In-plane Surface Displacements Research Articles

Design of Staggered Halbach EMAT to Generate SH Guided Wave in Pipe Structures

This research investigates the application of Staggered Electromagnetic Acoustic Transducer (EMAT), mainly focusing on the beam steering capabilities of Shear Horizontal (SH) Guided Waves in pipe structures. As a specific case of EMAT, Staggered EMAT introduces a lateral movement in the magnet rows so that the wave propagation occurs at an angle. A three-dimensional model of double row Staggered Halbach EMAT is developed and a finite element analysis is carried out in an aluminium pipe with high radius to thickness ratio. To obtain better signal-to-noise ratio (SNR), the size of the magnets and the number of magnets in a row are optimized by studying multiple cases. For all the configurations, the in-plane surface displacement is studied keeping the wavelength of the transducer constant. The corresponding frequency is derived from the dispersion curve for SH0 wave mode. The results shows that there is significant increase in the amplitude of the in-plane surface displacement with the increase in magnet height and the number of magnets in a row, ultimately leading to the signal with higher amplitude and better SNR. The study then analyses Staggered Halbach EMATs where the second row of magnets is displaced by the maximum value of half of the wavelength. The interference between the waves generated from the two magnet rows resulted in the directivity change of the guided wave, thereby achieving the steering of the SH wave by the maximum value of 27°. The finding of this study shows the enhanced beam steering capabilities of Staggered EMATs, particularly in the field of pipeline monitoring and can lead to more precise and effective detection of structural defects. Keywords: Staggered Halbach EMAT, Beam Steering, SH Guided Wave, Pipeline Inspection

Role of build orientation on quasi-static and dynamic fracture responses of additively manufactured AlF357 and AlSi10Mg alloys

In this work, a popular additive manufacturing (AM) aluminum alloy - AlSi10Mg and a new AM aluminum alloy - AlF357 are fabricated using Laser-Powder Bed Fusion ( L -PBF) approach to evaluate quasi-static and dynamic fracture behaviors. Four build orientations - horizontal, vertical, flat, and diagonal - are assessed. A Kolsky pressure bar apparatus along with ultrahigh speed photography is used to carry out the dynamic fracture experiments. In-plane surface displacements near cracks are measured using Digital Image Correlation (DIC) to evaluate the fracture parameters directly. A hybrid experimental-numerical approach that combines DIC measurements and finite element analysis is implemented to extract critical energy release rate and crack growth resistance behaviors. The effect of build orientation is found to be significant on the quasi-static fracture behavior with the horizontal and flat orientations having the best and worst fracture responses, respectively. Under dynamic loading conditions, however, the effects of build orientation are marginal. Both AlF357 and AlSi10Mg show strain-rate sensitivity and change in fracture mechanism under dynamic loading conditions with ~175% and ~200% increase in critical energy release rate. AlF357 consistently outperforms AlSi10Mg in both quasi-static (~30%) and dynamic (~10%) loading conditions.

Soft flexural waves and self-localization of wrinkling modes of single- and few-layer graphene under compression in a compliant matrix

This Research Letter studies the evolution under external compression of the wrinkling modes of single- and few-layer graphene or another two-dimensional atomic crystal embedded in or placed on a compliant matrix, or on a dense fluid in a gravitational field. An analytical model based on the nonlinear bending elasticity of the graphene is developed, which shows that the compressive surface stress causes spatial localization of the extended sinusoidal wrinkling mode with a solitonlike envelope, with the localization length decreasing with overcritical external strain. The parameters of the extended sinusoidal wrinkling mode are determined from the conditions of the anomalous softening of the flexural surface acoustic wave with predominant out-of-plane and suppressed in-plane surface displacements, propagating along the graphene in a compliant anisotropic matrix. Self-localization of the wrinkling modes finally results in the formation of strongly localized modes with approximately one-period sinusoidal profiles and external-strain-independent wavelengths. Self-localization of the wrinkling modes is governed by the derived Ginzburg-Landau-type nonlinear envelope-function equation with a negative dispersive term, which we relate with the graphene-nonlinearity-induced repulsion between soft flexural surface acoustic waves with negative effective mass. One- and two-dimensional wrinkling patterns and two types of strongly localized graphene wrinkling modes with different symmetry are described.

