Determination of effective stress intensity factors under mixed-mode from digital image correlation fields in presence of contact stresses and plasticity

Digital image correlation (DIC) is more and more popular to monitor fatigue crack growth and to determine the stress intensity factors. However, the posttreatment of the recorded displacement fields becomes tricky when the crack faces are not stress-free and when crack tip plasticity becomes significant. Several posttreatment methods to locate the crack tip and measure the effective stress intensity factors in such cases are compared, using finite element method-computed displacement fields, and then used on real DIC fields. An approach coupling DIC and finite element method is proposed to estimate the contact stresses along the crack.     

Measurement of discontinuous displacement/strain using mesh-based digital image correlation

In this study, a method for evaluating discontinuous displacement and strain distributions using digital image correlation (DIC) is proposed. A finite element mesh-based DIC method is used for measuring displacements while taking into account displacement and strain discontinuities. Smoothed displacements are thus obtained, and strains are computed from the measured displacements using the finite element mesh again. Discontinuous strains can be obtained by the proposed method using a split finite element mesh. The effectiveness of this method is validated by applying it to measure the displacement and strain in a triaxially woven fabric composite containing numerous free boundaries, to measure displacements around a crack and the displacement and strain around the interface between dissimilar materials. Results show that the discontinuous displacement and strain distributions can be measured by the proposed method. The proposed method is expected to be applicable for the experimental evaluations of various structures and members, including displacement and strain discontinuities such as free boundaries, cracks, and interfaces.     

Comparison of Different Techniques for Strain Monitoring of a Biaxially Loaded Cruciform Specimen

Abstract: This study focuses on the evaluation of several strain measuring techniques for the instrumentation of an in‐plane biaxial test bench. Strain gages, electronic speckle pattern interferometry (ESPI) and digital image correlation (DIC) were used combined or separately to measure the strains in the central gauge area of a biaxially loaded cruciform composite specimen. Applicability of the technique for this specific test and accuracy of the results are important parameters in the evaluation process of the different strain measuring techniques. The results of the three techniques are compared with the results obtained with a 3D finite element (FE) model. It is shown that DIC is the most promising technique because of its full‐field character and ability to cope with vibrations of the test bench. The main drawback remains its incapability to correlate across discontinuities.     

Nonlinear analysis via global–local mixed finite element approach

A computational algorithm, based on the combined use of mixed finite elements and classical Rayleigh–Ritz approximation, is presented for predicting the nonlinear static response of structures; The fundamental unknowns consist of nodal displacements and forces (or stresses) and the governing nonlinear finite element equations consist of both the constitutive relations and equilibrium equations of the discretized structure. The vector of nodal displacements and forces (or stresses) is expressed as a linear combination of a small number of global approximation functions (or basis vectors), and a Rayleigh–Ritz technique is used to approximate the finite element equations by a reduced system of nonlinear equations. The global approximation functions (or basis vectors) are chosen to be those commonly used in static perturbation technique; namely a nonlinear solution and a number of its path derivatives. These global functions are generated by using the finite element equations of the discretized structure. The potential of the global–local mixed approach and its advantages over global–local displacement finite element methods are discussed. Also, the high accuracy and effectiveness of the proposed approach are demonstrated by means of numerical examples.     

A Point‐wise Approach to the Analysis of Complex Composite Structures Using Digital Image Correlation and Thermoelastic Stress Analysis

Thermoelastic stress analysis (TSA) and digital image correlation (DIC) are used to examine the stress and strain distributions around the geometric discontinuity in a composite double butt strap joint. A well‐known major limitation in conducting analysis using TSA is that it provides a metric that is only related to the sum of the principal stresses and cannot provide the component stresses/strains. The stress metric is related to the thermoelastic response by a combination of material properties known as the thermoelastic constant (coefficient of thermal expansion divided by density and specific heat). The thermoelastic constant is usually obtained by a calibration process. For calibration purposes when using orthotropic materials, it is necessary to obtain the thermoelastic constant in the principal material directions, as the principal stress directions for a general structure are unknown. Often, it is assumed that the principal stress directions are coincident with the principal material directions. Clearly, this assumption is not valid in complex stress systems, and therefore, a means of obtaining the thermoelastic constants in the principal stress directions is required. Such a region is that in the neighbourhood of the discontinuities in a bonded lap joint. A methodology is presented that employs a point‐wise manipulation of the thermoelastic constants from the material directions to the principal stress directions using full‐field DIC strain data obtained from the neighbourhood of the discontinuity. A comparison of stress metrics generated from the TSA and DIC data is conducted to provide an independent experimental validation of the two‐dimensional DIC analysis. The accuracy of a two‐dimensional plane strain finite element model representing the joint is assessed against the two experimental data sets. Excellent agreement is found between the experimental and numerical results in the adhesive layer; the adhesive is the only component of the joint where the material properties were not obtained experimentally. The reason for the discrepancy is discussed in the paper.     

