acceptable, Local DIC outperforms Global DIC, while the opposite is true in the case for which the bias requirements are more stringent. Finally, the quadratic versions of both DIC versions are shown to significantly outperform their respective linear versions.

     

Direct Extraction of Cohesive Fracture Properties from Digital Image Correlation: A Hybrid Inverse Technique

The accuracy of an adopted cohesive zone model (CZM) can affect the simulated fracture response significantly. The CZM has been usually obtained using global experimental response, e.g., load versus either crack opening displacement or load-line displacement. Apparently, deduction of a local material property from a global response does not provide full confidence of the adopted model. The difficulties are: (1) fundamentally, stress cannot be measured directly and the cohesive stress distribution is non-uniform; (2) accurate measurement of the full crack profile (crack opening displacement at every point) is experimentally difficult to obtain. An attractive feature of digital image correlation (DIC) is that it allows relatively accurate measurement of the whole displacement field on a flat surface. It has been utilized to measure the mode I traction-separation relation. A hybrid inverse method based on combined use of DIC and finite element method is used in this study to compute the cohesive properties of a ductile adhesive, Devcon Plastic Welder II, and a quasi-brittle plastic, G-10/FR4 Garolite. Fracture tests were conducted on single edge-notched beam specimens (SENB) under four-point bending. A full-field DIC algorithm was employed to compute the smooth and continuous displacement field, which is then used as input to a finite element model for inverse analysis through an optimization procedure. The unknown CZM is constructed using a flexible B-spline without any “a priori” assumption on the shape. The inversely computed CZMs for both materials yield consistent results. Finally, the computed CZMs are verified through fracture simulation, which shows good experimental agreement.     

Grain-scale processes governing shear band initiation and evolution in sands

A variety of experimental techniques have been used to advance understanding of strain localization phenomena in sands. However, all of these methods have fallen short in characterizing the evolution of the grain-scale processes that necessarily control shear band formation and growth in sands. This paper presents results of application of the non-destructive displacement measurement technique of digital image correlation (DIC) to measure two- and three-dimensional surface displacements on plane strain and axisymmetric sand specimens over short time steps. The abundance of local displacement data, high level of accuracy, and nearly continuous (spatially and temporally) record of displacement evolution afforded by the DIC technique has finally enabled a means to quantify local displacements to particulate-scale intensity. The data have been used to evaluate the local displacement mechanisms leading to the triggering of the formation of persistent shear bands, the timing of shear band formation with regard to the achievement of peak stress, and the character of displacements within fully formed shear bands. Insights are offered regarding the relation between strain localization and global stress-strain behavior, and the ensuing interpretations of shear banding as a hardening or softening phenomenon. Comparison of behavior between plane strain and triaxial tests offer additional perspective on the influences of three-dimensional stresses and boundary conditions on shear banding. The results further shed light on the micro-deformation mechanisms (i.e. buckling columns) responsible for the observed local strain non-uniformities that characterize “steady-state” shear band evolution.     

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.     

On the Use of NURBS Functions for Displacement Derivatives Measurement by Digital Image Correlation

In this paper, we propose to investigate the potential improvement of using Non-Uniform Rational B-Spline (NURBS) functions for displacement measurements by digital image correlation (DIC). The aim is at improving the performance of DIC to capture with low uncertainty and low noise levels not only the displacement field but also its derivatives. Indeed, when the displacement field is used to feed constitutive law identification procedures, displacement derivatives are required and thus may be measured with robustness. Two examples illustrate the potential of NURBS for DIC: a compressive test on a wood sample and a bending test on a steel beam. For the latter, beam kinematics are adopted and NURBS are used in order to capture the variation of the curvature (second derivative of the displacement) along the beam axis. For these two examples, an error study based on a decomposition of the error into the correlation error and the interpolation error, is carried out and shows the great potential of NURBS functions for DIC.     

Inverse Estimation of Cohesive Fracture Properties of Asphalt Mixtures Using an Optimization Approach

