Accurate Strain Measurements Research Articles

Strain Transfer Analysis of Embedded Fiber Bragg Grating Strain Sensor

Abstract Due to the difference in the physical and mechanical properties between the optical fiber, protective layer, adhesive layer, and the host material, the strains measured by a fiber Bragg grating (FBG) sensor may not be the actual strains of the host material, which impedes the reliable applications of FBG sensors. To overcome this problem, in this paper, the strain transfer formula was derived by using elastic analysis, the shear-lag method, and several reasonable assumptions taking into account temperature variations and nonaxial stresses, which was an improvement to an existing study (Li, H. N., Zhou, G. D., Ren, L., and Li, D. S., “Strain Transfer Analysis of Embedded Fiber Bragg Grating Sensor Under Nonaxial Stress,” Optic. Eng., Vol. 46, No. 5, 2007, 054402). The analytical results were validated by simulating the behavior of a bare optical fiber through finite element analysis. The data enabled the identification of the parameters that influence the strain transfer from the host material to the embedded FBG sensors and the impact of the temperature variation and sensor alignment angle on the measurement accuracy. This work provided additional knowledge for the improvement of the existing strain transfer theory of FBG sensors in order to achieve a more accurate strain measurement with this sensing technology.

Design of a split Hopkinson pressure bar with partial lateral confinement

This paper presents the design of a modified split Hopkinson pressure bar (SHPB) where partial lateral confinement of the specimen is provided by the inertia of a fluid annulus contained in a long steel reservoir. In contrast to unconfined testing, or a constant cell pressure applied before axial loading, lateral restraint is permitted to develop throughout the axial loading: this enables the high-strain-rate shear behaviour of soils to be characterised under conditions which are more representative of buried explosive events. A pressure transducer located in the wall of the reservoir allows lateral stresses to be quantified, and a dispersion-correction technique is used to provide accurate measurements of axial stress and strain. Preliminary numerical modelling is utilised to inform the experimental design, and the capability of the apparatus is demonstrated with specimen results for a dry quartz sand.

Accuracy of Quasi-Static Bending Strain Measurement using Scanning Laser Doppler Vibrometry (SLDV)

This paper presents an investigation into the use of 1D scanning laser Doppler vibrometry for the measurement of quasi-static bending strain, on a beam, from measured out-of-plane deflections. To calculate the bending strain from measured deflections, a Savitzky-Golay differentiation filter is used. An experimental investigation was conducted to determine how the strain estimate would be affect by the spatial interval between measurement points, amplitude of loading, and the numerical parameters used within the Savitzky-Golay differentiation filter. A number of findings, from the investigations undertaken are presented. The bending strain measurement technique is best approximated by using a third-order polynomial in the Savitzky-Golay differentiator filter. An accurate bending strain measurement can be produced at any spatial interval, as long as the filter width spans a fixed distance. In addition, changes in applied load have no effect on the accuracy of the technique. This technique has significant application for the measurement of localised bending strain on the surface of structures or materials that are cyclically loaded and subjected to harsh environmental conditions, such as elevated temperatures.

Self-sensing and strengthening effects of reinforced concrete structures with near-surfaced mounted smart basalt fibre–reinforced polymer bars

A new retrofitting system is proposed for reinforced concrete structures with application of near-surfaced mounted smart basalt fibre–reinforced polymer bar. The distributed optical fibre sensing technology, namely pre-pump pulse Brillouin optical time-domain analysis, is applied as the sensing technology for the smart bar. Then the proposed system is explained in detail from both self-sensing and strengthening. Finally, some experiments were implemented with reinforced concrete beams to verify the actual effects. From the results, it is concluded that the ultimate strength and the stiffness after steel rebar yielding can be increased obviously due to the high strength and ultimate strain of the smart basalt fibre–reinforced polymer bar. Meanwhile, the structure strain distribution can be measured with the smart basalt fibre–reinforced polymer bar, with which some key parameters can be well assessed, such as crack location, crack width, displacement and bending moment. However, the self-sensing effects indeed have been obviously influenced by the strain measurement accuracy especially after concrete cracking. Therefore, it is meaningful to improve the sensing accuracy especially for complicated strain. Additionally, some prestress upon the smart basalt fibre–reinforced polymer bar can improve both sensing and strengthening performance.

