Experimental Digital Image Correlation Research Articles

Metrics to evaluate constitutive model fitness based on DIC experiments

AbstractFull‐field optical experimental techniques such as Digital Image Correlation (DIC) enable measurement of information‐rich heterogeneous strain states. The aim of Material Testing 2.0 is to capitalise on this and design experimental setups for efficient material characterisation using inverse identification techniques such as the Virtual Fields Method (VFM). In that case, however, a priori knowledge of the constitutive model is required, which sometimes is not a trivial task. This limitation can be overcome by identifying multiple constitutive models using the same DIC strain fields and comparing their performance. In this work, we present a methodology to evaluate model performance and compare different constitutive models based on quantitative metrics. DIC experiments were performed on an S‐shaped high density polyethylene test sample under uniaxial load. The heterogeneous DIC strain fields were used in combination with the VFM to identify parameters of hyperelastic constitutive models with increasing complexity. Two deterministic metrics, the equilibrium gap indicator (EGI) and the reconstructed axial force ratio (RAFR), were defined and used to compare the performance of these constitutive models. The impact of spatial smoothing on DIC strain fields was studied by calculating the EGI and RAFR using a digital twin of the DIC experiments. EGI and RAFR metrics provide complementary information regarding the material behaviour, and both are necessary to make an informed choice. In this case study, hyperelastic constitutive models were found not to capture the material stiffness well in the small strain regime. A linear‐elastic contribution exponentially decaying with the equivalent shear stress was added to the hyperelastic models and the corresponding model parameters identified using the VFM. The elastic‐hyperelastic constitutive models were found to perform better than their purely hyperelastic counterparts.

Deformation and Fracturing Behaviors of Sandstone Disc Containing a Circular Inclusion under Diametrical Compression: Insights from Integrated SG and DIC Experiments

Weak inclusions play a significant role in regulating the deformation and fracturing behavior of rock masses. In this study, sandstone specimens filled with circular inclusions were subjected to diametrical compression until failure. The local strain concentration intensity and cracking process at the rock-inclusion interface were specifically investigated using the integrated strain gauge (SG) and digital image correlation (DIC) techniques. The experimental results reveal that the presence of inclusions introduces more complex deformation and fracturing behaviors in the infilled sandstone specimens. The stiffness of the infilled sandstones, with either low-strength or high-strength inclusions, initially increases and then decreases as the inclusion diameter increases. The effective load-carrying capacity of the infilled sandstone is influenced by the competing effects of inclusion enhancement and hole weakening. Moreover, a more pronounced strain concentration occurs at the inclusion boundary when the inclusion diameter is larger and the inclusion strength is lower. The crack mode in the infilled red sandstone is independent of the strength of the inclusion. For larger hole diameters, fracture planes form along the compression line, whereas interfacial debonding occurs in red sandstone with smaller hole diameters. Finally, the stress distribution characteristics along the loaded diameter and transverse diameter were analyzed using elastic finite element analyses, which can well explain the cracking mechanism of the infilled disc specimens.

Application of Bilinear Softening Laws and Fracture Toughness of Foamed Concrete

This study examined the fracture and failed performance of foamed concrete materials by testing normalized notched beams under three-point bending via three methods: inverse analysis, digital image correlation (DIC), and finite element modeling (FEM). It also discussed both experimental and FEM characteristics. However, inverse analysis is only applicable for specimens with a notch height of 30 mm. Bilinear softening of the tested beams was estimated to identify the fracture energy (GF), critical crack length (ac), and elastic modulus (E). Additionally, the fracture toughness was calculated by adopting the double-K method (initiation fracture, unstable fracture, and cohesive fracture). Two-dimensional FEA modeling of the fracture was conducted using the traction-separation law (TSL), incorporating the extended finite element method (XFEM) and cohesive zone (CZM) techniques. A finite element sensitivity for the XFEM and CZM was performed, with the global mesh size of 2 and the damage stabilization cohesion of 1 × 10−5 showed good convergence and were used in other models. Further comparison of the DIC experiment findings with those from the FEM demonstrated good agreement in terms of crack propagation simulation.

