Measuring Strains through the Thickness of a Composite Structural Specimen Subjected to Bending

This study concerns the central reinforced zone of a composite structural specimen. In order to estimate the strain distribution during a series of three and four-point bending tests, several optical fiber Bragg grating sensors have been embedded in various levels of the ply stack. Simultaneously, surface strain field measurements by 3-D digital image correlation are undertaken. Both techniques show a general linear distribution of longitudinal strains through the thickness of the thick zone but values are slightly different. A numerical model is developed and a test-calculation dialogue is carried out. The complementary information given by the two optical techniques for in-core and surface measurements reveals the importance of considering structural and edge effects.     

Surface and interior strain fileds measured by multiple-embedded-grid moiré and strain gages

Surface and interior straini fields in thick specimens of polycarbonate have been measured by an embedded-multiple-grid moiré method. Interior gratings are photographed through intervening gratings. Coherent optical processing of grating records creates moiré fringe pattern. A correction procedure was developed to eliminate moiré errors caused by strain-induced gradients of refractive index. This procedure utilizes the refraction distribution as obtained from observation of a grating from opposite sides of a specimen. No measurements other than the normal moiré observations are required in order to find actual strains. The correction technique should be useful in refining the results obtained when other optical methods are used in three-dimensional situations. The method is utilized to determine strains on the surfaces and at the mid-and quarter-planes of thick compact tension specimens. Results obtained, after correction, agree with measurements made with embedded strain gages. Maximum tensile strain occurs on the midplane. The findings are rationalized by consideration of thickness and proximity to the crack tip.     

A fiber optic sensor for transverse strain measurement

A fiber optic sensor capable of measuring two independent components of transverse strain is described. The sensor consists of a single Bragg grating written into high-birefringent, polarization-maintaining optical fiber. When light from a broadband source is used to illuminate the sensor, the spectra of light reflected from the Bragg grating contain two peaks corresponding to the two orthogonal polarization modes of the fiber. Two independent components of transverse strain in the core of the fiber can be computed from the changes in wavelength of the two peaks if axial strain and temperature changes in the fiber are zero or known. Experiments were performed to determine the response of the sensor by loading an uncoated sensor in diametral compression over a range of fiber orientations relative to the loading. The results of these experiments were used with a finite element model to determine a calibration matrix relating the transverse strain in the sensor to the wavelength shifts of the Bragg peaks. The performance of the sensor was then verified by measuring the transverse strains produced by loading the fiber in a V-groove fixture.     

Full-Spectral Interrogation of Fiber Bragg Grating Sensors Exposed to Steady-State Vibration

In this paper we measure for the first time the full-spectral response of a fiber Bragg grating (FBG) sensor subjected to vibration. We consider two cases: with and without an initial spectral distortion due to non-uniform strain along the length of the FBG. Previous work has measured only the dynamic response at a single wavelength which is valid when no spectral distortion is present. FBG sensors are mounted near the notch tip on a double edge notch specimen that is also subjected to harmonic vibration. We measure the full-spectral response of the FBG at 100 kHz applying an interrogator recently developed by the authors. The measurements of the FBG response with an initial spectral distortion clearly show the transient response and are verified through simulation. Finally, we demonstrate that the use of the high-speed, full-spectral interrogator permits the separation of the spectral distortion and the harmonic vibration from the FBG response signal through classical filtering and can therefore be applied to measure non-uniform strain fields in noisy environments.     

Shear properties and a stress analysis obtained from vinyl-ester losipescu specimens

The use of losipescu specimens for the determination of the shear properties of a vinyl-ester resin was investigated. The antisymmetric four-point bend and the Adams and Walrath fixtures were studied for their suitability in loading these specimens. Photoelastic and strain-gage data in addition to published finite-element results show that the latter fixture distorts the stress field in the gage section. The antisymmetric four-point bend fixture is found to give the purest shear-stress field in the gage section and to yield the most reliable shear-modulus values. A refined photoelastic analysis shows that the shear-stress distribution between the notch roots is essentially uniform with a relative maximum or minimum at the centroid depending on the depths of the notches. Also, stress risers of up to 30 percent are observed near the notch roots. Except at the roots, finite-element predictions are presented which are in excellent agreement with photoelastic data. The failure mode of this vinyl-ester resin is tensile and the corresponding tensile stress calculated from the average shear stress in the gage section of the losipescu specimen is in excellent agreement with failure data acquired in tension.     