Evaluating the use of digital image correlation for strain measurement in historic tapestries using representative deformation fields

An analysis technique to assess the viability of digital image correlation (DIC) in tracking the full‐field strains across the surface of hanging historic tapestries is presented. Measurement uncertainty related to the use of the inherent tapestry image in tracking displacements is investigated through use of “synthetic” deformation fields. The latter are generated by mapping the details of a given tapestry image into finite element analyses. The combination of self‐weight loading, material non‐linearity, and image specific heterogeneity (related to slit stitching, damage, and patch‐restorations) serve to generate a bespoke deformation field complex enough to assess the reliability of DIC measurements. Accuracy is evaluated by comparing measured results with the original known deformations. The technique demonstrates that the optimum imaging settings and the choice of subset size for DIC analysis are strongly influenced by the tapestry image and the goal of the measurement, they are found using a compromise between conflicting objectives: minimising measurement error while maximising resolution.     

Multiple‐view Shape and Deformation Measurement by Combining Fringe Projection and Digital Image Correlation

Abstract: We present a new method that combines the fringe projection and the digital image correlation (DIC) techniques on a single hardware platform to simultaneously measure both shape and deformation fields of three‐dimensional (3‐D) surfaces with complex geometries. The method in its basic form requires only a single camera and single projector, but this can be easily extended to a multi‐camera multi‐projector system to obtain complete 360° measurements. Multiple views of the surface profile and displacement field are automatically co‐registered in a unified global coordinate system, thereby avoiding the significant errors that can arise through the use of statistical point cloud stitching techniques. Experimental results from a two‐camera two‐projector sensor are presented and compared with results from both a standard stereo‐DIC approach and a finite element model.     

Time‐resolved integrated digital image correlation

This paper discusses a method that provides the direct identification of constitutive model parameters by intimately integrating the finite element method (FEM) with digital image correlation (DIC), namely, directly connecting the experimentally obtained images for all time increments to the unknown material parameters. The problem is formulated as a single minimization problem that incorporates all the experimental data. It allows for precise specification of the unknowns, which can be, but are not limited to, the unknown material properties. The tight integration between FEM and DIC enables for identification while providing necessary regularization of the DIC procedure, making the method robust and noise insensitive. Through this approach, the versatility of the FE method is extended to the experimental realm, enhancing the analyses of existing experiments and opening new experimental opportunities. Copyright © 2015 John Wiley & Sons, Ltd.     

Influence of the constraint effect on the fatigue crack growth rate in S355 J2 steel using digital image correlation

Displacement fields around the fatigue crack tip for a constant value of stress intensity factor (SIF) range were measured using digital image correlation (DIC) technique on the S355 J2 steel grade. The data obtained were resolved into the T‐stress evaluation and quantification of its influence on the fatigue crack growth rate. The higher order terms of the Williams expansion (WE) were calculated as well. The displacements of a set of points outside of the plastic zone were selected for application of the over‐deterministic method (ODM) to obtain several initial WE terms. The computed values of T‐stress show good agreement with finite element analysis and literature. It was shown by collected experimental displacement, that the level of constraint influences the fatigue crack propagation rate.     

Nanoscale deformation measurement of microscale interconnection assemblies by a digital image correlation technique

The continuous miniaturization of microelectronic devices and interconnections demand more and more experimental strain/stress analysis of micro-?and nanoscale components for material characterization and structure reliability analysis. The digital image correlation (DIC) technique, with the aid of scanning probe microscopes, has become a very promising tool to meet this demand. In this study, an atomic force microscope (AFM) was used to scan and digitally image micro-interconnection assemblies in a micro-thermoelectric cooler. AFM images of the scan region of interest were obtained separately when the microelectronic device was operated before and after the cooling and heating stages. The AFM images were then used to obtain the in-plane deformation fields in the observed region of the micro-assembly. AFM image correlation is performed for nanoscale deformation analysis using the authors' AFM-DIC program. The results show that the observed region was subjected to cyclic strains when the device worked between its cooling and heating stages, and cyclic strain in the vertical direction was found to be a significant deformation mode. The thermally induced deformation behavior of the micro-assembly device was modeled by finite element analysis (FEA). Both thermal-electric analysis and thermal stress analysis were conducted on a 3D finite element model of the device. It is shown that the experimental results were able to validate the finite element analysis results.     