Tensile cracking in asphalt pavements due to vehicular and thermal loads has become an experimental and numerical research focus in the asphalt materials community. Previous studies have used the discrete element method (DEM) to study asphalt concrete fracture. These studies used trial-and-error to obtain local fracture properties such that the DEM models approximate the experimental load-crack mouth opening displacement response. In the current study, we identify the cohesive fracture properties of asphalt mixtures via a nonlinear optimization method. The method encompasses a comparative investigation of displacement fields obtained using both digital image correlation (DIC) and heterogeneous DEM fracture simulations. The proposed method is applied to two standard fracture test geometries: the single-edge notched beam test, SE(B), under three-point bending, and the disk-shaped compact tension test, DC(T). For each test, the Subset Splitting DIC algorithm is used to determine the displacement field in a predefined region near the notch tip. Then, a given number of DEM simulations are performed on the same specimen. The DEM is used to simulate the fracture of asphalt concrete with a linear softening cohesive contact model, where fracture-related properties (e.g., maximum tensile force and maximum crack opening) are varied within a predefined range. The difference between DIC and DEM displacement fields for each set of fracture parameters is then computed and converted to a continuous function via multivariate Lagrange interpolation. Finally, we use a Newton-like optimization technique to minimize Lagrange multinomials, yielding a set of fracture parameters that minimizes the difference between the DEM and DIC displacement fields. The optimized set of fracture parameters from this nonlinear optimization procedure led to DEM results which are consistent with the experimental results for both SE(B) and DC(T) geometries.     

Deformation measurements by digital image correlation: Implementation of a second-order displacement gradient

This paper outlines the procedure for refining the digital image correlation (DIC) method by implementing a second-order approximation of the displacement gradients. The second-order approximation allows the DIC method to directly measure both the first- and second-order displacement gradients resulting from nonlinear deformation. Thirteen unknown parameters, consisting of the components of displacement, the first- and second-order displacement gradients and the gray-scale value offset, are determined through optimization of a correlation coefficient. The previous DIC method assumes that the local deformation in a subset of pixels is represented by a first-order Taylor series approximation for the displacement gradient terms, so actual deformations consisting of higher order displacement gradients tend to distort the infinitesimal strain measurements. By refining the method to measure both the first- and second-order displacement gradients, more accurate strain measurements can be achieved in large-deformation situations where second-order deformations are also present. In most cases, the new refinements allow the DIC method to maintain an accuracy of ±0.0002 for the first-order displacement gradients and to reach ±0.0002 per pixel for the second-order displacement gradients.     

Grid Method for Microscale Discontinuous Deformation Measurement

The objective of this paper is to explore both grid method and Digital Image Correlation (DIC) technique for microscale and discontinuous displacement measurements, such as those associated with crack tips. First, the principle of the grid method is revisited. The grid method and DIC technique are then applied to computer generated images to calculate the displacement field around crack tips. Finally, the grid method is applied to actual experimental images of fracture tests which are conducted inside a Scanning Electron Microscope (SEM) chamber. A new technique is developed to generate microscale pattern that is suitable for both grid method and DIC technique. The displacement fields calculated from grid method are compared with those from DIC technique to identify the strengths and weaknesses of each technique for the microscale and discontinuous displacement measurements. It has been determined that grid method can obtain data closer to the discontinuity than DIC; however, DIC produces smoother displacement fields at the far field. Using this new pattern generation technique, both grid method and DIC technique can be applied to the fracture test at the microscale to complement with each other to achieve the best experiment results.     

Fast, Robust and Accurate Digital Image Correlation Calculation Without Redundant Computations

High-efficiency and high-accuracy deformation analysis using digital image correlation (DIC) has become increasingly important in recent years, considering the ongoing trend of using higher resolution digital cameras and common requirement of processing a large sequence of images recorded in a dynamic testing. In this work, to eliminate the redundant computations involved in conventional DIC method using forward additive matching strategy and classic Newton–Raphson (FA-NR) algorithm without sacrificing its sub-pixel registration accuracy, we proposed an equivalent but more efficient DIC method by combining inverse compositional matching strategy and Gauss-Newton (IC-GN) algorithm for fast, robust and accurate full-field displacement measurement. To this purpose, first, an efficient IC-GN algorithm, without the need of re-evaluating and inverting Hessian matrix in each iteration, is introduced to optimize the robust zero-mean normalized sum of squared difference (ZNSSD) criterion to determine the desired deformation parameters of each interrogated subset. Then, an improved reliability-guided displacement tracking strategy is employed to achieve further speed advantage by automatically providing accurate and complete initial guess of deformation for the IC-GN algorithm implemented on each calculation point. Finally, an easy-to-implement interpolation coefficient look-up table approach is employed to avoid the repeated calculation of bicubic interpolation at sub-pixel locations. With the above improvements, redundant calculations involved in various procedures (i.e. initial guess of deformation, sub-pixel displacement registration and sub-pixel intensity interpolation) of conventional DIC method are entirely eliminated. The registration accuracy and computational efficiency of the proposed DIC method are carefully tested using numerical experiments and real experimental images. Experimental results verify that the proposed DIC method using IC-GN algorithm and the existing DIC method using classic FA-NR algorithm generate similar results, but the former is about three to five times faster. The proposed reliability-guided IC-GN algorithm is expected to be a new standard full-field displacement tracking algorithm in DIC.     