埋入式封装的光纤光栅传感器应变传递分析

推导了布拉格光纤光栅传感器所测应变与实际结构应变的关系,得出了平均应变传递率并与实际试验结果进行比较. 根据应变传递率确定了光纤的临界粘接长度,并推导了多层粘接时的应变传递情况,讨论了影响应变传递率的因素. 结果表明,光纤光栅的粘贴长度必须大于临界粘贴长度,且光纤光栅传感器所测应变需要加以修正才能得到实际结构应变.     

An Embedded 3D Strain Tensor Sensor Based on the Eshelby’s Inclusion

A new design for an embedded strain sensor is proposed in this paper. Based on Eshelby’s inclusion model, it may be used to measure the full 3D strain or stress tensor within any solid body. Currently, common embedded strain sensors are only capable of 1D measurements. The spherical shape of our sensor allows the stress or strain that would exist in the structure without the sensor to be calculated with the aid of the Eshelby theorem (in the case of elastic behavior). We used fiber Bragg gratings to measure the deformation of the sphere - other techniques are also available. Experimental testing was performed in two settings. The first test measured the performance of a polymethylmethacrylate prototype under fluid pressure load. In a second test, a steel prototype sensor was embedded in a standardized concrete specimen under axial compression, and was successfully used to measure 3D strain in real conditions.     

Measurement of three-dimensional Mode-I stress intensity factor using multiple embedded grid moire technique

Multiple embedded grid moire and strain gage techniques are used to calculate the variation in Mode-I stress intensity factor throughout the thickness of ASTM E-399 standard compact tension specimens of Merlon polycarbonate. The specimen grids near the crack tip on the surface and in the interior were recorded for the unloaded condition and for various loaded states using high resolution photographic techniques. Optical processing produced moire patterns from which the change in the crack opening displacement could be determined. From the information about the crack opening displacement in the region of the crack tip, the Mode-I stress intensity factor was calculated for various interior planes and on the surface of the specimen. The stress intensity factor was found to be higher in the midplane than on the surface, and it causes crack initiation to start at the midplane.     

基于准分布式FBG传感器的均质材料内部应变测试的试验研究

采用环氧树脂材料作为试验载体,使用没有任何保护性封装的、运用波分复用技术在同一光纤上刻入三个布拉格光栅的基础FBG传感器,来监测液体树脂流动及固化成型的全过程,并使用固化成型的环氧树脂板进行三点弯曲试验。将所得数据与有限元模拟数值解进行比较,来验证在去除封装、将传感器自身应变影响降到最低的情况下,FBG传感网络是否依然能够有效地反映出试验对象在各种情况下的内部应变。本文给出了FBG光纤光栅在逐级静力荷载加载下材料内部三点弯曲的应变图,并通过数值计算分析了未封装光纤在复合材料内部受力过程中的力学性能。     

Large strain field near a notch-tip under tension

This paper considers the plane strain notch-tip filed in a rubber-like material under tension. Based on a new constitutive relation, the asymptotic equations of the near tip field are derived and solved. It is shown that the notch tip field is composed of two narrowing sectors and an expanding sector. The dominant stress and strain near the notch tip are found to be in a state of uniaxial tension.     