Dynamic fracture behavior of additively manufactured Scalmalloy®: Effects of build orientation, heat-treatment and loading-rate

Scalmalloy® specimens are fabricated using Laser Beam Powder Bed Fusion to investigate the role of build orientation, loading-rate, and heat-treatment on critical energy release rate and crack growth resistance behaviors. Four build orientations - horizontal, vertical, flat, and diagonal - are assessed under dynamic loading conditions. The experiments are carried out in a split-Hopkinson pressure bar apparatus on edge-notched three-point bend geometries. The specimens with the horizontal build are studied also under quasi-static loading conditions to gain some insight into strain-rate sensitivity. The horizontal and flat build specimens are heat-treated for dynamic tests to study the effect of heat-treatment on high strain-rate fracture performance. The in-plane surface displacements near the crack are directly measured using Digital Image Correlation and ultrahigh-speed photography to evaluate the fracture parameters in each of these cases. A hybrid experimental-numerical approach that combines DIC measurements with finite elements is employed to evaluate the fracture behavior. The differences in the critical energy release rates and post-initiation fracture behaviors of Scalmalloy® under different conditions are quantified. The diagonal and horizontal builds outperform the vertical and flat builds in terms of dynamic crack initiation and growth characteristics. The quasi-static crack initiation and growth of the horizontal build specimens show significant strain-rate sensitivity relative to the dynamic counterparts. The heat-treatment of specimens result in marginal improvement of the dynamic fracture performance but does not affect the crack growth resistance behavior. Based on microstructural analyses, the melt-pool boundary orientation relative to crack front extension direction correlates well with the measured dynamic crack initiation and growth performance metrics.

Identification of process-induced residual stresses in 3D woven carbon/epoxy composites by combination of FEA and blind hole drilling

Process-induced residual stresses in 3D woven carbon-epoxy composites are studied by blind hole drilling experiments interpreted with finite element (FE) modeling. It is assumed that residual stresses are primarily caused by the difference in thermal expansion coefficients of the constituents which are modelled as temperature-dependent linear elastic solids. The impact of residual stresses is quantified by drilling blind holes in the composite panels and mapping the resulting in-plane surface displacements by electronic speckle pattern interferometry. Mesoscale finite element models are used to correlate these surface displacements with the volumetric distribution of the residual stresses in the composite. This is done by determining the effective temperature drop ΔTeff that results in the same predictions for the surface displacements as experimentally measured. The effective temperature drop approach allows to use linear elastic models while approximately accounting for various nonlinear effects occurring in the material during processing. The models are also used to establish the sensitivity of the predicted results to the exact location of a hole and its depth.

Quantification of plastic shrinkage cracking in mortars using digital image correlation

This study presents a digital image correlation (DIC) technique for the detection and quantification of plastic shrinkage cracking in thin restrained mortar overlays applied on concrete substrates. The non-contact 2D-DIC technique enables measurements of in-plane surface strain and displacement under continuous monitoring. A post-processing procedure to compute various crack parameters, such as crack location, width, length and area on the specimen surface is presented, which enables the crack patterns to be synthesized and digitally reproduced from DIC data. The formation of surface cracking is illustrated in histograms facilitating a quantitative analysis. The crack width measurements obtained by DIC data were verified using an optical microscope. The temperature evolution, evaporation rate and free shrinkage behaviour of unrestrained mortar specimens were also tested to increase the knowledge of the early-age behaviour. This method is intended for evaluation of various shrinkage mitigation strategies in cement-based mortars and other repair mortars.

Utilizing numerical models to identify process-induced residual stresses in 3D woven carbon/epoxy composites

A combined experimental-numerical procedure is proposed to evaluate residual stresses in 3D woven carbon/epoxy composites. It is assumed that residual stresses are caused by the difference in thermal expansion coefficients of the constituents. The impact of residual stresses is quantified by drilling blind holes in the composite panels and mapping the resulting in-plane surface displacements by digital image correlation and electronic speckle pattern interferometry. Then mesoscale finite element models of the composite are used to determine the effective temperature drop ΔTeff that results in the same predictions for hole drilling. The local distributions of residual stress are given by the finite element simulations of the cooling by this temperature drop ΔTeff

On Evaluation of Stress Intensity Factor from In-Plane and Transverse Surface Displacements

Experimental approaches to the evaluation of stress intensity factor (SIF) of through-cracked plate components are currently based on the classical plane stress (2D) asymptotic power series expansion of strains or displacements near the crack tip (Williams’ solution). Besides the plasticity effects, the quantitative evaluation of SIF has to take into account a finite domain of convergence of the series expansion as well as three-dimensional (3D) effects, which prevail in the close vicinity of the crack tip. In this paper we demonstrate and confirm that attempts to fit Williams’ solution to experimental data in the near crack tip region can provide misleading results. In addition, it is verified that the SIF can be linked to the transverse displacements in the region controlled by 3D effects, and in particular, by 3D corner singularity. Under mode I loading, the transverse displacement field in this region is uniform, and largely unaffected by the higher order terms of the asymptotic power series expansion, which make this way of the evaluation of SIF particularly attractive for experimental measurements.