DIC Challenge: Developing Images and Guidelines for Evaluating Accuracy and Resolution of 2D Analyses

With the rapid spread in use of Digital Image Correlation (DIC) globally, it is important there be some standard methods of verifying and validating DIC codes. To this end, the DIC Challenge board was formed and is maintained under the auspices of the Society for Experimental Mechanics (SEM) and the international DIC society (iDICs). The goal of the DIC Board and the 2D–DIC Challenge is to supply a set of well-vetted sample images and a set of analysis guidelines for standardized reporting of 2D–DIC results from these sample images, as well as for comparing the inherent accuracy of different approaches and for providing users with a means of assessing their proper implementation. This document will outline the goals of the challenge, describe the image sets that are available, and give a comparison between 12 commercial and academic 2D–DIC codes using two of the challenge image sets.     

Spatial DIC Errors due to Pattern-Induced Bias and Grey Level Discretization

Digital image correlation (DIC) is an optical metrology method widely used in experimental mechanics for full-field shape, displacement and strain measurements. The required strain resolution for engineering applications of interest mandates DIC to have a high image displacement matching accuracy, on the order of 1/100th of a pixel, which necessitates an understanding of DIC errors. In this paper, we examine two spatial bias terms that have been almost completely overlooked. They cause a persistent offset in the matching of image intensities and thus corrupt DIC results. We name them pattern-induced bias (PIB), and intensity discretization bias (IDB). We show that the PIB error occurs in the presence of an undermatched shape function and is primarily dictated by the underlying intensity pattern for a fixed displacement field and DIC settings. The IDB error is due to the quantization of the gray level intensity values in the digital camera. In this paper we demonstrate these errors and quantify their magnitudes both experimentally and with synthetic images.

     

Crack Path Selection in Microstructurally Tailored Inhomogeneous Polymers

In this work the photodegradation of a polyethylene co-polymer, ECO, is exploited to generate inhomogeneous arrangements of model “granular” media that aids in the experimental study of crack path selection problems. The advantage of our approach is that the well-known sensitivity of ECO’s properties to ultraviolet (UV) light allows knowledge of both grain and grain boundary response a priori to performing the experiments. A model granular arrangement with identical grain structure and of three different levels of grain boundary strength was constructed. Each microstructure was loaded in uniaxial tension, and the resulting strain fields were recorded using digital image correlation (DIC). Depending on the applied load and the local microstructure, crack initiation and growth occurred differently: either one main crack developed and became responsible for failure, or an initial crack formed but arrested, and a host of secondary cracks appeared at different critical locations, including grain boundaries and grain interiors. Thus, the experimental configuration can be used to produce controllable amounts of intergranular vs. transgranular failure. The DIC results were correlated with global load–displacement measurements and were compared to finite element models using ABAQUS that simulated the configurations tested in each case. A von Mises and Tresca yield criterion was used to illustrate areas where failure was possible, and the results were favorably compared with the experimental failure initiation sites in each case.     

A generalized multilength scale nonlinear composite plate theory with delamination

A new type of plate theory for the nonlinear analysis of laminated plates in the presence of delaminations and other history-dependent effects is presented. The formulation is based on a generalized two length scale displacement field obtained from a superposition of global and local displacement effects. The functional forms of global and local displacement fields are arbitrary. The theoretical framework introduces a unique coupling between the length scales and represents a novel two length scale or local-global approach to plate analysis. Appropriate specialization of the displacement field can be used to reduce the theory to any currently available, variationally derived, displacement based (discrete layer, smeared, or zig-zag) plate theory.The theory incorporates delamination and/or nonlinear elastic or inelastic interfacial behavior in a unified fashion through the use of interfacial constitutive (cohesive) relations. Arbitrary interfacial constitutive relations can be incorporated into the theory without the need for reformulation of the governing equations. The theory is sufficiently general that any material constitutive model can be implemented within the theoretical framework. The theory accounts for geometric nonlinearities to allow for the analysis of buckling behavior.The theory represents a comprehensive framework for developing any order and type of displacement based plate theory in the presence of delamination, buckling, and/or nonlinear material behavior as well as the interactions between these effects.The linear form of the theory is validated by comparison with exact solutions for the behavior of perfectly bonded and delaminated laminates in cylindrical bending. The theory shows excellent correlation with the exact solutions for both the inplane and out-of-plane effects and the displacement jumps due to delamination. The theory can accurately predict the through-the-thickness distributions of the transverse stresses without the need to integrate the pointwise equilibrium equations. The use of a low order of the general theory, i.e. use of both global and local displacement fields, reduces the computational expense compared to a purely discrete layer approach to the analysis of laminated plates without loss of accuracy. The increased efficiency, compared to a solely discrete layer theory, is due to the coupling introduced in the theory between the global and local displacement fields.     

