Advances in Strain Gauge Measurement on Composite Materials

Abstract: This article gives an overview on the application of strain gauge techniques to the analysis of the strains in composite materials. The orthotropic behaviour of the composite influences the performance of strain gauges that are calibrated for use on isotropic materials. The article considers therefore the typical topics of the strain gauge technology applied to composites with particular reference to the compensation of thermal output, the measurement of the coefficients of thermal expansion, the determination of the strain and stress state, the influence of the misalignment error, the reinforcement effect, the determination of the stress intensification factor, the analysis of residual stresses by the hole drilling method and the effect of transverse sensitivity on the measurement of strains along the fibres.     

Ring gauge for biaxial strain analysis

The ring gauge performs the same function as a strain gauge rosette by providing three independent signals from which may be deduced the three unknowns in a biaxial strain system, viz. the magnitudes of the principal strains and the directions of the principal axes relative to a datum direction. It is analogous to a delta rosette but possesses advantages over the usual method of cementing three gauges to the surface of the material.     

Computer aided analysis of strain rosette data

In this paper a computer program has been developed for analysing the strain gauge rosettes by considering the transverse sensitivity of all gauges. The program is capable of calculating principal strains, maximum shear strain, principal stresses, maximum shear stress and principal directions from the data obtained by using strain gauge rosettes of various configurations. The gauge factor and transverse sensitivity of all gauges in the rosette must be the same.     

Two analogous methods for estimating the compressive strength of fibrous composites

In this paper, an analogy is made between the solution of micro-buckling of fibrous composites using a three-dimensional model and that of biaxial bending of reinforced concrete short columns. Two approaches are used; the first one uses a reciprocal formula and the second one uses a bilinear approximation to the non-dimensional stresses interaction equation, to estimate the compressive stress in a fibrous composite. The initial misalignment angles of composite fibers, which are the main parameters in the determination of the compressive strength of fibrous composites, are analogous to load eccentricities in concrete columns. The initial misalignment angles in both directions perpendicular to the axis of the fibers are defined by sinusoidal curves. The compressive strength of different fibrous composites, which also depends on the nonlinear shear stress–strain relationship of the matrix material, is estimated using the present approaches. The results obtained in this study agree well with experimental and analytical results available in the literature.     

光纤缠绕式应变传感器

研究了一种可用于机敏复合材料与结构状态监测的本征型强度调制光纤应变传感器,它由两根以上多模光纤相互缠绕绞合形成。分析了该传感器的应变传感原理,得到其既能测量拉应变、又能测量压应变的结论。传感器对应变的响应具有良好的线性和重复性,灵敏度高,无迟滞现象。对植入碳纤维/环氧复合材料内的光纤缠绕型应变传感器的实验结果与理论分析一致,表明该传感器是适合于机敏复合材料与结构状态监测的较为理想的光纤传感器。     

Optimum location of a three strain gauge rosette for measuring mixed mode stress intensity factors

This paper analyzes the errors inherent to the determination of mixed mode stress intensity factors from data obtained by using a three strain gauge rosette. The analysis shows that the errors are mainly due the third characteristic value (3/2) and its corresponding coefficients. It is also shown that the errors do not depend on the orientation angle of the rosette, the angle between the strain gauges and the material properties. The error mainly depends on its location (radius, angle), being linear in the radius. For pure mode I, an angle of 90° will completely eliminate the error due to the angle, while for pure mode II, a 0° angle will minimize it. The normalized variation of the errors with the angle at any radius is shown for different ratios of the corresponding coefficients of the third characteristic value. The analytical results are applied to a numerical example of an edge crack subjected to mixed mode loading. From the numerical example, it is recommended to use two strain gauge rosettes at the same angle, and linearly extrapolate their results, if errors less than 15% for a mixed mode field are desired.     

Direct measurements of non-linear stress-strain curves and elastic properties of metal matrix composite sandwich beams with any core material

A theory for measuring non-linear stress-strain curves and elastic properties of metal matrix composite (MMC) sandwich beams subjected to pure bending loads is discussed. The beam is made from any core material sandwiched between an upper facing of unreinforced metal and a lower facing of MMC with unidirectional fibre reinforcement or vice versa. The model developed shows that the determination of the position of the neutral axis is critical to the measurements discussed in this paper. The analysis removes the restriction of the effects of the core. With the aid of this model, we show that the position of the neutral axis can be determined directly from surface strain measurements. Measurements of neutral axis position lead directly to the determination of the beam elastic properties and, thus, directly obtained from surface strain measurements. It is shown that the model predicts longitudinal stresses and strains within any layer of the beam. The analysis includes the limiting case of a very weak core material. A consequence of this model is the determination of the MMC facing fibre volume fraction. A detailed error analysis predicts that the longitudinal elastic modulus of an MMC material facing can be obtained with an uncertainty between 4 and 6% if the surface strain measurements and beam dimensions can be obtained with an uncertainty of 1%. The volume fraction can be obtained within 10% uncertainty, although better methods are available for that measurement.     