Development of 3-D Digital Image Correlation Using a Single Color-Camera and Diffractive Speckle Projection

A method for performing three-dimensional (3-D) Digital Image Correlation (DIC) using a single color-camera is described. The method takes advantage of the three independent Red-Green-Blue (RGB) color signals available on a color-camera sensor to gain 3-D displacement information. Conventional two-dimensional (2-D) DIC of an applied surface pattern is recorded using the pixels of one color to obtain in-plane surface displacements. Out-of-plane displacements are measured using telecentric speckle projection, illuminated in a second color. Separate 2-D DIC measurements of the two color pattern images provide full-field 3-D displacement measurements. This approach significantly reduces the spatial computations compared to conventional dual-camera 3-D DIC. This single color-camera method is expanded upon to enable the technique to measure 3-D displacements of non-planar specimens. The technique provides sufficient additional information to enable independent measurement and correction of camera perspective errors. Results of rigid body displacements for a planar and cylindrical surface are presented as well as a complex 3-D deformation of a rubber sample.

An Out-of-Plane Motion Compensation Strategy for Improving Material Parameter Estimation Accuracy with 2D Field Measurements

In-plane surface displacements, when measured with 2D Digital Image Correlation (2D-DIC), are very sensitive to out-of-plane displacement components. Any out-of-plane motion of the surface can pollute the measured field by introducing artificial displacements. These displacements are difficult to separate from the underlying response of the surface and thereby limit the application of 2D-DIC in inverse problems where the test specimen has significant motion in the out-of-plane direction. In the context of inverse problems, we propose to partially relax this condition of no out-of-plane motion in 2D-DIC. With this approach, only the out-of-plane rigid-body motion of the specimen surface, which is initially in-plane, needs to be avoided while the requirement of surface deformations to be primarily in-plane is essentially waived. Compensation, based on the pinhole camera model, for out-of-plane displacements of the surface in response to applied load is included within the error function of the minimization problem. The improvements in material parameter estimation, obtained by using the proposed compensation strategy, are demonstrated by an example. The proposed technique makes it possible to utilize 2D-DIC with a simple conventional lens for an increased number of inverse problems; and in the process avoiding the computational and experimental difficulties associated with 3D measurement methods as well as the high cost and magnification limitations of a telecentric lens.

The Uniaxial Tensile Response of Porous and Microcracked Ceramic Materials

The uniaxial tensile stress–strain behavior of three porous ceramic materials was determined at ambient conditions. Test specimens in the form of thin beams were obtained from the walls of diesel particulate filter honeycombs and tested using a microtesting system. A digital image correlation technique was used to obtain full‐field 2D in‐plane surface displacement maps during tensile loading, and in turn, the 2D strains obtained from displacement fields were used to determine the Secant modulus, Young's modulus, and initial Poisson's ratio of the three porous ceramic materials. Successive unloading–reloading experiments were performed at different levels of stress to decouple the linear elastic, anelastic, and inelastic response in these materials. It was found that the stress–strain response of these materials was nonlinear and that the degree of nonlinearity is related to the initial microcrack density and evolution of damage in the material.

3D Digital Imaging Correlation: Applications to Tire Testing

Abstract Three-dimensional digital imaging correlation (DIC) techniques are a viable method for measuring surface displacements and strains on tires. DIC provides the capability to measure the full-field noncontact tire surface deformation and strain state, which supports multiple objectives: validation of tire models based on finite element (FE) predictions, setting targets for improving FE predictions and providing insight into the tire deformation state under static and dynamic conditions. A method for verifying the accuracy of the DIC measurement process is presented whereby a thin, rectangular test sample of rubber material is subjected to a combination of strains and rigid body motions of known amounts. Once the measurement technique is proven accurate with a simple specimen, the focus shifts to the objectives explained above. Tire surface strains will be discussed for purposes of validating model predictions of sidewall and belt edge strains. Several types of specimen geometries will be reviewed and their effect on material properties will be presented. Also, the DIC technique can provide insight into complex physical problems that may otherwise be very difficult to measure. Some examples presented here include tire sidewall standing waves at high speeds and strains near tread lugs of agricultural tires. The DIC measurement method is an accurate, noncontacting full field technique for measuring in-plane surface displacements and strains of the magnitudes encountered in tire analysis. This technique serves many functions and has become a valuable tool for both tire testing and development.