Fatigue crack closure: A myth or a misconception?

In this paper, we have extended our previous study on fatigue crack closure to examine the phenomenon of crack opening displacement (COD) and its impact on the crack tip fields in both 2D and 3D specimen geometries using full‐field experimental measurements and integrated finite element modelling. Digital image correlation (DIC) and digital volume correlation (DVC) were used to measure the near‐tip material responses on the surfaces (DIC) and the interior (DVC) of the specimens. Materials with elastic‐plastic and large plastic characteristics were chosen for the study, where plasticity‐induced premature contact between the crack flanks is known to occur. Displacement maps around the cracks were obtained using DIC and DVC at selected load increments and were introduced as boundary conditions into the finite element (FE) models to obtain the “effective” crack driving force in terms of J‐integral, and the results were compared with those “nominal” from the standard FE analysis. Both visual observation and compliance curves were used to determine the “crack opening” levels; whilst the impacts of the crack opening on the crack driving force J and the normal strains ahead of the crack tip were evaluated in 2D and 3D. The results from the study indicate that, crack closure, although clearly identifiable in the compliance curves, does not appear to impact on global crack driving force, such as J‐integral, or strains ahead of the crack tip; hence, it may well be a misconception.     

Formulation of Lucas–Kanade Digital Image Correlation Algorithms for Non‐contact Deformation Measurements: A Review

Digital image correlation (DIC) metrology has been increasingly used in a wide range of experimental mechanics research and applications. The DIC algorithm used so far is however limited mostly to the classic forward additive Lucas–Kanade type. In this paper, a survey is given about the formulation of other types of Lucas–Kanade DIC algorithms that have been appeared in computer vision, robotics, medical image analysis literature and so on. Concise notations consistent with the finite deformation kinematics analysis in continuum mechanics are used to describe all Lucas–Kanade DIC algorithms. An intermediate image is introduced as a frame of reference to clarify the so‐called compositional algorithms in a two‐frame DIC analysis. Explicit examples about the additive and compositional updating of deformation parameters are given for affine deformation mapping. Extensions of these algorithms to the so‐called consistent or symmetric types are also presented. The equivalency of final numerical solutions using additive, compositional and inverse compositional algorithms is shown analytically for the case of affine deformation mapping. In particular, the inverse compositional algorithm for affine image subset deformation is highlighted for its superior computational efficiency. While computationally less efficient, consistent and symmetric algorithms may be more robust and less biased and their potentials in experimental mechanics applications remain to be explored. The unified formulation of these Lucas–Kanade DIC algorithms collected all together in this paper can serve as a useful guide for researchers in experimental mechanics to further evaluate the merits as well as limitations of these non‐classic algorithms for image‐based precision displacement measurement applications.     

Investigation of the Uncertainty of DIC Under Heterogeneous Strain States with Numerical Tests

Abstract: In this research, numerical 2D digital image correlation (DIC) tests are carried out to assess the uncertainty of DIC under heterogeneous strain states. DIC is implemented to measure the deformation of the numerically deformed images with respect to the undeformed counterparts, which are taken from the real tensile specimens. The tensile specimens are made of three materials, that is, steel DC06, steel DX54D+Z and aluminium alloy Al6016 and cut into three different geometries, namely one standard design and two complex designs. The specimens are all painted manually with random speckle patterns. The original images are deformed by imposed displacement fields, which are obtained by simulating uni‐axial tensile tests of the specimens with finite element analysis (FEA). In this way, the errors sourcing from the hardware of the image system are excluded. According to the geometries of the specimens, homogeneous and heterogeneous strain states are achieved by FEA. The optimum mesh sizes of the models are identified to minimise theirs influence on the imposed fields. The impacts of subset sizes, step sizes and strain window sizes are studied for an optimum correlation. Finally, the influence of the strain state is investigated. It is found that the DIC accuracy and precision decrease under highly heterogeneous strain states.     

