DIC-Based Surface Motion Correction for ESPI Measurements

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

Simultaneous Measurement of Plate Natural Frequencies and Vibration Mode Shapes Using ESPI

The natural frequencies and vibration mode shapes of flat plates are simultaneously measured using ESPI. The method involves measuring the surface shape of a vibrating plate at high frame rate using a modified Michelson interferometer and high-speed camera. The vibration is excited here by impact; white (random) noise could alternatively be used. Fourier analysis of the acquired data gives the natural frequencies and associated mode shapes. The analytical procedure used has the advantage that it simultaneously identifies full-field quantitative images of all vibration modes with frequencies up to half the sampling frequency. In comparison, the ESPI time-averaging and the traditional Chladni methods both require that the plate be excited at each natural frequency to allow separate qualitative measurements of the associated mode shapes. The Instrumented Hammer method and Laser Doppler Vibrometry give quantitative measurements but require sequential sampling of individual points on the test surface to provide full-field results. Example ESPI measurements are presented to illustrate the use and capabilities of the proposed plate natural frequency and mode shape measurement method.     

Residual Stress Determination Using Cross-Slitting and Dual-Axis ESPI

Hole-drilling and Electronic Speckle Pattern Interferometry (ESPI) are used to measure residual stresses in metal specimens. The slitting method is chosen as an alternative to the more commonly used hole-drilling method because it involves less material removal and leaves large areas of highly deformed material available to be measured. However the conventional single-slitting method is sensitive only to the stress component perpendicular to the slit direction, and thus has a strong directional bias. Conventional ESPI has a similar bias because it responds to surface displacements in a specific sensitivity direction. In this paper, a novel cross-slitting method with dual-axis ESPI measurements is proposed to address both directional biases. Cross-slitting is introduced as a means of releasing all in-plane stress components. The dual-axis ESPI system uses diagonal-mirror and shutter devices to provide surface displacement measurements in orthogonal in-plane directions. The combination of the cross-slit and dual-axis measurement gives isotropic sensitivity to the in-plane residual stress components. Experimental measurements are described that illustrate the capability and effectiveness of the cross-slitting/ESPI technique.     

Hole-Drilling Residual Stress Measurement with Artifact Correction Using Full-Field DIC

A full-field, multi-axial computation technique is described for determining residual stresses using the hole-drilling method with DIC. The computational method takes advantage of the large quantity of data available from full-field images to ameliorate the effect of modest deformation sensitivity of DIC measurements. It also provides uniform residual stress sensitivity in all in-plane directions and accounts for artifacts that commonly occur within experimental measurements. These artifacts include image shift, stretch and shear. The calculation method uses a large fraction of the pixels available within the measured images and requires minimal human guidance in its operation. The method is demonstrated using measurements where residual stresses are made on a microscopic scale with hole drilling done using a Focused Ion Beam – Scanning Electron Microscope (FIB-SEM). This is a very challenging application because SEM images are subject to fluctuations that can introduce large artifacts when using DIC. Several series of measurements are described to illustrate the operation and effectiveness of the proposed residual stress computation technique.     

Comparison Between Surface and Near-Surface Residual Stress Measurement Techniques Using a Standard Four-Point-Bend Specimen

Background

Determination of near-surface residual stresses is challenging for the available measurement techniques due to their limitations. These are often either beyond reach or associated with significant uncertainties.

Objective

This study describes a critical comparison between three methods of surface and near-surface residual stress measurements, including x-ray diffraction (XRD) and two incremental central hole-drilling techniques one based on strain-gauge rosette and the other based on electronic speckle pattern interferometry (ESPI).

Methods

These measurements were performed on standard four-point-bend beams of steel loaded to known nominal stresses, according to the ASTM standard. These were to evaluate the sensitivity of different techniques to the variation in the nominal stress, and their associated uncertainties.

Results

The XRD data showed very good correlations with the surface nominal stress, and with superb repeatability and small uncertainties. The results of the ESPI based hole-drilling technique were also in a good agreement with the XRD data and the expected nominal stress. However, those obtained by the strain gauge rosette based hole-drilling technique were not matching well with the data obtained by the other techniques nor with the nominal stress. This was found to be due to the generation of extensive compressive residual stress during surface preparation for strain gauge installation.