In-plane compressive response of composite sandwich panels with local-tight honeycomb cores

In the present study, honeycomb cores with periodic tight zones were proposed for carbon-fiber and aluminum-honeycomb sandwich panels by flattening hexagon-shaped cells of honeycomb walls. In-plane compression tests were performed for sandwich panels with three types of local-tight honeycomb cores to evaluate the effects of the local-tight configurations on mechanical properties and failure modes. Experimental results indicated that the mechanical properties of sandwich specimens were effectively increased by using the proposed local-tight honeycomb cores. In particular, the specific energy absorption of sandwich specimens with a local-orthogonal-tight core was increased by 400.46%. In addition, Digital Image Correlation (DIC) technique was employed to further investigate the compressive behaviors of the sandwich specimens with and without local-orthogonal-tight honeycomb cores. The experimental measurements and detailed DIC observations indicated that the local-orthogonal-tight honeycomb core sandwich structures, which provided improved load transferring paths and reduced mismatch between the high-stiffness face sheets and low-stiffness core, exhibited progressive crushing failure modes.

Solving digital image correlation with neural networks constrained by strain-displacement relations.

The use of supervised neural networks is a new approach to solving digital image correlation (DIC) problems, but the existing methods solely adopt the black-box neural network, i.e., the mapping from speckle image pair (reference image and deformed image) to multiple deformation fields (displacement fields and strain fields) is directly established without considering the physical constraints between the fields, causing a low level of accuracy that is even inferior to that of Subset-DIC. In this work, we proposed a deep learning model by introducing strain-displacement relations into a neural network, in which the effect of errors both in displacement and strain are considered in the network training. The back-propagation process of the proposed model is derived, and the solution scheme is implemented by Python. The performance of the proposed model is evaluated by simulation and real DIC experiments, and the results show that adding physical constraints to the neural network can significantly improve prediction accuracy.

Experimental stress determination of blunt notches under combinations of modes I and II loading

An appropriate evaluation of the stress field for designing new or optimizing existing engineering structures is required. The primary goal of this paper is to use the digital image correlation (DIC) approach to ascertain the stress field around the root of various blunt notches. At first, extensive tests were performed using the Brazilian Disc (BD) specimen containing three distinct notches (U, VO, and Keyhole) under diverse loading conditions, including pure mode I, pure mode II, and mixed-mode I/II. The displacement fields output from the DIC experiments were employed as the input data for a computer program, and the coefficients of the stress and displacement fields were then determined utilizing the over-deterministic technique. Afterward, the computed coefficients were used to calculate the analytical stress field around the notch root by considering singular and higher-order terms for each notch type. Subsequently, the finite element (FE) method was employed to verify the accuracy of the stress field obtained from the DIC experiments. In addition, the influence of some major parameters such as notch opening angle, notch tip radius, and geometry on the stress distribution was investigated. This study validated the efficiency of the DIC approach in determining the unknown stress coefficients of rounded notches, especially the first non-singular term of the stress expansion, which is revealed to have a considerable impact on appraising the exact stress field around the notch curvature.

Calibration of coherent optical fiber bundle with LCD screen for deformation measurements

Owning to its flexibility, high temperature resistance, and freedom from electromagnetic interference, coherent optical fiber bundle (COFB) is widely used in special imaging applications. However, limited by the manufacturing process, the fiber arrangement of COFB is prone to misalignment, resulting in imaging distortions that are not easily corrected. This limits the application of COFB in the field of optical measurement, making it difficult to meet the requirements of high-precision deformation measurement. To effectively calibrate the misalignment distortion and recover the original image information, this study proposes an easy-to-implement and highly accurate misalignment distortion calibration method. The LCD screen was used as the calibration reference to display a pre-designed regular arrangement pattern. The mapping relationship between the fiber output and the screen display information was confirmed using a correlation algorithm. The proposed method requires only 36 images to achieve misalignment calibration for 450 × 450 fibers. The image reconstruction results show that the proposed method can not only achieve global misalignment calibration, but also successfully eliminate honeycomb artifacts, thus enhancing the accuracy and practicality of COFB for deformation measurement. In addition, a COFB-based digital image correlation (DIC) system was established and a set of typical DIC experiments were implemented. The experimental results show that the proposed calibration method can significantly improve the deformation measurement accuracy of the COFB-based DIC system, and the accuracy of the two-dimensional (2D) displacement field measurement result is improved from 0.50 pixels to 0.03 pixels.