Quasi-static and dynamic fracture of graphite/epoxy composites: An optical study of loading-rate effects

Strain-rate effects on fracture behavior of unidirectional composite materials are studied. Single-edge notched multi-layered unidirectional graphite composites (T800/3900-2) are investigated to examine fracture responses under static and dynamic loading conditions using a digital speckle correlation method. The fracture parameters for growing cracks are extracted as a function of fiber orientation. A 2D digital image correlation (DIC) method is used to obtain time-resolved full-field in-plane surface displacements when specimens are subjected to quasi-static and impact loading. Stress intensity factor and crack extension histories for pure mode-I and mixed mode cases are extracted from the full-field displacements. When compared to the dynamic stress intensity factors at crack initiation, the static values are found to be consistently lower. The stress intensity factor histories exhibit a monotonic reduction under dynamic loading conditions whereas an increasing trend is seen after crack initiation under quasi-static loading cases. This is potentially due to dominant crack face fiber bridging effects in the latter cases.

Friction and shear fracture of an adhesive contact under torsion

The shear failure or stiction of an adhesive contact between a poly(dimethylsiloxane) (PDMS) rubber and a glass lens has been investigated using a torsional contact configuration. As compared to linear sliding, torsion presents the advantage of inducing a shear failure under a pure mode III condition, while preserving the cylindrical symmetry of the contact. The surface of the transparent PDMS substrate was marked using a network of dots in order to monitor continuously the in-plane surface displacements during the stiction process. Using a previously developed inversion procedure (A. Chateauminois and C. Fretigny, Eur. Phys. J. E 27, 221 (2008)), the corresponding surface shear stress distributions were obtained from the displacement fields. Stiction was found to involve the progressive shrinkage of a central adhesive zone surrounded by an annular microslip region. Adhesion effects were especially evidenced from a stress overshoot at the boundary of the adhesive zone. The experimental data were analysis using an extension to torsional contact of the Maugis-Dugdale approach's to adhesive contacts which takes into account frictional effects. This model allowed to extract an effective adhesion energy in the presence of friction, which dependence on kinetics effect is briefly discussed.

Optical calibration for both out-of-plane and in-plane displacement sensitivity of acoustic emission sensors

The use of piezoelectric sensors for acoustic emission (AE) monitoring provides an extremely sensitive detection method of AE events. The sensors are used to detect the stress waves, resulting from an AE event, which arrive at the surface of a structure. The sensors provide high sensitivity, and are generally based on a high- Q design where the sensor is used to detect AE events around its resonance. Sensitivity calibration of these sensors is essential for accurate assessment of the AE measurement and particularly important for sensors mounted on safety critical structures. This paper proposes an optical method which enables both the out-of-plane and in-plane displacement sensitivity of an AE sensor to be established independently from each other. In the method, a laser homodyne interferometer is used to measure the out-of-plane and in-plane displacement of the surface of a large test block excited by a repeatable source transducer. The out-of-plane displacement is measured by aligning the laser beam perpendicular to the surface with time gating of the receive waveform used to isolate only the direct arrival of the longitudinal wave produced by the piston source transducer. For the in-plane displacement measurement, the laser beam is aligned parallel to the surface to intersect a small optically reflective step with the time waveform being gated to measure only the direct shear arrival produced using a normal incidence shear wave source transducer. In each case, the interferometer measurement is followed by coupling the sensor under test to the measurement surface, which is then exposed to the same acoustic field and the sensor output signal measured. This substitution method allows the sensor sensitivity to be obtained in terms of volts per unit displacement for both the out-of-plane and the in-plane surface displacement. The method provides a comprehensive description of an AE sensor response to different planes of displacement and offers the potential for a traceable sensor calibration to units of length.