光纤光栅传感网络应用于玻璃纤维复合材料构件损伤检测的试验研究

将光纤光栅传感网络埋入玻璃纤维复合材料试件后,通过无损试件与有损试件的准静态弯曲对比试验研究,分析了测量过程中反映损伤位置以及损伤程度的光纤光栅参数。然后使用ANSYS有限元软件对其进行数值模拟计算,并将数值模拟的结果与试验测得的结果相对比,验证了应用光纤光栅传感网络利用准静态加载方法测量损伤的可行性以及准确性。本文研究结果可为利用FBG光纤传感网络对实际工程中复合材料结构的在线健康监测提供实验基础。     

In situ determination of adhesive shear moduli using strain gages

A new, convenient and cost-effective method of determining in situ adhesive shear moduli using strain gages is proposed and evaluated. Thick-adherend lap shear specimens with stacked gage rosettes at the center of the bond line are loaded in tension for adhesive shear strain measurement. Experimental and numerical results indicate that the test specimen has a nonuniform adhesive shear stress (or strain) distribution in the test section and that this distribution (except at the center point of the bond line) is greatly affected by load eccentricity. In addition to the nonuniformity in the shear stress distribution, the issue of material nonhomogeneity in the gage-covered region affects the strain gage measurement. By taking into account these two issues and assuming linear-elastic behavior, two approaches for converting the gage-measured shear strain into the adhesive shear strain are developed and verified by experiment. It is shown that the strain gage measurement associated with either of two conversion techniques can determine the in situ adhesive shear moduli, which are comparable with moiré experiment and KRG-1 extensometer measurements.     

Fiber Bragg Grating Based Stress Measurement for Films Deposited onto Cylindrical Surfaces

Shape of a substrate directly influences the residual stress in thin film coatings. In this study, a method involving Fiber Bragg Grating (FBG) was used to measure residual stress in a film deposited on a cylindrical surface. An FBG has a cylindrical surface and its Bragg wavelength shifts continuously when a film is being deposited on the sensor’s surface. Herein, we calculated the residual strain in the film from the wavelength shift of the Bragg grating by studying the transfer of the residual strain of the cylindrical film to the core of the optical fiber substrate during deposition. By employing the energy method, we derived expressions that related the strain in the core of fiber to the residual strain in single layer films, bilayer films, and multilayer cylindrical films. As an example, we demonstrated a detailed process for testing the stress and the strain distribution across a nickel (Ni) film electrodeposited on the surface of a nickel-phosphorus (Ni-P) alloy-coated optical fiber. The results indicated that the measured strain repeatability was less than 500 μ? and the strain sensitivity was more than ?2 × 10^?3 pm/μ?, when the thickness of the film was less than 5 μm. The negative sign on the strain sensitivity indicated that the tensile strain in the film produced compressive strain in the core of the optical fiber. The FBG sensor system has high test speed, and integrates measurement and signal transmission. This method provides an effective and convenient approach to measure stress in a film deposited on a cylindrical surface.     

Two new optical techniques to measure strain

A grating engraved on the surface to be analyzed is utilized to measure strain. The grating is illuminated by a monochromatic, plane wavefront. A lens produces the diffraction spectrum of the grating, and an opaque screen is located in the plane of the spectrum. A window allows a single diffraction order to go through the screen. Two techniques are presented. In the point-by-point technique, the illuminating wavefront is reduced to a very small area. Behind the window a light sensor detects the changes of light intensity that are produced by loading the specimen. In the field technique, an image of the specimen is produced, and the light sensor is located in the image plane. In both cases, changes of light intensity are related to strains. Using crossed gratings, a rosette strain gage is obtained. Examples of application of both techniques are presented, showing a very good agreement between the strains measured by the proposed methods and by independent means.     

Reliability assessment of a bi-material notch: Strain energy density factor approach

Joints of different materials have many applications in structural engineering and microelectronics. In the present contribution the joint is modelled as a bi-material notch. The singular stress field near the notch tip is investigated. Depending on the notch geometry and materials, the stress field can have one or two singularities. It is shown that to study the problem of a crack onset at the notch, both terms have to be taken into account. Criteria for the direction and for crack nucleation are formulated. The approach utilizes the knowledge of the strain energy density factor distribution in a bi-material notch vicinity.     