A deep learning approach for inverse design of gradient mechanical metamaterials

Mechanical metamaterials with unique micro-architectures possess excellent physical properties in terms of stiffness, toughness, vibration isolation, and thermal expansion. Meanwhile, meta-structures in organisms or geography operate efficiently under complex service conditions thanks to their heterogeneous and gradient distribution of naturally evolved micro-architectures that are difficult to obtain by forward design. In this paper a multi-network deep learning system that satisfies the different design property requirements of microstructures is proposed, and the network predicts the configuration with 99.09% accuracy. The analogy between color space and mechanical parameter space is used to transform parametric design into pixel matching. The microstructures are prepared by AM (additive manufacturing) and their properties are verified by DIC (Digital Image Correlation) experiments (the property error of the structures was less than 2%). Multiscale inverse design of multifunctional and gradient mechanical metamaterials is realized, with special attention payed to the automatic customization of biomimetic structures. The design flow takes only 2 s and the geometric connectivity between microstructure units is considered to ensure compatibility between adjacent microstructures for AM. The proposed design strategy accelerates the emergence of high-performance structures, and provides a reference for topology optimization design of mechanical metamaterials.

DIC/DSI based studies on the local mechanical behaviors of HR3C/T92 dissimilar welded joint during plastic deformation

In this study, both the digital image correlation (DIC) and depth-sensing indentation (DSI) measurements were performed to investigate the non-uniform local mechanical behaviors of HR3C/T92 dissimilar welded joint during plastic deformation. The macro-scale DIC experiments showed the uneven distribution and transfer phenomena of the plastic deformation in the welded samples. The grain-scale DIC measurements further revealed that the strain localization was closely related to the local microstructures. To understand the correlation of the non-uniform deformation behavior with the local microstructure in the welded samples, the electron backscatter diffraction (EBSD) tests in the as-received state and ex-situ optical microscope (OM) observations during the tensile deformation process were conducted. The slip morphologies were found to be different across the welded joint, and the grain-scale strain localizations were proved to be closely related with the behaviors of the slip bands. Moreover, ex-situ DSI tests were also carried out to determine the local mechanical properties of the HR3C/T92 dissimilar welded joint during the tensile deformation process. The basic elasto-plastic properties (elastic modulus, yield strength, and hardening parameters) in particular zones of the welded joint were estimated by using the multi-fidelity deep neural network method combined with indentation characteristic parameters. The non-uniform deformation behavior of the HR3C/T92 welded joint during tensile loading was further simulated by using the finite element method based on the estimated elasto-plastic properties of the welded joint, and a general agreement between the simulated result and experimental tensile curve has been obtained.

Peridynamic Approach to Digital Image Correlation Strain Calculation Algorithm

Digital image correlation is an experimental optical non-contact full field displacement and strain evaluation method based on the surface subsets tracking with photo cameras, digital images processing, and numerical computation. However, the full field of strain computation is a challenging problem, mainly because the displacement field to be differentiated is not continuous, individual subsets are tracked by the optical digital image correlation system. Moreover, the numerical differentiation can also amplify the noise of the displacement field inducing thus strain errors when the displacement data are poor. The peridynamics theory (which equations are cast in terms of spatial integrals of displacements, instead of spatial derivatives in the classical continuum mechanics) based algorithm is considered in this study and applied for the experimental digital image correlation displacement field to analyze possible peridynamic differentiation method advantages. A strains convergence analysis between the digital image correlation and peridynamic differentiation methods is done in this study. The integro-differential strain calculation as an alternative method is validated against digital image correlation and finite element simulation strain fields. It is also shown that the digital image correlation, a noisy displacement field, still provides an accurate and low level noise strain evaluation based on the proposed method.