Conclusion

The ESPI method is proven to be the most suitable hole-drilling technique for measuring near-surface residual stresses within distances close to the surface that are beyond the penetration depth of x-ray and below the resolution of the strain gauge rosette based hole-drilling method.

     

Hybrid stress analysis of perforated composites using strain gages

A strain gage hybrid method is described for determining individual stresses on the boundary and in the neighborhood of cutouts in orthotropic composites. Results agree with independent measurements and finite element analysis. Few measured strain data are needed, and the measured strains originate away from the hole. Ability to determine the stresses on the edge of a cutout from nonboundary measurements recognizes the difficulties in obtaining reliable measurements very near an edge while circumventing the challenge of attempting to bond gages to the transverse curved surface of a small hole or notch. The method also alleviates the problem of not knowing a priori where the most serious stress will occur on the geometric boundary and, hence, where to locate strain gages.     

Whole-field strain measurement in a pin-loaded plate by electronic speckle pattern interferometry and the finite element method

The strain field in an epoxy plate loaded in tension through a steel pin is determined using electronic speckle pattern interferometry (ESPI) and the finite element method (FEM). In a dual-beam illumination speckle interferometer, the in-plane component of the displacement at the plate's surface is accurately measured using a four-step phase-shifting algorithm. Digital image processing algorithms have been developed for noise reduction and strain calculation directly in the computer from the phase map with a strain gage length of about 0.4 mm. A whole-field strain map is obtained, as well as distributions of strain concentration factor, in critical regions near the hole of the plate. FEM is used to perform a nonlinear contact analysis accounting for friction effects at the pin/hole interface. The agreement between experimental results and numerical predictions is good. In terms of speed, accuracy and ease of use, dual-beam ESPI appears to be a superior method of whole-field strain analysis.     

Full-field surface-strain and displacement analysis of three-dimensional objects by speckle interferometry

A method of full-field measurement of displacements as well as strain on arbitrarily curved surfaces is introduced. The speckle effect of coherent light is utilized to produce fringes due to displacements. Unlike the fringes produced by holographic interferometry, these fringes have a unique interpretation in relating to displacements and they localize on the surface. Three measurements are required to determine the three components of displacement; and, knowing the geometry of the object, its surface strains can be deduced. Three ways of recording displacement fringes, namely, real time, double exposure and superposition, are described.     

Computation of Full-field Strains Using Principal Component Analysis

The primary output from several full-field deformation measurement techniques, e.g., Digital Image Correlation (DIC), is the displacement vector at a dense grid of points covering the area of interest. Since such displacement data inherently contain noise, they are usually smoothed first and then differentiated to obtain strains. Another common approach is to use finite-element shape functions for the strains and compute them by treating the measured displacements as nodal displacements. In this paper, we propose a novel method for strain calculation from full-field data, based on the multivariate analysis technique of Principal Component Analysis (PCA) using which we first obtain the singular values and singular vectors for each component of the displacement field. By choosing only the dominant singular values and their corresponding singular vectors, we show that the dimensionality of the displacement data is sharply reduced and a significant portion of the noise is eliminated. Moreover, the shapes of the dominant singular vectors offer physical insight into dominant deformation patterns. We demonstrate the accuracy of the proposed technique by applying it to two cases each of homogeneous and inhomogeneous strain fields and show that in all cases the proposed method yields excellent results.     

Full-field strain measurement using a luminescent coating

In this paper we describe an optical-based technique, called strain sensitive skin (S³), for measuring in-plane strain data on structural members under static load. The technique employs a coating consisting of a luminescent dye and polymer binder that is applied to the surface of a test part via conventional aerosol techniques. Proper illumination stimulates the dye, which in turn emits higher wavelength luminescence. The excitation and emission intensities have different wavelengths; therefore, enabling optical filtering to separate the two signals. The optical strain response is intensity based. A network of randomized microcracks within the binder scatters the waveguided luminescence from the excited dye molecules. The amount of scattered luminescence is related to the changes in the microcrack openings and orientations via mechanical strain. Various calibration tests show the optical strain response to be proportional to the sum of in-plane principal strains. With this new experimental testing tool, full-field high-resolution strain measurements can be acquired. The optical strain response of this new sensor is minimally dependent on viewing and lighting directions, rendering the technique viable to imaging and determining strain fields for three-dimensional complex geometries.     

