Integrated Digital Image Correlation Research Articles

Parameter identification of a phase-field fracture model using integrated digital image correlation

Phase-field fracture (PFF) modeling is a popular approach to model and simulate fracture processes in solids. Accurate material parameters and boundary conditions are of utmost importance to ensure a good prediction quality of numerical simulations. In this work, an Integrated Digital Image Correlation (IDIC) algorithm is proposed to calibrate boundary conditions, Poisson’s ratio, fracture energy and internal length, all at once, by using the phase-field model itself and images of a deforming sample. The presented approach is applied to virtual experiments mimicking a single edge notched shear test and implemented in the open-source deal.II-based software pfm-cracks and the digital image correlation library Correli 3.2. The reliability of the results is investigated for different levels of acquisition noise, thereby demonstrating high robustness and accuracy for a wide range of noise levels. The conditioning of the problem is analyzed via sensitivity fields for all parameters and the eigendecomposition of the Hessian matrix used in the IDIC algorithm.

Bayesian approach to micromechanical parameter identification using Integrated Digital Image Correlation

Micromechanical parameters are essential in understanding the behavior of materials with a heterogeneous structure, which helps to predict complex physical processes such as delamination, cracks, and plasticity. However, identifying these parameters is challenging due to micro-macro length scale differences, required high resolution, and ambiguity in boundary conditions, among others. The Integrated Digital Image Correlation (IDIC) method, a state-of-the-art full-field deterministic approach to parameter identification, is widely used but suffers from high sensitivity to boundary data errors and is limited to identification of parameters within well-posed problems. This article employs Bayesian approach to estimate micromechanical shear and bulk moduli of fiber-reinforced composite samples under plane strain assumption, and to improve handling of boundary noise. The main purpose of this article is to quantify the effect of uncertainty in the boundary conditions in the stochastic setting. To this end, the Metropolis–Hastings Algorithm (MHA) is employed to estimate probability distributions of bulk and shear moduli and boundary condition parameters using IDIC, considering a fiber-reinforced composite sample under plane strain assumption. The performance and robustness of the MHA are compared to two versions of deterministic IDIC method, under artificially introduced random and systematic errors in kinematic boundary conditions. Although MHA is shown to be computationally more expensive and in certain cases less accurate than the recently introduced Boundary-Enriched IDIC, it offers significant advantages, in particular being able to optimize a large number of parameters while obtaining statistical characterization as well as insights into individual parameter relationships. The paper furthermore highlights the benefits of the non-normalized approach to parameter identification with MHA (leading, within deterministic IDIC, to an ill-posed formulation), which significantly improves the robustness in handling the boundary noise.

Integrated digital image correlation for micro-mechanical parameter identification in multiscale experiments

Micromechanical constitutive parameters are important for many engineering materials, typically in microelectronic applications and material design. Their accurate identification poses a three-fold experimental challenge: (i) deformation of the microstructure is observable only at small scales, requiring SEM or other microscopy techniques; (ii) external loadings are applied at a (larger) engineering or device scale; and (iii) material parameters typically depend on the applied manufacturing process, necessitating measurements on material produced with the same process. In this paper, micromechanical parameter identification in heterogeneous solids is addressed through multiscale experiments combined with Integrated Digital Image Correlation (IDIC) in conjunction with various possible computational homogenization schemes. To this end, some basic concepts underlying multiscale approaches available in the literature are first reviewed, discussing their respective advantages and disadvantages from the computational as well as experimental point of view. A link is made with recently introduced uncoupled methods, which allow for identification of material parameter ratios at the microscale, still lacking a proper normalization. Two multiscale methods are analysed, allowing to bridge the gap between microstructural kinematics and macroscopically measured forces, providing the required normalization. It is shown that an integrated experimental--computational scheme provides relaxed requirements on scale separation. The accuracy and performance of the discussed techniques are analysed by means of virtual experimentation under plane strain and large strain assumptions for unidirectional fibre-reinforced composites. The robustness against image noise is also assessed.