Full-Field Displacement Measurement Method of Metal-As-Insulation Pancake at Liquid Nitrogen Temperature

In situ measurement of metal-as-insulation (MI) high temperature superconductor (HTS) pancake deformation gives insight to its actual mechanical state. Measurement of hoop strain for inner / outer turn of MI pancake is usually made by strain gauges. This measurement is however local and faces electromagnetic compatibility (EMC) and thermal issues. Non-contact full-field displacement measurement is an interesting alternative solution. This technique is based on digital image correlation (DIC), which derives the displacement field in specified region of interest (ROI) by correlation between the deformed state image and the reference state image. In this article, we present a novel DIC experiment setup for displacement measurement of MI pancake in cryogenic cooling. The setup is validated by a cooling test of 304 stainless steel disc. Then, it is used for cooling test of MI pancake made of co-wound copper beryllium - 304 stainless steel tapes. Both tests are done at 80 K by conduction cooling using liquid nitrogen. Finally, experimental results are compared to numerical results obtained from an analytical formulation of the mechanical equilibrium using generalized plane strain assumption.

A PORCINE FORELEG FINITE ELEMENT MODEL FOR SURFACE WAVE CHARACTERIZATION

Injuries from BB shots are responsible for thousands of injuries each year, with many resulting in contusions or superficial embedments to the extremities. To help better understand the injury biomechanics of BB shots, a porcine foreleg finite element model was selected for comparison with some documented porcine ballistic experiments. The model was created by segmenting a porcine leg computerized tomography (CT) scan into the major bones, skin, and soft tissues, and then generating a mesh from the resulting geometries. A previously published hyperelastic material model was incorporated to represent the skin’s non-linear mechanical behavior. The pig leg model was used to simulate the skin response to 87.1 and 114.6 m/s stainless steel BB shots. The simulation matched the non-penetrative behavior from the experiments, predicting peak dynamic deformations of 12.6 and 25.4 mm respectively. MatLab was used to collect the movement of surface nodes and reconstruct continuous surfaces every 0.5 ms. The position and speed of the impact-induced wave was non-linear and did not depend on the BB initial velocity. Future work is needed to compare the simulation results against experimental digital image correlation (DIC) data, increase the time and spatial resolution of simulated sampling surface, and eventually include dynamic material data to account for skin damage with increasing BB initial velocity.

Examining lung mechanical strains as influenced by breathing volumes and rates using experimental digital image correlation

BackgroundMechanical ventilation is often employed to facilitate breathing in patients suffering from respiratory illnesses and disabilities. Despite the benefits, there are risks associated with ventilator-induced lung injuries and death, driving investigations for alternative ventilation techniques to improve mechanical ventilation, such as multi-oscillatory and high-frequency ventilation; however, few studies have evaluated fundamental lung mechanical local deformations under variable loading.MethodsPorcine whole lung samples were analyzed using a novel application of digital image correlation interfaced with an electromechanical ventilation system to associate the local behavior to the global volume and pressure loading in response to various inflation volumes and breathing rates. Strains, anisotropy, tissue compliance, and the evolutionary response of the inflating lung were analyzed.ResultsExperiments demonstrated a direct and near one-to-one linear relationship between applied lung volumes and resulting local mean strain, and a nonlinear relationship between lung pressures and strains. As the applied air delivery volume was doubled, the tissue surface mean strains approximately increased from 20 to 40%, and average maximum strains measured 70–110%. The tissue strain anisotropic ratio ranged from 0.81 to 0.86 and decreased with greater inflation volumes. Local tissue compliance during the inflation cycle, associating evolutionary strains in response to inflation pressures, was also quantified.ConclusionVentilation frequencies were not found to influence the local stretch response. Strain measures significantly increased and the anisotropic ratio decreased between the smallest and greatest tidal volumes. Tissue compliance did not exhibit a unifying trend. The insights provided by the real-time continuous measures, and the kinetics to kinematics pulmonary linkage established by this study offers valuable characterizations for computational models and establishes a framework for future studies to compare healthy and diseased lung mechanics to further consider alternatives for effective ventilation strategies.