Investigation of the Tensile Behavior of Recycled Asphalts in the Small-Strain Domain with the Grid Method

Under mechanical loading, asphalt mixtures exhibit in their bulk heterogeneous strain fields characterized by localized gradients concentrated within the binder. Measuring such fields constitutes a challenge for the full-field measurement methods currently used in the experimental mechanics community. This is particularly true when the objective is to measure strains in the linear viscoelastic domain, which is characterized by low strain levels (about some 200 με). In the present study, the strain distribution is measured on the surface of several recycled asphalt pavements (RAP) subjected to direct tensile tests. Four asphalt mixtures incorporating respectively 0%, 20%, 40% and 100% of RAP are studied. The tests are performed using a servo-controlled machine for rheological tests (MAER) and the local strain fields are measured using the Grid Method (GM). Out-of-Plane Motions (OPM) and camera noise are the main causes of disturbance that significantly affect the strain measurements. A method is proposed here to compensate the OPM. It is specially dedicated to bituminous mixtures. Sensor noise is filtered over time to improve the measurement resolution. Obtained results indicate that such compensations allow the use of GM to obtain quantitative measurements of the asphalt deformation in the small-strain domain. Finally, the behavior of the different samples are compared and the effect of RAP inclusion on the local strain distribution is observed and characterized.     

A Robust Finite Element-based Filter for Digital Image and Volume Correlation Displacement Data

Background

Digital Image and Volume Correlation (DIC and DVC) are non-contact measurement techniques that are used during mechanical testing for quantitative mapping of full-field displacements. The relatively high noise floor of DIC and DVC, which is exasperated when differentiated to obtain strain fields, often requires some form of filtering. Techniques such as median filters or least-squares fitting perform poorly over high displacement gradients, such as the strain localisation near a crack tip, discontinuities across crack flanks or large pores. As such, filtering does not always effectively remove outliers in the displacement field.

Objective

This work proposes a robust finite element-based filter that detects and replaces outliers in the displacement data using a finite element method-based approximation.

Methods

A method is formulated for surface (2D and Stereo DIC) and volumetric (DVC) measurements. Its validity is demonstrated using analytical and experimental displacement data around cracks, obtained from surface and full volume measurements.

Results

It is shown that the displacement data can be filtered in such a way that outliers are identified and replaced. Moreover, data can be smoothed whilst maintaining the nature of the underlying displacement field such as steep displacement gradients or discontinuities.

Conclusions

The method can be used as a post-processing tool for DIC and DVC data and will support the use of the finite element method as an experimental–numerical technique.

     

ESPI技术对外贴纤维混凝土加固承载的实验研究

采用电子散斑干涉技术,对外贴碳纤维加固混凝土梁的外贴材料位移的分布特征,进行了全场实时测量,通过实验获得的散斑干涉条纹图可以得到外贴材料与混凝土梁的粘结传力长度随粘结长度及初始载荷之间的关系;了解用于加固的碳纤维材料的应变分布特点和产生梁侧剥离破坏时的碳纤维表面位移(应变)的演化过程。实验还说明了电子散斑干涉技术不仅可用于位移的测量,而且也可用于结构安全监测和破坏预报。文中给出了对C20D、C25A和C60C侧贴碳纤维板加固在不同载荷作用直到构件破坏前的位移测试及对试件C60C轴线上的剪应力分析结果。     

Full-field calculation of hole drilling residual stresses from electronic speckle pattern interferometry data

A mathematical method is proposed for calculating residual stresses from hole drilling electronic speckle pattern interferometry (ESPI) data, independent of rigid-body motions. Even though the signal-to-noise ratio of typical ESPI data is modest, the method achieves good computational stability by averaging a large amount of data. It does this without excessive numerical effort by exploiting known trigonometric relationships among the data. The resulting stress calculations are very rapid, and are well suited for future application to non-uniform stress measurements.     

Incremental Computation Technique for Residual Stress Calculations Using the Integral Method

The Integral Method for determining residual stresses involves making surface deformation measurements within a sequence of small increments of material removal depth. Typically, the associated matrix equation for solving the residual stresses within each depth increment is ill-conditioned. The resulting error sensitivity of the residual stress evaluation makes it essential that data measurement errors are minimized and that the residual stress solution method be as stable as possible. These two issues are addressed in this paper. The proposed method involves using incremental deformation data instead of the total deformation data that are conventionally used. The technique is illustrated using an example ESPI hole-drilling measurement.     