Impact of motion blur on stereo‐digital image correlation with the focus on a drone‐carried stereo rig

Stereo‐digital image correlation (DIC) is a wide‐spread technique in the field of experimental mechanics for measuring shape, motion, and deformation and it is frequently used for material identification by using inverse methods (e.g., virtual fields method and finite element model updating). New applications emerge due to the reached maturity level of the technique, which poses new challenges towards reaching a desired level of accuracy in operating conditions. In this work, the possibility of a drone carrying an in‐house‐made portable DIC setup is explored, and the effect of the drone‐induced vibrations on the accuracy of stereo‐DIC for shape and strain measurement is evaluated. During acquisition, the relative motion between the camera system and the measured item generates motion‐blurred images. The effect of this phenomenon on the precision of stereo‐DIC is further evaluated in this paper.     

An iterative procedure for determining effective stress–strain curves of sheet metals

An iterative correction procedure using 3D finite element analysis (FEA) was carried out to determine more accurately the effective true stress–true strain curves of aluminum, copper, steel, and titanium sheet metals with various gage section geometries up to very large strains just prior to the final tearing fracture. Based on the local surface strain mapping measurements within the diffuse and localized necking region of a rectangular cross-section tension coupon in uniaxial tension using digital image correlation (DIC), both average axial true strain and the average axial stress without correction of the triaxiality of the stress state within the neck have been obtained experimentally. The measured stress–strain curve was then used as an initial guess of the effective true stress–strain curve in the finite element analysis. The input effective true stress–strain curve was corrected iteratively after each analysis session until the difference between the experimentally measured and FE-computed average axial true stress–true strain curves inside a neck becomes acceptably small. As each test coupon was analyzed by a full-scale finite element model and no specific analytical model of strain-hardening was assumed, the method used in this study is shown to be rather general and can be applied to sheet metals with various strain hardening behaviors and tension coupon geometries.     

Application of digital image correlation at the microscale in fiber-reinforced composites

Digital image correlation (DIC) is applied to analyzing the deformation mechanisms under transverse compression in a fiber-reinforced composite. To this end, compression tests in a direction perpendicular to the fibers were carried out inside a scanning electron microscope and secondary electron images obtained at different magnifications during the test. Optimum DIC parameters to resolve the displacement and strain field were computed from numerical simulations of a model composite and they were applied to micrographs obtained at different magnifications (250×, 2000×, and 6000×). It is shown that DIC of low-magnification micrographs was able to capture the long range fluctuations in strain due to the presence of matrix-rich and fiber-rich zones, responsible for the onset of damage. At higher magnification, the strain fields obtained with DIC qualitatively reproduce the non-homogeneous deformation pattern due to the presence of stiff fibers dispersed in a compliant matrix and provide accurate results of the average composite strain. However, comparison with finite element simulations revealed that DIC was not able to accurately capture the average strain in each phase.     

A simple analytical crack tip opening displacement approximation under random variable loadings

A simple analytical approximation is proposed in this paper to calculate the crack tip opening displacement under general random variable amplitude loadings. This approximation is based on a modified Dugdale model for cyclic loadings. The discussion is first given under constant amplitude loading and is extended to several simple cases under variable amplitude loadings. Following this, a general algorithm is proposed under general random variable loadings. Numerical examples are verified with finite element simulations. Following this, hardening effect is included by including a hardening correction function. The proposed analytical approximation is very efficient compared to the direct finite element simulation. The solution can be used for detailed fatigue crack growth analysis under random variable amplitude loadings.     

Reduction method for the non-linear analysis of symmetric anisotropic panels

Reduction method and computational procedures are presented for reducing the size of the analysis model and the number of degrees of freedom used in predicting the non-linear response of symmetric anisotropic panels. The two key elements of the method are (a) operator splitting, or decomposition of the characteristic arrays of the finite element model into sums of orthotropic and non-orthotropic contributions, (b) application of a reduction method through the successive use of the finite element method and the classical Rayleigh-Ritz technique. The finite element method is first used to generate a small number of global approximation vectors (or modes). Then the amplitudes of these modes are computed by using the classical Rayleigh-Ritz technique. The global approximation vectors are selected to be those commonly used in single (or multiple) parameter perturbation techniques, namely a non-linear solution corresponding to zero non-orthotropic arrays and a number of its derivatives with respect to an anisotropic tracing parameter (and possibly, to a load or arc-length parameter in the solution space). The size of the analysis model used in generating the global approximation vectors is identical to that of the corresponding orthotropic structure. The effectiveness of the proposed reduction method is demonstrated by means of a numerical example, and its potential for solving quasi-symmetric non-linear problems of anisotropic panels is discussed.