Understanding the role of bond point strain in the mechanical response of nonwoven polypropylene materials

A method was developed to study micromechanics of a bond point in nonwoven polypropylene materials. The micromechanical behavior of the thermal bonded nonwovens was studied using the digital image correlation (DIC) technique to understand the bond points deformation during mechanical stretching. An electrospray technique was used as a fast and reliable method to create the speckle pattern on the nonwovens. Various parameters of the electrospraying and their influence on the pattern accuracy and repeatability was studied and the best pattern in terms of dot size and distribution was determined from experimentation. Plasma treatment also proved to be essential to enhance the uniform distribution and adherence of the particles on the surface. Unloaded DIC experiments were carried out and proved the accuracy of technique with errors of lower than 0.5% strain. An automated high-resolution tensile apparatus was built and loaded DIC experiments were carried out using the device. The fabric was tested in Machine Direction (MD) direction and Cross Direction (CD) directions, both showing good correlation with low errors. Average strain values in bond points were plotted against total strain in fabric and the results showed noticeable amounts of strains developed in the bond points, contradictory to most of the FEM models which consider no deformation in the bond points. Results also indicated that in MD direction deformation, bond points can experience more than 30% of the overall strain presented in the fabric.

Graded Kirigami Composites for Programmed Strain Distributions

AbstractStretchable devices and components have emerged as a vital platform for wearable electronics, biomedical sensors, and soft robotics. However, the soft‐rigid interfaces that arise when integrating rigid components with soft and deformable substrates can cause stress concentrations, leading to premature failure of devices at these multi‐material interfaces. Here, a stiffness‐graded kirigami composite is introduced to control strain transitions at soft‐rigid interfaces. The graded composite consists of soft elastomers bonded to rigid kirigami films with defined beam architectures to tune the stiffness gradient along the loading direction. Kirigami geometry is designed by coupling finite element analysis with experimental digital image correlation to achieve diverse strain profiles for flexible interfaces. Furthermore, an inverse design method is utilized to determine kirigami patterns to obtain predefined strain fields. These stiffness‐graded kirigami composites create opportunities for more robust soft‐rigid interfaces and defect‐tolerant stretchable devices and robots.

A comparison of domain integral and multi-parameter methods for the strain intensity factor estimation of rigid line inclusion using digital image correlation

A comparative study is carried out between two methods to estimate the strain intensity factor of a rigid line inclusion using the displacement and strain fields from digital image correlation (DIC). The two methods are (i) a proposed hybrid domain integral method and (ii) the linear over-deterministic least-squares technique involving multi-parameter displacement field equations (multi-parameter method). The multi-parameter method uses the displacement data obtained from the DIC experiments to find the unknowns in the multi-parameter equation. The proposed hybrid methodology uses a domain integral method to calculate the strain intensity factor using the full-field displacement and strain data obtained from DIC. The strain intensity factor estimated using the proposed domain integral method, and the multi-parameter method agrees with the analytical estimate. The influence of the size of the annular region and the mesh sensitivity is also reported. The sensitivity to the variance and bias errors in measurement for both the methods is investigated. To investigate the effect of variance error, a Gaussian noise is introduced over the reference and deformed images before post-processing, and its influence on the strain intensity factor estimate is discussed. The effect of random perturbations of displacements and strains on the strain intensity factor estimates is also investigated. The domain integral method is less sensitive to the variance error when compared to the multi-parameter solution approach. Further, the bias errors due to uncorrected lens distortions, over-smoothing of data, and DIC algorithm adopted are introduced into the measurements, and its effect on both the methods is investigated. The multi-parameter method is less sensitive to bias errors when compared to the domain integral method. Therefore, it is recommended that the domain integral method may be used for the experimental determination of strain intensity factor in measurements with variance errors and the multi-parameter method for measurements with bias errors.