Characterization of Thermo-mechanical parameters of Nickel-Based single crystal superalloys under high-temperature by modified I-DIC method

Understanding the evolution law of thermo-mechanical parameters of nickel-based single crystal superalloys under high-temperature is significant for modeling, application, and structural optimization. In this study, a modified integrated digital image correlation (I-DIC) method is developed to characterize its thermo-mechanical properties. Particle Swarm Optimization (PSO) and Gradient-Based optimization algorithm are introduced to the modified I-DIC method. The orthotropic thermo-mechanical constitutive model for nickel-based single crystal superalloys is evaluated and the relative five constitutive parameters at temperatures ranging from 600 ℃ to 1000 ℃ are inversed simultaneously by the modified I-DIC method. Comparison between experiments and simulations confirms that the suggested model is reliable and the modified parameter inversion method is accurate and effective. The results show that the parameters vary with temperature. The coefficient of thermal expansion (CTE) and Poison’s ratio increased with increasing temperature, while Young’s modulus and shear modulus decreased with increasing temperature.

Effect of asymmetric material entrance on lubrication in cold rolling

An Integrated Digital Image Correlation (IDIC) method has been applied to the cold rolling process, the images clearly visualise the geometry of the roll bite and the inlet zone. A key, novel finding is that despite using coils and applying entry tension, the strip can enter asymmetrically in the rolling mill. Moreover, it is shown that asymmetric strip feeding results in an uneven lubricant film thickness between top and bottom strip surface. A method is detailed to feed the strip truly symmetrically in the mill, a procedure that is necessary for a meaningful experimental validation of lubricant film thickness models. For symmetric rolling processes the measured film thickness corresponds significantly better with the theory than for asymmetric processes.

Calibration of crystal orientation and pattern center of EBSD using integrated digital image correlation

The accuracy of electron backscatter diffraction indexation has long been limited by pattern center determination, and numerous hardware and software methods have been proposed to improve the calibration. Here, an Integrated Digital Image Correlation (IDIC) procedure is proposed to determine simultaneously crystal orientation and pattern center by registering experimental and simulated electron diffraction patterns. To assess the performance and robustness of the procedure, numerous case studies are reported. Noise sensitivity is first explored on virtual data to assess convergence conditions and result uncertainty up to high noise level and small detector size. Two experimental data sets are further exploited. First, a high-definition detector shows that crystal orientation uncertainty as low as 3×10−2 degrees can be achieved, that is at least 80% less than commercial Hough-transformation based indexation method. Different sample tilt angles are tested, IDIC indexation proves much more tolerant with imprecise tilt angles than common EBSD indexation methods. Second, fast EBSD acquisitions with a coarse definition performed during an in-situ tensile test are analysed. A quantification of the residual noise allows one to formulate an optimized IDIC functional with a proper pixel-wise weight. With the latter refinement a two-pass procedure leads to a much enhanced precision of the determination of crystal orientation, giving access to more precise evaluation of maps of geometrically necessary dislocation densities.

Residual-based pattern center calibration in high-resolution electron backscatter diffraction

High resolution electron backscatter diffraction is an emerging technique of micro-structural characterization which can be used for local elastic strain measurement. Pattern center (PC) coordinate, an important parameter which affects accuracy of HR-EBSD, should be carefully calibrated before calculation. An integrated digital image correlation (IDIC) algorithm can extract the deformation gradient tensor and return the residual between reference and targeted images simultaneously. We propose to use the residual value as a criterion to calibrate PC, as an accurate PC value, accompanied with sample tilt parameters, results in slightly lower level of residuals when using simulated diffraction patterns. Though the reduction of residual value is small in the calibration process, our experimental dataset shows that the calibrated PC value will reduce the retrieved Von Mises strain, which results from the reduction of phantom strain caused by errors in the initially-guessed PC values given by the commercial software DynamicS.

Full-field identification of mixed-mode adhesion properties in a flexible, multi-layer microelectronic material system

The identification of relevant adhesion properties is important for the development of microelectronic systems, e.g., microprocessors, light-emitting diodes, etc. This is best done on an actual device, rather than on dedicated specimens, because such properties are highly specimen specific. This paper discusses how the full-field identification method of integrated digital image correlation (IDIC) can be used to identify three mixed-mode cohesive zone parameters of a flexible, organic light-emitting diode (OLED) from a single mechanical test. A tri-axial, micro-mechanical testing setup is employed for the in situ, on-device delamination experiment, employing optical microscopy.The microscopic magnification, required for capturing the relevant kinematics, prevents the experimentally imposed loading conditions to be captured within the field of view. Virtual experiments are firstly conducted to optimize the local boundary conditions therefore required by the finite element simulation within the IDIC-framework, and which constitutes the cohesive zone model. The virtual experiments also allow for selecting an adequate load-case for the actual experiment, in order to maximize the kinematic sensitivity of IDIC with respect to the three mixed-mode cohesive zone parameters, and identify them accurately. The image residual, minimized in IDIC, together with the convergence behavior towards the associated global minimum, provide adequate measures for assessing the trustworthiness of the solution.The optimized load-case is subsequently used to trigger delamination of a 50 [μm] thick barrier stack from its substrate in a real in situ experiment on a flexible OLED. The optimized boundary conditions from the virtual experiments are used in a corresponding simulation for identifying the three mixed-mode cohesive zone parameters by IDIC. The optimization scheme within IDIC was found to be robust against deviating initial guesses, and consistently converged to a unique solution for the cohesive zone parameters.