Finding the position of tumor inhomogeneities in a gel-like model of a human breast using 3-D pulsed digital holography

3-D pulsed digital holography is a noninvasive optical method used to measure the depth position of breast tumor tissue immersed in a semisolid gel model. A master gel without inhomogeneities is set to resonate at an 810 Hz frequency; then, an identically prepared gel with an inhomogeneity is interrogated with the same resonant frequency in the original setup. Comparatively, and using only an out-of-plane sensitive setup, gel surface displacement can be measured, evidencing an internal inhomogeneity. However, the depth position cannot be measured accurately, since the out-of-plane component has the contribution of in-plane surface displacements. With the information gathered, three sensitivity vectors can be obtained to separate contributions from x, y, and z vibration displacement components, individual displacement maps for the three orthogonal axes can be built, and the inhomogeneity's depth position can be accurately measured. Then, the displacement normal to the gel surface is used to find the depth profile and its cross section. Results from the optical data obtained are compared and correlated to the inhomogeneity's physically measured position. Depth position is found with an error smaller than 1%. The inhomogeneity and its position within the gel can be accurately found, making the method a promising noninvasive alternative to study mammary tumors.

AE Sensor Calibration for Out-of-Plane and In-Plane Displacement Sensitivity

This paper proposes a method for both the out-of-plane and in-plane displacement sensitivity calibration of an acoustic emission (AE) sensor. In the method, a laser homodyne interferometer is used to measure the out-of-plane and in-plane displacement of the surface of a large test block excited by a repeatable source transducer. The out-of-plane displacement is measured by aligning the laser beam perpendicular to the surface with time gating of the receive waveform used to isolate only the direct arrival of the longitudinal wave produced by the piston source transducer. For the in-plane displacement measurement, the laser beam is aligned parallel to the surface to intersect a small optically reflective step with the time waveform being gated to measure only the direct shear arrival produced using a normal incidence shear wave source transducer. In each case, the interferometer measurement is followed by coupling the sensor under test to the measurement surface, which is then exposed to the same acoustic field and the sensor output signal measured. This substitution method allows the sensor sensitivity to be obtained in terms of volts per unit displacement for both the out-of-plane and in-plane surface displacement. The method allows a comprehensive description of an AE sensor response to different planes of displacement and offers the potential for a traceable sensor calibration to units of length.

The excitation and detection of Lamb waves with planar coil electromagnetic acoustic transducers

Planar coil electromagnetic acoustic transducers (EMATs) are investigated for the excitation and detection of Lamb waves in nonferromagnetic metallic wave-guides. Such EMATs are attractive for certain applications due to their omni-directional sensitivity to wave modes with predominantly in-plane surface displacement, such as the So Lamb wave mode. A model is developed that enables the modal content of the radiated Lamb wave field from a transmitting EMAT to be calculated, and the output voltage from a receiving EMAT to be predicted when a Lamb wave mode is incident on it. The predictions from this model are compared with experimental data obtained from 12 different EMATs tested on a 5-mm thick aluminum plate, and good agreement is obtained. The model then is used to analyze the different effects that contribute to the overall Lamb wave modal sensitivity of an EMAT. The relationship between coil geometry and wavelength is examined.

Phase-shifting moire´ interferometry based on a liquid crystal phase modulator

A new method for phase-shifting moiré interferometry is proposed and studied experimentally. A nematic liquid crystal cell is employed as a phase modulator to realize the phase-shifting technique for the conventional moiré interferometry. The phase retardation of the liquid crystal cell is calibrated by measuring transmitted light intensities. By letting one of coherent beams pass through a liquid crystal cell and controlling the phase retardation via suitable voltages across the cell, the phase map that provides quantitative data regarding the in-plane surface displacement can be created. The use of the liquid crystal phase modulator in the moiré optical arrangement has several advantages over alternative methods.

Compressive response and failure of braided textile composites: Part 1—experiments

Experimental results obtained by examining the planar biaxial compression/tension response of carbon 2D triaxial braided composites (2DTBC) are reported in this paper. These experiments were motivated by a need to examine the failure of 2DTBC in a state of stress that would be similar to what is experienced by the walls of a tubular member under compressive crush loads. Results obtained from a series of biaxial tests that were conducted with different proportional displacement loading ratio combinations of compression and tension are reported. In all cases, the dominant failure mechanism under such a stress state is the buckling of the bias and axial tows within the composite. Full field surface displacement data is acquired concurrently during all biaxial and some uniaxial tests using the technique of digital speckle photography. Digital images of the specimen surface that is illuminated with a He–Ne laser are acquired at discrete time intervals during the loading history using a high-resolution digital camera. These images are stored and analyzed to obtain the incremental inplane surface displacement field, Δ u( x, y) and Δ v( x, y). From these, the incremental inplane surface strains Δ ε x , Δ ε y and Δ γ xy are obtained by numerical differentiation. The present paper, which is the first in a two part series, is devoted to the biaxial experimental results pertaining to 2DTBC failure.