Uniaxial material damping measurements using a fiber optic lattice: A discussion of its performance envelope

Damping is the internal transfer of kinetic energy to other forms of energy. Today, most methods use either bending or torsional vibration to measure damping. This means that the strain field in the specimen is nonhomogeneous. If the damping of the tested material is linear, strain-independent, the values acquired with these traditional methods will be equal to the intrinsic material damping of the material. If, however, the damping is strain-dependent, nonlinear, the measured value will be an average of the damping of the specimen, and not equal to its intrinsic material damping. To address this problem, a method is required to experimentally determine the damping in uniaxial tension in order to produce the same strain level in all parts of the test specimen and hence obtain a measurement of the intrinsic material damping. Using such a method, it is possible to view the material damping as the phase angle between the stress and the strain in a harmonic oscillation. In this paper, a method is suggested for measuring this phase shift in uniaxial tension to determine the material damping properties. It uses a tensile test machine, an optical fiber Bragg grating technique and a lock-in amplifier. Measurements with the phase shift technique have been suggested previously, but its performance envelope has been overestimated. In this paper, the performance envelope is discussed and restricted. It is shown that the envelope depends on the specimen length, loss factor and test frequency. An optical strain measurement method is also believed to help avoid many electrical measurement problems seen with the originally proposed method.     

Plated and Intact Femur Strains in Fracture Fixation Using Fiber Bragg Gratings and Strain Gauges

This paper presents an experimental methodology to determine plated and intact femur strains using fiber Bragg gratings and strain gauges. A plated and an intact synthetic femur were used and loaded under a simplistic static load of 600 N. A stainless steel (316L) plate was used to fixate a simulated 45° fracture on one femur. Strains were recoded at the same sites on both femurs. Strain shielding is shown to be more pronounced at the distal region of the plated femur. The experimental methodology based on fiber Bragg grating sensors is a novel approach to assess bone plate strains, which could also be used to obtain biologic tissue and implant surface strains in locations where conventional strain gauge use is not technically feasible.     

Strain gage method for determining stress intensities of sharp-notched strips

An efficient and simple strain gage method for determining the stress intensities of sharp-notched strips is proposed. The bisector of the notch angle is inclined to the edge so that the mixed-mode loading is created simultaneously at the notch tip. A theory of determining the stress intensities using strain gages is described on the basis of the two-dimensional theory of elasticity. Experiments on specimens with various notch shapes are carried out to verify the theoretical results. Experimental results are in good agreement with theoretical results.     

Scanning moiré at high magnification using optical methods

Methods of employing scanning moiré at high magnification are developed and demonstrated. Modern lithographic techniques for producing custom moiré gratings with a frequency up to 250l/mm are described. On a probing station equipped with a video system, pseudo-color moiré fringes are produced using the scannning lines of the color charge-coupled-device (CCD) camera. Fringe multiplication from 1 to 5 is possible with correct combinations of magnification and grating pitch. An analysis is given to show that strain sensitivity depends only on the number of scanning lines used to record the image. The grating pitch and the magnification are important because they reduce the gage length of the strain measurement. The high-magnification scanning moiré was used to study plastic- strain fields in an aluminum tensile specimen. Local disturbances in the strain field were observed at 2 to 2.5 percent applied strain. These discontinuities became more significant at higher levels of applied strain.     

Use of Spectral Conditions to Separate Strain and Temperature Effects in Fibre Bragg Grating Sensors Embedded in Load-Carrying Anisotropic Laminates

This work presents a further development of the methods of simultaneous determination of temperature and axial strain using a single fibre Bragg grating (FBG). The reflected spectrum of composite-embedded FBG sensors has been analyzed in order to separate temperature and load effects. We found out that during the curing process of the laminates, a superstructure has been introduced on the FBG. Analyzing this effect, a temperature and strain separation was implemented by simply calculating and comparing the integrated intensity of the spectral response signal. A mathematical four-parametric model has been developed to calculate the reflected spectrum of a superstructured fibre Bragg grating. The mathematically achieved data has been evaluated with experimentally determined data from fibre Bragg gratings embedded in glass-fibre reinforced composite materials.