Correction of Scanning Electron Microscope Imaging Artifacts in a Novel Digital Image Correlation Framework

The combination of digital image correlation (DIC) and scanning electron microscopy (SEM) enables to extract high resolution full field displacement data, based on the high spatial resolution of SEM and the sub-pixel accuracy of DIC. However, SEM images may exhibit a considerable amount of imaging artifacts, which may seriously compromise the accuracy of the displacements and strains measured from these images. The current study proposes a unified general framework to correct for the three dominant types of SEM artifacts, i.e. spatial distortion, drift distortion and scan line shifts. The artifact fields are measured alongside the mechanical deformations to minimize the artifact induced errors in the latter. To this purpose, Integrated DIC (IDIC) is extended with a series of hierarchical mapping functions that describe the interaction of the imaging process with the mechanics. A new IDIC formulation based on these mapping functions is derived and the potential of the framework is tested by a number of virtual experiments. The effect of noise in the images and different regularization options for the artifact fields are studied. The error in the mechanical displacement fields measured for noise levels up to 5% is within the usual DIC accuracy range for all the cases studied, while it is more than 4 pixels if artifacts are ignored. A validation on real SEM images at three different magnifications confirms that all three distortion fields are accurately captured. The results of all virtual and real experiments demonstrate the accuracy of the methodology proposed, as well as its robustness in terms of convergence.

Simultaneous full-field multi-experiment identification

Identification of constitutive parameters relies mainly on their sensitivity to the measurands. In particular, the specific static and kinematic responses controlled by each parameter of interest has to be captured by full-field measurements. The development of modern constitutive models has led to many new and interesting sample geometries and loading histories, aiming at maximizing the sensitivity to their delicate material parameters, especially through their kinematics of interest. However, it is often impossible to design an experiment that activates all material parameters of interest, and thus multiple experiments are needed. This paper discusses a methodology for combining the data from such multi-experiments into a single identification process to calibrate a complete set of parameters at once. Many different ways of merging experimental data exist, leading to unbiased identifications of the parameters of interest. However, only one optimal procedure leads to minimal uncertainty, taking into account the noise of each acquisition source. The proposed identification method is a natural extension of inverse methods such as Finite Element Method Updating (FEMU) with appropriate weights or Integrated Digital Image Correlation (I-DIC). This procedure is illustrated by the identification of the planar parameters of the so-called Hill48 anisotropic yield surface together with an exponential isotropic hardening law of AA2219.

Mechanical Shape Correlation: A novel integrated digital image correlation approach

Mechanical Shape Correlation (MSC) is a novel Integrated Digital Image Correlation (IDIC) based technique used for parameter identification. Digital images taken during an experiment are correlated and coupled to a Finite Element model of the specimen, in order to find the correct parameters in this numerical model. In contrast to regular IDIC techniques, where the images consist of a grayscale speckle pattern applied to the sample, in MSC the images are projections based on the contour lines of the test specimen only. This makes the technique suitable in cases where IDIC cannot be used, e.g., when large deformations and rotations cause parts of the sample to rotate in or out-of-view, or when the speckle pattern degrades due to large or complex deformations, or when application of the pattern is difficult because of small or large specimen dimensions. The method targets problems for which the outline of the specimen is large with respect to the volume of the structure and changes significantly upon deformation. The technique is here applied to virtual experiments with stretchable electronic interconnects, for identification of both elastic and plastic properties. Furthermore, attention is paid to the influence of algorithmic choices and experimental issues. The method reveals good convergence and adequate initial guess robustness. The results are promising and indicate that the method can be used in cases of either large, complex or three-dimensional displacements and rotations on any scale.