光弹性复合材料应变-光定律研究

本文在考察Agawal近似应变——光定律的基础上,提出了新的近似应变——光定律.它克服了Agawal近似应变——光定律当主应变分向靠近材料主方向时产生较大误差的弊病,提高了复合材料光弹性近似分析的精度,为复合材料正变异性光弹性分析的工程应用奠定了基础.     

A micromechanical characterization of angular bidirectional fibrous composites

A micromechanical numerical algorithm to efficiently determine the homogenized elastic properties of bidirectional fibrous composites is presented. A repeating unit cell (RUC) based on a pre-determined bidirectional fiber packing is assumed to represent the microstructure of the composite. For angular bidirectional fiber distribution, the symmetry lines define a parallelepiped unit cell, representing the periodic microstructure of an angular bidirectional fiber composite. The lines of symmetry extrude a volume to capture a three dimensional unit cell. Finite element analysis of this unit cell under six possible independent loading conditions is carried out to study and quantify the homogenized mechanical property of the cell. A volume averaging scheme is implemented to determine the average response as a function of loading in terms of stresses and strains. The individual elastic properties of the constituents’ materials, as well as, the composite can be assumed to be completely isotropic to completely anisotropic. The output of the analysis can determine this degree. The logic behind the selection of the unit cell and the implementation of the periodic boundary conditions as well as the constraints are presented. To verify this micromechanics algorithm, the results for four composites are presented. The results in this paper are mainly focused on the impact of the fiber cross angles on the stiffness properties of the composites chosen. The accuracy of the results from this micromechanics modeling procedure has been compared with the stiffness/compliance solutions from lamination theory. The methodology is to be accurate and efficient to the extent that periodicity of the composite material is maintained. In addition, the results will show the impact of fiber volume fraction on the material properties of the composite. This micromechanics tool could make a powerful viable algorithm for determination of many linear as well as nonlinear properties in continuum mechanics material characterization and analysis.     

ON A GENERAL METHOD OF COMPENSATION IN STRAIN GAUGE WORK

If gauges or rosettes identical with those used in testing are affixed to a compensating bar under known stresses and of the same material as the test piece, the required stresses are obtained directly in terms of the known compensating stress and of the measured resistance changes. Cross-sensitivity, gauge factor and constants of elasticity of the test piece cancel out and errors due to inaccurate assumptions for their values are avoided. If the test strains, elastic or non-elastic, are required and the elastic compensating strain is known, Poisson's ratio of the compensator enters into the evaluation. A region of the test piece where stresses or strains are known may serve as a compensator.
One compensating rosette or two single compensating gauges suffice for any number of identical testing gauges. Initial zero balance may not always be needed and special circuits facilitate evaluation, which lends itself to simple self-contained automation. An analogue unit suggested for incorporation in a strain meter allows direct display of principal stresses and directions from rosette measurements.     

Strain Measurement on Composites: Effects due to Strain Gauge Misalignment

Abstract: The present work analyses the errors affecting the strains measured by misaligned strain gauges installed on orthotropic‐composite laminae. Various analytical relationships are derived showing that, besides the fibre and strain gauge orientations, the misalignment error in unidirectional off‐axis orthotropic composite samples depends also on the lamina stiffness properties (E₁, E₂, ν₁₂, G₁₂). If the fibres are aligned with the loading axis, it is found that the higher Poisson's ratio ν₁₂ is the only elastic property influencing the misalignment error. Experimental results are shown confirming the theoretical predictions.     