Experimental Investigation of Open-Hole Compression Strength of Carbon Epoxy Composite Material and Determination of Localized Strains Using Digital Image Correlation Technique

The biggest application of the fiber-reinforced composites are in the field of military and commercial aircrafts. Carbon fibers either alone or with the Kevlar 49 fibers, are widely used as main material in many aero plane wing, fuselage and empennage components. Composites materials have wide applications in different industries because of it has very different properties from the metals and polymers. In the drilling of Carbon/Epoxy Composites the cut surface quality is very much dependent on the drilling parameters set during drilling which further effect the strength of the hole during extension/compression loading. In this research, Carbon Fiber Epoxy Composite material is drilled with the standard carbide drill bit and Open Hole Compression (OHC) tests are performed on the Universal Testing Machine. The Digital Image Correlation (DIC) technique is used to find out the strain distribution around the hole during compression loading. From the experimental method and DIC, maximum strength of carbon epoxy composite is achieved by drilling at 1600-2400 mm/min in presence of notch. It was also observed that failure of the structure is dependent on the drilling feed rate and 1600-2400 mm/min was the optimized drilling range.

Thermally induced strain in joints with dissimilar adherends bonded with a flexible adhesive

In this study, assemblies comprising poly(methyl methacrylate) (PMMA) bonded to glass were subjected to a temperature gradient from +30 °C to −40 °C at 0% humidity. Their behaviour was recorded using a 3D digital image correlation (DIC) setup. The deformations and the thermally induced surface strain development, due to thermal loading, were recorded using a stereo camera system with two charge-coupled device (CCD) cameras. Narrow field measurements were performed near the edges of the joint where a high concentration of peeling and shear strains might be expected. With the use of commercial DIC software, the thermal deformation of the structure and the developed surface strain fields (εxx, γxy, εyy) are analysed. Joints with different bond line thickness (0.5 mm, 2 mm, 3.2 mm) of the silicone adhesive were investigated. The continuous image capture with the CCD cameras allowed identification of the failure conditions and the exact moment of failure of the bonded assembly. Additionally, the DIC experiment results were evaluated with the help of finite-element analysis results, which are in excellent agreement. This showed that the DIC method can be successfully applied for the investigation of thermally induced strains in adhesively bonded assemblies and thus contribute to understanding of the underlying thermal/mechanical behaviour of bonded systems.

Evaluation of crack propagation behavior of porous polymer membranes

This study experimentally and numerically investigated the crack propagation behavior of porous polymer membranes in order to identify the criterion for crack propagation. A notch was introduced into the membrane as an initial crack (pre-crack), and a uniaxial loading was applied to produce stable crack propagation. During the test, crack propagation was observed using a CCD camera and the digital image correlation (DIC) method. The strain around the pre-crack tip at the onset of crack propagation was measured experimentally using the DIC method. We found that large-scale yielding developed before crack propagation. Stable crack propagation was observed for all tensile tests. In parallel, a homogeneous model that mimicked the porous polymer membrane was created using the finite element method (FEM) to investigate the stress/strain distribution around the crack tip. This study adopted the yield criterion proposed by Deshpande and Fleck. The computed strain distribution was compared with the experimental results, and the distributions were found to be similar. The strain distribution obtained by the DIC method and FEM computation yielded a J-integral value, which could be used to investigate the criterion for crack propagation. Regardless of the initial crack length, the J-integral value at the onset of crack propagation was a constant value for all tests. We concluded that we successfully determined the criterion for crack propagation in the porous polymer membrane. Our comprehensive study using DIC experiments and FEM computations is useful for identifying the crack propagation behavior of a porous polymer membrane and for determining the criterion for crack propagation.

Methodology for DIC-based evaluation of the fracture behaviour of solder materials under monotonic and creep loadings

New lead-free solder alloys for electronic packaging contain doping elements conferring upon them improved properties in terms of ease of processibility and strength under high temperature operation conditions. Studies on their resistance to quasi-static rupture remain however relatively limited. In this work, the SAC-based solder alloy, known as InnoLot, is considered and its rupture under monotonic and creep loadings is investigated experimentally and numerically. The Digital Image Correlation (DIC) technique is employed to evaluate the stress intensity factor, as well as the J- and C(t)-integrals, from full-field measurements on notched specimens. The numerical formulations of the theoretical concepts for computation of the physical fracture quantities are provided in the framework of the DIC algorithm. Results derived from the DIC experiments are compared with predictions given by finite element models, and good agreement is found in general. The observed discrepancies can be explained by lack of resolution of the optical setup measurements in the infinitesimal strain regime or by uncertainty associated with the identified material parameters used in the evaluation of stresses from the acquired strains.