Mixed-mode cohesive zone parameters from integrated digital image correlation on micrographs only

Mixed-mode loading conditions strongly affect the failure mechanisms of interfaces between different material layers as typically encountered in microelectronic systems, exhibiting complex material stacking and 3D microstructures. The integrated digital image correlation (IDIC) method is here extended to enable identification of mixed-mode cohesive zone model parameters under arbitrary levels of mode-mixity. Micrographs of a mechanical experiment with a restricted field of view and without any visual data of the applied far-field boundary conditions are correlated to extract the cohesive zone model parameters used in a corresponding finite element simulation. Reliable or accurate force measurement data is thereby not available, which constitutes a complicating factor. For proof-of-concept, a model system comprising a bilayer double cantilever beam specimen loaded under mixed-mode bending conditions is explored. Virtual experiments are conducted to assess the sensitivities of the technique with respect to mixed-mode loading conditions at the interface. The virtual experiments reveal the necessity of (1) optimizing the applied local boundary conditions in the finite element model and (2) optimizing the region of interest by analyzing the model’s kinematic sensitivity relative to the cohesive zone parameters. From a single test-case, exhibiting a range of mode-mixity values, the mixed-mode cohesive zone model parameters are accurately identified with errors below 1%. The IDIC-procedure is shown to be robust against large variations in the initial guess values for the parameters.Real mixed-mode bending experiments are conducted on bilayer specimens comprising two spring steel beams and an epoxy adhesive interface, under different levels of mode-mixity. The mixed-mode cohesive zone model parameters are identified, demonstrating that IDIC is a powerful technique for characterizing interface properties of interfaces, imaged with a limited field of view, as is typically the case in microelectronic applications.

A consistent full-field integrated DIC framework for HR-EBSD

A general, transparent, finite-strain Integrated Digital Image Correlation (IDIC) framework for high angular resolution EBSD (HR-EBSD) is proposed, and implemented through a rigorous derivation of the optimization scheme starting from the fundamental brightness conservation equation in combination with a clear geometric model of the Electron BackScatter Pattern (EBSP) formation. This results in a direct one-step correlation of the full field-of-view of EBSPs, which is validated here on dynamically simulated patterns. Strain and rotation component errors are, on average, (well) below 10−5 for small (Eeq=0.05%) and medium (Eeq=0.2%) strain, and below 3×10−5 for large strain (Eeq=1%), all for large rotations up to 10° and 2% image noise. High robustness against poor initial guesses (1° misorientation and zero strain) and typical convergence in 5 iterations is consistently observed for, respectively, image noise up to 20% and 5%. This high accuracy and robustness rivals, when comparing validation on dynamically simulated patterns, the most accurate HR-EBSD algorithms currently available which combine sophisticated filtering and remapping strategies with an indirect two-step correlation approach of local subset ROIs. The proposed general IDIC/HR-EBSD framework lays the foundation for future extensions towards more accurate EBSP formation models or even absolute HR-EBSD.

On micromechanical parameter identification with integrated DIC and the role of accuracy in kinematic boundary conditions

Integrated Digital Image Correlation (IDIC) is nowadays a well established full-field experimental procedure for reliable and accurate identification of material parameters. It is based on the correlation of a series of images captured during a mechanical experiment, that are matched by displacement fields derived from an underlying mechanical model. In recent studies, it has been shown that when the applied boundary conditions lie outside the employed field of view, IDIC suffers from inaccuracies. A typical example is a micromechanical parameter identification inside a Microstructural Volume Element (MVE), whereby images are usually obtained by electron microscopy or other microscopy techniques but the loads are applied at a much larger scale. For any IDIC model, MVE boundary conditions still need to be specified, and any deviation or fluctuation in these boundary conditions may significantly influence the quality of identification. Prescribing proper boundary conditions is generally a challenging task, because the MVE has no free boundary, and the boundary displacements are typically highly heterogeneous due to the underlying microstructure. The aim of this paper is therefore first to quantify the effects of errors in the prescribed boundary conditions on the accuracy of the identification in a systematic way. To this end, three kinds of mechanical tests, each for various levels of material contrast ratios and levels of image noise, are carried out by means of virtual experiments. For simplicity, an elastic compressible Neo-Hookean constitutive model under plane strain assumption is adopted. It is shown that a high level of detail is required in the applied boundary conditions. This motivates an improved boundary condition application approach, which considers constitutive material parameters as well as kinematic variables at the boundary of the entire MVE as degrees of freedom in the IDIC procedure, assuring that both are identified with equal precision and importance. This problem has been studied in the literature with a different method, i.e. Finite Element Method Updating framework.