Hybrid experimental–numerical analysis of basic ductile fracture experiments for sheet metals

A basic ductile fracture testing program is carried out on specimens extracted from TRIP780 steel sheets including tensile specimens with a central hole and circular notches. In addition, equi-biaxial punch tests are performed. The surface strain fields are measured using two- and three-dimensional digital image correlation. Due to the localization of plastic deformation during the testing of the tensile specimens, finite element simulations are performed of each test to obtain the stress and strain histories at the material point where fracture initiates. Error estimates are made based on the differences between the predicted and measured local strains. The results from the testing of tensile specimens with a central hole as well as from punch tests show that equivalent strains of more than 0.8 can be achieved at approximately constant stress triaxialities to fracture of about 0.3 and 0.66, respectively. The error analysis demonstrates that both the equivalent plastic strain and the stress triaxiality are very sensitive to uncertainties in the experimental measurements and the numerical model assumptions. The results from computations with very fine solid element meshes agree well with the experiments when the strain hardening is identified from experiments up to very large strains.     

Identification of orthotropic elastic constants using the Eigenfunction Virtual Fields Method

The Virtual Fields Method (VFM – Pierron and Grediac, 2012), an inverse method based on the principle of virtual work (PVW), is being increasingly used to estimate mechanical properties of materials from full-field deformations obtained from techniques such as Digital Image Correlation, moiré and speckle interferometry and grid methods. By making specific choices for virtual fields (VFs) in PVW, one obtains a system of algebraic equations, which is then solved for the unknown material constants. Recently, a new variant of VFM, known as the Eigenfunction Virtual Fields Method (EVFM) has been proposed (Subramanian, 2013). In EVFM, principal components of the measured (i.e. true) strain fields are used to systematically generate VFs. We extend EVFM to orthotropic elastic materials in this work, and estimate the relevant material parameters from full-field strain data generated from a finite-element model of an unnotched Iosipescu test. Varying levels of Gaussian white noise are added to the synthetic strain data to evaluate the sensitivity of EVFM to input noise. It is observed that for low to moderate noise, the material properties estimated by the proposed method are relatively insensitive to noise. However, when noise levels are high, the proposed method yields large variance in some of the computed properties when compared to the state-of-the-art optimized piecewise continuous VFM (Toussaint et al., 2006; Pierron and Grediac, 2012). Some of the large variance in properties estimated from noisy data using EVFM is traced to the sensitivity of the third dominant eigenfunction and modifications to the proposed method to address this issue are suggested.     

A multilevel treatment of moiré fringe data using finite elements

Finite element procedures are applied to the modeling, analysis and visualization of experimental moiré data. Smoothing elements are introduced and evaluated with respect to data sparseness and error. A one-dimensional smoothing element is uniquely coupled with the method of principal curves to extract moiré fringe centers. A two-dimensional smoothing element is then used to produce a full-field representation given the fringe locations. The moiré technique is applied to the four-point bend experiment, and the surface-modeling technique is used to obtain displacement and gradient (strain) information.     

Multi-Functional Measurement Using a Single FBG Sensor

This paper describes the measurement of average strain, strain distribution and vibration of a cantilever beam made of Carbon Fiber Reinforced Plastics (CFRP), using a single Fibre Bragg Grating (FBG) sensor mounted on the beam surface. Average strain is determined from the displacement of the peak wavelength of reflected spectrum from the FBG sensor. Two unstrained reference FBG sensors were used to compensate for temperature drift. Measured strains agree with those measured by a resistance foil strain gauge attached to the sample. Stress distributions are measured by monitoring the variation in the full width at half maximum (FWHM) values of the reflected spectrum, using a proposed optical analytical model, described in the paper. FWHM values were measured for both the cantilever test beam and for a reference beam, loaded using a four-point bending rig. The trend of the stress distribution for the test beam matches with our analytical model, however with a relatively large noise present in the experimentally determined data. The vibration of a cantilever beam was measured by temporal analysis of the peak reflection wavelength. This technique is very stable as measurements are not affected by variations in the signal amplitude. Finally an application of FBG sensors for damage detection of CFRP plates, by measuring the natural frequency, is demonstrated. With small defects of different sizes applied to the CFRP plate, the natural frequency decreased with damage size.