Digital Image Correlation Technique for Strain Measurement of Aluminium Plate

The Digital image correlation technique recently developed is an image identification technique to be applied for measuring the object deformation. This technique is capable of correlating the digital images of an object before and after deformation and further determining the displacement and strain field of an object based on the corresponding position on the image. Digital Image Correlation (DIC) is an upcoming experimental stress –strain analysis technique and has certain advantages over others. DIC can be tested on almost all material with a large area of inspection and no pre treatment is required as compared to other optical methods. DIC uses the principle of image correlation and produces strain field by analyzing the movement of marked points on the subject. The Digital Image Correlation (DIC) is a state of art technique that can be used for accurate strain measurement. Because of its capability for fast data acquisition, this technique is well suited for the characterization of material properties both in the elastic and plastic ranges. It also has advantages of full field, non- contact, and considerately high accuracy for displacement and strain measurements. The MATLAB software is an innovate system that uses the digital image correlation technique to provide strain measurements in a two-dimensional contour map for planar surface specimens.

Packaged in-line Mach–Zehnder interferometer for highly sensitive curvature and flexural strain sensing

The paper presents an innovative packaging approach to allow highly sensitive in-line Mach–Zehnder interferometer (IMZI) sensor to be used for accurate measurement of curvature and flexural strain specifically in civil engineering. The sensor which consists of two tapers is protected within a polypropylene package to survive in harsh, in-the-field conditions. The package design employs cost effective materials without compromising the curvature and flexural strain sensitivity which are 85.2dBm−1 and 0.0148dB/μϵ. The accuracy of measurement results is further verified by obtaining the flexural modulus for the steel which is in good agreement with theoretical value.

In-vivo validation of a new clinical tool to quantify three-dimensional myocardial strain using ultrasound.

Three-dimensional (3D) strain analysis based on real-time 3-D echocardiography (RT3DE) has emerged as a novel technique to quantify regional myocardial function. The goal of this study was to evaluate accuracy of a novel model-based 3D tracking tool (eSie Volume Mechanics, Siemens Ultrasound, Mountain View, CA, USA) using sonomicrometry as an independent measure of cardiac deformation. Thirteen sheep were instrumented with microcrystals sutured to the epi- and endocardium of the inferolateral left ventricular wall to trace myocardial deformation along its three directional axes of motion. Paired acquisitions of RT3DE and sonomicrometry were made at baseline, during inotropic modulation and during myocardial ischemia. Accuracy of 3D strain measurements was quantified and expressed as level of agreement with sonomicrometry using linear regression and Bland-Altman analysis. Correlations between 3D strain analysis and sonomicrometry were good for longitudinal and circumferential strain components (r = 0.78 and r = 0.71) but poor for radial strain (r = 0.30). Accordingly, agreement (bias ± 2SD) was -5 ± 6 % for longitudinal, -5 ± 7 % for circumferential, and 15 ± 19 % for radial strain. Intra-observer variability was low for all components (intra-class correlation coefficients (ICC) of respectively 0.89, 0.88 and 0.95) while inter-observer variability was higher, in particular for radial strain (ICC = 0.41). The present study shows that 3D strain analysis provided good estimates of circumferential and longitudinal strain, while estimates of radial strain were less accurate between observers.

Strain Limit States for Circular RC Bridge Columns

Described in this paper are strain limit states for reinforced concrete bridge columns. A total of 30 large scale reinforced concrete bridge columns were subjected to either reversed cyclic loading or real seismic load histories as part of this research program. Through the use of a non-contact three-dimensional (3-D) position measurement system, accurate strain measurements that are not possible with conventional instrumentation were made, which allowed for development of strain limits for serviceability, spiral yielding, and reinforcing bar buckling limit states. The proposed bar buckling strain limit was compared to an existing drift-based approach and one formulated using finite element analysis for columns in the data set and the literature.