Image-based interface characterization with a restricted microscopic field of view

Accurate characterization of adhesion properties in microelectronic systems is challenging due to (1) the far-field load application that often falls outside the microscopic field of view, (2) the ultra-small loads associated with specimen deformation, and (3) the load-case and specimen dependent interface response. To overcome these challenges, a generic method based on Integrated Digital Image Correlation (IDIC) is proposed, which identifies cohesive zone model parameters (of an arbitrary model not intrinsic to the identification method), by correlating images of a delamination process from a restricted field of view at the microscopic scale, whereby far-field loading data cannot be exploited.To quantify the effects of potential error sources on the performance of the proposed IDIC-routine, virtual experimentation is first conducted. Inaccurate application of boundary conditions in the FE-model of IDIC is thereby shown to be the most critical source of error. Subsequently, a real double cantilever beam (DCB) experiment has been analyzed as a well-defined test-case for characterization of adhesion properties. Since the Young’s modulus of the bulk material is generally well known, the imaged, elastically deforming bulk material acts as a force sensor. External load measurement can therefore be omitted from the identification process, thereby rendering the interface identification method independent of the particular test method. The implemented IDIC-algorithm is shown to be robust for accurately identifying the two cohesive zone parameters of interest: the work of separation Gc and the critical opening displacement δc.

On the identifiability of the Hill-1948 model with one uniaxial tensile test

A uniaxial experiment is performed on an ultra-thin specimen made of 17-7 precipitation hardened stainless steel. An anti-wrinkling setup allows for the characterization of the mechanical behavior with Integrated Digital Image Correlation (IDIC). The result shows that a single uniaxial experiment investigated via IDIC possesses enough data (and even more) to characterize a complete anisotropic elastoplastic model.

I-DIC-based identification strategy of failure criteria: application to titanium and nickel-based alloys

Integrated digital image correlation (I-DIC) is used to probe three different failure criteria on two high performance alloys. The approach consists of two steps. First, the mechanical state of each analyzed test is determined as best as possible by calibrating the parameters of a given elastoplastic law. Thin and thick samples are studied, which induce totally different states of equivalent plastic strain. Second, the state of stresses on the actual fractured surface is assessed by post-processing the 3D finite strain simulations of the I-DIC framework. These data are used to analyze different local criteria. It is found that a maximum eigen stress criterion is well adapted to the studied materials.

Multi-Parameter Inversion and Thermo-Mechanical Deformation Decoupling using I-DIC

The simultaneous and accurate identification of multiple thermo-mechanical parameters of superalloy materials in complicated service condition is an important and difficult problem. In this paper, an integrated digital image correlation (I-DIC) method was developed to address this issue. For the first time, thermo-mechanical deformation was inversed and decoupled by using I-DIC combined with an inhomogeneous high-temperature thermo-mechanical loading and optical band-pass filter imaging system. Results show that the proposed method has advantages such as high independence, short computing times, easy operation, and a small probability of error accumulation. Therefore, I-DIC is an effective and promising tool for multi-parameter inversion and thermo-mechanical deformation decoupling in practical engineering conditions.

Integrated digital image correlation applied to elastoplastic identification in a biaxial experiment

The identification of the parameters of several constitutive laws is performed with the integrated digital image correlation (IDIC) technique in a biaxial experiment for a cruciform specimen made of stainless steel. The sought material parameters are assessed with the contribution of both reaction forces (from load sensors) and displacement fields (measured via digital image correlation). For each constitutive law a global residual quantifying the model error is assessed.

Integrated Digital Image Correlation considering gray level and blur variations: Application to distortion measurements of IR camera

The acquisition of images with different modalities may involve different alterations with respect to an ideal model. Inhomogeneous brightness and contrast, blur due to non-ideal focusing, distortions are common. It is proposed herein to account for such effects for instance by registering a calibration target image with an actual optical image to measure lens distortions. An Integrated Digital Image Correlation (I-DIC) algorithm is proposed to account for the above artifacts and the algorithm is detailed. The resolution and uncertainty of the technique are first investigated on synthetic images, and then applied to the measurement of distortions for infrared (IR) images. The procedure is shown to reduce drastically the residual level assessing the validity of the image formation model, but more importantly allowing for a much improved registration of images.