Dual-Porosity Coarse-Scale Modeling and Simulation of Highly Heterogeneous Geomodels

Accurate upscaling of highly heterogeneous subsurface reservoirs remains a challenge in the context of modeling of flow and transport. In this work, we address this challenge with emphasis on the representation of the displacement efficiency in coarse-scale modeling. We propose a dual-porosity upscaling approach to handle displacement calculations in high resolution and highly heterogeneous formations. In this approach, the pore space is arranged into two levels of porosity based on flow contribution, and a dual-porosity dual-permeability flow model is adapted for coarse-scale flow simulation. The approach uses fine-scale streamline information to transform a heterogeneous geomodel into a coarse dual-continuum model that preserves the global flow pathways adequately. The performance of the proposed technique is demonstrated for two heterogeneous reservoirs using both black oil (waterflooding) and compositional (gas injection) modeling approaches. We demonstrate that the coarse dual-porosity models predict the breakthrough times accurately and reproduce the post-breakthrough responses adequately. This is in contrast to conventional single-porosity upscaling techniques that overestimate breakthrough times and displacement efficiencies (sweep). By preserving large-scale heterogeneities, coarse dual-porosity models are demonstrated to be significantly less sensitive to the level of upscaling, when compared to conventional single-porosity upscaling. Accordingly, the proposed upscaling approach is a relevant and suitable technique for upscaling of highly heterogeneous geomodels.     

Residual Stress Measurement Using Hole Drilling and Integrated Digital Image Correlation Techniques

The effectiveness of optical (mostly interferometric) methods for the measurement of residual stresses is largely demonstrated in literature. Nevertheless, these techniques are still confined to optical laboratories due to their high sensitivity to vibrations which makes it very difficult to perform the measurement in an industrial environment. Digital Image Correlation (DIC) has recently been proposed as a possible solution to this problem: this non-interferometric technique is much less affected by vibrations, but its sensitivity is relatively low, thus negatively affecting the accuracy of results. This work proposes to use a variant of Digital Image Correlation, known as Integrated DIC (iDIC), in combination with the hole drilling technique. Since iDIC directly incorporates in its formulation the displacement field related to hole drilling, it overcomes most of the problems of standard DIC; in this way it is possible to obtain accurate results without using interferometric techniques.     

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.     

METHOD BASED ON DUAL-QUADRATIC PROGRAMMING FOR FRAME STRUCTURAL OPTIMIZATION WITH LARGE SCALE

The optimality criteria (OC) method and mathematical programming (MP) were combined to found the sectional optimization model of frame structures. Different methods were adopted to deal with the different constraints. The stress constraints as local constraints were approached by zero-order approximation and transformed into movable sectional lower limits with the full stress criterion. The displacement constraints as global constraints were transformed into explicit expressions with the unit virtual load method. Thus an approximate explicit model for the sectional optimization of frame structures was built with stress and displacement constraints. To improve the resolution efficiency, the dual-quadratic programming was adopted to transform the original optimization model into a dual problem according to the dual theory and solved iteratively in its dual space. A method called approximate scaling step was adopted to reduce computations and smooth the iterative process. Negative constraints were deleted to reduce the size of the optimization model. With MSC/Nastran software as structural solver and MSC/Patran software as developing platform, the sectional optimization software of frame structures was accomplished, considering stress and displacement constraints. The examples show that the efficiency and accuracy are improved.     

Assessment of Digital Image Correlation Measurement Errors: Methodology and Results

Optical full-field measurement methods such as Digital Image Correlation (DIC) are increasingly used in the field of experimental mechanics, but they still suffer from a lack of information about their metrological performances. To assess the performance of DIC techniques and give some practical rules for users, a collaborative work has been carried out by the Workgroup “Metrology” of the French CNRS research network 2519 “MCIMS (Mesures de Champs et Identification en Mécanique des Solides / Full-field measurement and identification in solid mechanics, http://www.ifma.fr/lami/gdr2519)”. A methodology is proposed to assess the metrological performances of the image processing algorithms that constitute their main component, the knowledge of which being required for a global assessment of the whole measurement system. The study is based on displacement error assessment from synthetic speckle images. Series of synthetic reference and deformed images with random patterns have been generated, assuming a sinusoidal displacement field with various frequencies and amplitudes. Displacements are evaluated by several DIC packages based on various formulations and used in the French community. Evaluated displacements are compared with the exact imposed values and errors are statistically analyzed. Results show general trends rather independent of the implementations but strongly correlated with the assumptions of the underlying algorithms. Various error regimes are identified, for which the dependence of the uncertainty with the parameters of the algorithms, such as subset size, gray level interpolation or shape functions, is discussed.     

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.