Research on the performance of multifunctional distributed optical fiber sensing system based on the combination of Brillouin optical time-domain analysis and phase-sensitive optical time-domain reflectometer

There are many similarities between Brillouin optical time-domain analysis and phase-sensitive optical time-domain reflectometer in system topological structure. A multifunctional distributed optical fiber sensing system based on their similarities and the combination of their topological structure is presented. The system can monitor strain and temperature, as well as detect and locate the intrusions or disturbances along the sensing fiber. Suppose that X is the width of the optical pulse incident into the sensing fiber with the unit of nanosecond and Y is the minimum detectable distance with the unit of meter between two intrusions that are being detected simultaneously. The experiment results show that y changes linearly with x according to the equation: y=0.103x−0.452. By optimizing device parameters of the system, strain measurement accuracy of 3.17 μϵ and the temperature measurement accuracy of 0.45°C have been realized when the optical pulse width is 30 ns. On the other hand, two intrusions have been detected and located simultaneously with this multifunctional system. The results show that the pulse width and the minimum distance between two intrusions (Lmin) have a linear relationship. The theoretical analyses and the experiment results show it is applicable to use this multifunctional system for strain and temperature monitoring, and intrusion detecting.

Accurate strain measurements in highly strained Ge microbridges

Ge under high strain is predicted to become a direct bandgap semiconductor. Very large deformations can be introduced using microbridge devices. However, at the microscale, strain values are commonly deduced from Raman spectroscopy using empirical linear models only established up to ε100 = 1.2% for uniaxial stress. In this work, we calibrate the Raman-strain relation at higher strain using synchrotron based microdiffraction. The Ge microbridges show unprecedented high tensile strain up to 4.9% corresponding to an unexpected Δω = 9.9 cm−1 Raman shift. We demonstrate experimentally and theoretically that the Raman strain relation is not linear and we provide a more accurate expression.

Enhancement of strain measurement accuracy using optical extensometer by application of dual-reflector imaging

At present, the accuracy of strain measurement using a common optical extensometer with 2D digital image correlation is not sufficient for experimental applications due to the effect of out-of-plane motion. Therefore, this paper proposes a dual-reflector imaging method to improve the accuracy of strain measurement when using a common optical extensometer, with which the front and rear surfaces of a specimen can be simultaneously recorded in the sensor plane of a digital camera. By averaging the strain in two optical extensometers formed on the front and rear surfaces of a specimen, the effect of any slight out-of-plane motion can be eliminated and therefore the strain measurement accuracy can also be improved. Uniaxial tensile tests with an Al-alloy specimen, including static loading and continuous loading, were conducted to validate the feasibility and reliability of the proposed method. The strain measurement results obtained with the proposed method and those obtained with an electrical-resistance strain gauge were found to be in good agreement. The average errors of the proposed method for the two continuous loading tests were found to be 8 ± 10 με and −6 ± 8 με. Given that no correction sheet or compensation specimen is required, the proposed method is easy to implement and thus especially suitable for determining the mechanical properties of brittle materials due to the high level of accuracy with which strain can be measured.

Analysis of the structural response and failure of containers subjected to internal blast loading

A series of small-scale internal blast experiments were conducted to assess the structural response and failure mechanisms of metal containers subjected to internal blast loading for the enhancement of Vulnerability/Lethality (V/L) modelling. The experiments examined welded steel containers, both fully enclosed and flanged, against a range of charge sizes detonated internally. The deformation and strain profiles of the containers were measured and compared with the numerical simulation results. The numerical simulations replicated the deformation and strains at the centre of the containers with a reasonable degree of accuracy. However, initial numerical simulations using shell elements significantly under-predicted strain values at the welded joints where failure of the containers occurred. Metallographic analysis of the welded joints and the high-speed imagery post-experiment indicated that failure occurred due to large strains in the heat affected zone and weld bead interface, where the material strength is reduced. To perform these assessments, a refined geometrical model, using Lagrangian elements, was required. Results from the numerical simulations highlighted that the quasi-static overpressure was the key parameter from the blast wave in determining the maximum deformation of the container, enabling simplified loading conditions for the Lagrangian analysis. Simulations using Lagrangian elements for the container improved the accuracy of the edge strain measurements but still under predicted the experimental results, which highlighted the inability of these models to account for weld defects such as porosity and lack of fusion which act as stress concentrators, assisting ultimate failure of welded containers.