Approximate elastic-plastic analysis of the static and impact behaviour of polymer composite sandwich beams

An elastic-plastic beam bending model has been developed to simulate the post-upper skin failure energy absorption behaviour of polymer composite sandwich beams under three-point bending. The beam skins consist of woven and chopped strand glass, while the core is a resin impregnated non-woven polyester material known as Coremat. A polyester resin was used for the construction. The theoretical model consists of a central hinge dominated by a crushing core and tensile elastic strains in the lower skin. Experimental measurements of the non-linear force-deflection characteristics for the beam are compared to the theoretical predictions from the model, and it is shown that the shear crushing of the core has an important effect on the behaviour of the beam. The model shows that the most important material properties are the lower skin tensile failure strain and the core crushing strength. Dynamic effects are included in the model in the form of a strain rate dependence of the core crushing stress and the strain rate dependence of the failure strain in the lower skin. The increase in material strength with strain rate gives rise to an improved energy absorption capacity for the beam under impact loading.     

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

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

Two FORTRAN programs for rosette calculations

These programs calculate principal stresses, strains and directions from any rosette readings. The appropriate values are read in, the angles placed in the range 0 to 180° and the strains arranged in descending order. Next the necessary quantities are calculated and checked; a choice of output formats is provided together with an error message and diagnostic information if the check fails. One of the programs is written to accept strain readings on punched cards, the other accepts voltage readings on paper tape from a data logger. The programming language is FORTRAN IV. The programs have been used on an ICL 1903A computer.     

Strain gauge readings on a programmable pocket calculator

Programs and command instructions are described for three readily available and established programmable pocket calculators which are an aid to the reduction of readings for rosette strain gauges both into principal strains and stresses, and also to the corresponding maximum shear stresses.     

The effect of fibre misalignment on the compressive strength of unidirectional carbon fibre/epoxy

The effect of a misalignment angle between the fibres and loading axis of a unidirectional composite is analysed by considering the shear strains induced by the misalignment. It is shown that shear instability in the matrix drastically reduces the predicted compressive strength even for very small misalignments. The same trend is predicted for composites with initial fibre curvatures due to the misalignment angle associated with the curvature. The reduction in compressive strength often attributed to initial fibre curvature may therefore actually be due to fibre misalignment angles. Small misalignments are hard to avoid during the manufacture and testing of unidirectional composites and so these results cast serious doubts on the possibility of measuring a true ultimate compressive strength for this kind of material.     

A Comparison of Various Patterns of Three‐Dimensional Strain Rosettes

Abstract: The strain tensor, principal strains and precision of the estimates of these values are derived for a range of different layouts of three‐dimensional strain rosettes. These values are based on the Monte Carlo technique applied to experimental work which was carried out on transducers tested in different laboratories. The estimates of precision are determined theoretically and compared with results based on experimental findings. A new design of a miniature tri‐rectangular tetrahedral rosette was manufactured and tested. Results suggest that this transducer does not perform as well as the rectangular patterns.     

Establishing a new Forming Limit Curve for a flax fibre reinforced polypropylene composite through stretch forming experiments

In developing an understanding of the failure in natural fibre reinforced polymer composites, the failure limits of this class of the material system are required. It is found that the conventional Forming Limit Curve is not suitable to predict the failure initiated in the natural fibre composite as principal strains cannot differentiate the strain on the flax fibres and the polypropylene matrix. This study proposes a new Forming Limit Curve for the composite which expresses limiting fibre strain as a function of forming mode depicted by the ratio of minor strain to major strain. The new Forming Limit Curve, along with the Maximum Strain failure criterion have been successfully implemented in FEA simulations, and numerical simulations suggest that the former is more accurate. The current work provides an innovative method to predict the onset of failure in natural fibre composites, which can be applied in composite forming and structural design.     

State-of-strain evaluation with fiber Bragg grating rosettes: application to discrimination between strain and temperature effects in fiber sensors

An optical rosette that incorporates fiber Bragg gratings as strain gauges has been designed, fabricated, and tested. We investigated it by measuring the state of strain of a thin plate as the test structure submitted to an increasing load in a four-point bending configuration and for various angular orientations. This device has also been successfully investigated as a self-temperature-compensated in situ uniaxial strain sensor without any angular dependence and with high accuracy in recovery analysis, leading us to expect many industrial applications. Printed circuit processes or integrated optics on polymers would provide a means for accuracy, reproducibility, and integration in a mass-produced process.     

Random errors caused by temperature in magnitude of principal strains evaluated ith 3-element strain gauge rosettes

The effects of the uncertainties associated ith the apparent strain and gauge factor data, given by the manufacturer, in the evaluation of principal strains are examined. Principal strains are obtained by a reduction of the strains measured ith electrical resistance strain gauge rectangular or delta rosettes. The theoretical analysis points out the relevance of the effects caused.