On Conditioning of Resistive Strain Gage Channel Connected in Quarter Bridge Configuration in Measurement of Moderately Large Strains

In response to engineering needs of measuring moderate or large strains in metallic structures’ progress in resistance strain gages, technology resulted in widening the measurement range of this type of sensors to a range of 10–15%. For precision strain measurement applications, especially when a considerable number of measurement points are involved, single strain gage sensors are commonly used in quarter Wheatstone bridge configurations. Extension of measurement range to moderate strains requires taking into account inherent nonlinearities in signal transfer functions of the elements present in measurement chain. This work discusses in detail the most important ones, that is resistive gage sensor and quarter bridge measurement configuration nonlinearities to indicate that they are of the same order for moderate strains. Quite straightforward, shunt calibration procedure, taking into account these nonlinearities, is delivered or proposed enabling elimination of systematic errors. Thus, optimum accuracy of strain measurements matching the characteristics of components of strain measurement system can be conveniently achieved upon following simple steps. Inverse hyperbolic tangent—\( \epsilon \)Ln =tanh−1(2 ∙e0/Eex)—linking scalar logarithmic strain and bridge reduced output voltage is shown to be a transfer function of strain measurement system with gage sensor in quarter bridge configuration for moderate or large strains.

Distributed Long-Gauge Optical Fiber Sensors Based Self-Sensing FRP Bar for Concrete Structure

Brillouin scattering-based distributed optical fiber (OF) sensing technique presents advantages for concrete structure monitoring. However, the existence of spatial resolution greatly decreases strain measurement accuracy especially around cracks. Meanwhile, the brittle feature of OF also hinders its further application. In this paper, the distributed OF sensor was firstly proposed as long-gauge sensor to improve strain measurement accuracy. Then, a new type of self-sensing fiber reinforced polymer (FRP) bar was developed by embedding the packaged long-gauge OF sensors into FRP bar, followed by experimental studies on strain sensing, temperature sensing and basic mechanical properties. The results confirmed the superior strain sensing properties, namely satisfied accuracy, repeatability and linearity, as well as excellent mechanical performance. At the same time, the temperature sensing property was not influenced by the long-gauge package, making temperature compensation easy. Furthermore, the bonding performance between self-sensing FRP bar and concrete was investigated to study its influence on the sensing. Lastly, the sensing performance was further verified with static experiments of concrete beam reinforced with the proposed self-sensing FRP bar. Therefore, the self-sensing FRP bar has potential applications for long-term structural health monitoring (SHM) as embedded sensors as well as reinforcing materials for concrete structures.

On the sensitivity and repeatability of fiber Bragg grating sensors used in strain and material degradation measurement of magnesium alloys under cyclic loads

In the present study, for the first time, Fiber Bragg Grating (FBG) sensors are employed to measure the cyclic-strain induced on AZ31B extrusion samples during rotational bending tests (RBTs). The importance of this observation will be highlighted by considering the risk of failures under this circumstance in the modern technologies such as aerospace, while any in situ cyclic strain measurement has not been reported under RBTs. For this purpose, first, the accuracy of strain measurements captured by the FBG sensor in the elastic and plastic regimes is investigated by comparing the FBG measured strain with the data obtained simultaneously by a standard extensometer during uniaxial pull-push tests. The results confirm that the FBG sensor is able to measure the strain up to 1.3 % (plastic region) accurately. Next, the strains of the specimens are measured under different bending moments during RBTs in both the elastic and plastic regimes, hence monitoring the degradation of material during the test. The experiments uncover that the strain amplitude of the samples is decreased as the number of cycles increases in the plastic regime until the sample is stabilized. However, the strain response of the material under a bending moment of 2.5 Nm (in the elastic regime) remains constant during the test. This paper concludes that the measurement of strain amplitude evolution, with respect to the number of cycles, in a rotating bending cyclic test with FBG sensors is feasible with high level of accuracy and repeatability in the cyclic testing in the elastic region.

Examination of phonon deformation potentials for accurate strain measurements in silicon–germanium alloys with the whole composition range by Raman spectroscopy

The phonon deformation potentials (PDPs), p and q, of Si1−xGex with the whole range of the Ge concentration x were examined in detail in pursuit of accurate strain measurements by Raman spectroscopy. An oil-immersion Raman technique was adopted to extract the PDPs of Si1−xGex, in which a complex sample preparation process or a stress-introduction device is not necessary. The strain-shift coefficients bLO and bTO, which can be calculated using the obtained PDPs, were compared with the values in the literature, and we suggested which values were best for application to accurate strain measurements. Ab initio calculation was also performed to understand the behavior of the PDPs throughout the whole range of x in Si1−xGex.

High Precision Measurement of Strain Distribution by Integrated Dot Centroid Tracking Method (Fundamental Study for Accuracy of Error Reduction)

This paper presents the effectiveness of the error reduction methods for integrated dot centroid tracking method. Two important sources of error and noise are lens distortion and brightness intensity fluctuation on each pixel, which should be taken in account to achieve high accuracy of full-field strain measurement. The method can correct lens distortion at any focal distance between a digital camera and an object. Pixel based noise reduction method using Kalman filter and integrated image by multiple images was proposed. When we need very accurate strain field, the lens distortion should be removed as possible as we can. Due to the corrections, 0.1% strain accuracy is accomplished and total computation time is reduced in comparison with an arithmetic mean operations. The effectiveness of the idea is shown through experimental and numerical examples and the result of strain field measurement is presented and discussed.

Development of an Optical Fiber Sensor Interrogation System for Vibration Analysis

Since the introduction of dynamic optical fiber sensor interrogation systems on the market it has become possible to perform vibration measurements at frequencies up to a few kHz. Nevertheless, the use of these sensors in vibration analysis has not become a standard practice yet. This is mainly caused by the fact that interrogators are stand-alone systems which focus on strain measurements while other types of signals are also required for vibration analysis (e.g., force signals). In this paper, we present a fiber Bragg grating (FBG) interrogation system that enables accurate strain measurement simultaneously with other signals (e.g., excitation forces). The system is based on a Vertical Cavity Surface Emitting Laser (VCSEL) and can easily be assembled with relatively low-cost off-the-shelf components. Dynamic measurements up to a few tens of kHz with a dynamic precision of around 3 nanostrain per square-root Hz can be performed. We evaluate the proposed system on two measurement examples: a steel beam with FBG sensors glued on top and a composite test specimen with a fiber sensor integrated within the material. We show that in the latter case the results of the interrogation system are superior in quality compared to a state-of-the-art commercially available interrogation system.

On the Accuracy of Elastic Strain Field Measurements by Laue Microdiffraction and High-Resolution EBSD: a Cross-Validation Experiment

Determining the accuracy of elastic strain measurements in plastically deformed alloys is an experimental challenge. To develop a novel cross-validation procedure, a controlled elasto-plastic strain gradient was created in a stainless steel single crystal by four point bending deformation. The corresponding elastic strain field was probed, with an intragranular spatial resolution, in-situ by Laue microdiffraction and ex-situ by High Resolution EBSD. Good agreement is found for the two independent measurements and the predictions of a mechanical model, at plastic strains below 0.5 %. The accuracy of the measurements is estimated at 3.2 × 10 − 4 .

A new method for limit point determination in composite materials containing defects using image correlation

A new method is proposed to determine the onset of material failure in composite materials containing defects tested in tension. The new method is proposed since the load versus axial deformation plot from a tension test cannot be always used to identify the onset of material failure in a composite materials containing defects. Digital image correlation (DIC) methods can provide very accurate d4eformation and strain measurements. In this paper, a new DIC based method is proposed that can identify the onset of damage and thus the limit point in composite materials containing defects. In this method (1) surface topography is extracted from the three dimensional DIC data using two cameras; (2) the changes in the surface are monitored during the tension tests; (3) The onset of interlaminar damage is identified by comparing the surface height difference in the test specimen at different time steps; (4) the first derivative of the surface height difference is used to determine the onset of internal instabilities in the material and are correlated to interlaminar damage. Compared to existing standard methods that rely on the load-deformation response to determine the onset of damage, the proposed procedure more accurately defines the onset of interlaminar damage and thus the definition of the boundary of safe operation of the composite material system prior to damage onset.