The Reinforcement Effect of Strain Gauges Embedded in Low Modulus Materials

The reinforcement effect of electrical resistance strain gauges is well‐described in the literature, especially for strain gauges installed on surface. This paper considers the local reinforcement effect of strain gauges embedded within low Young modulus materials. In particular, by using a simple theoretical model, already used for strain gauges installed on the surface, it proposes a simple formula that allows the user to evaluate the local reinforcement effect of a generic strain gauge embedded on plastics, polymer composites, etc. The theoretical analysis has been integrated by numerical and experimental analyses, which confirmed the reliability of the proposed model.     

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.     

Assessment of strain gradients affecting the performance of 3-D strain rosettes – relevant to the analysis of cement mantle strains in total hip replacements

A large scale model analysis, using embedded strain gauges, of the strain distribution in the cement mantle surrounding a femoral prosthesis is underway. In order to predict, and so avoid, positions of locally high strain gradients in this model, a finite element and experimental analysis of a similar problem was undertaken. For this purpose, a loose fitting rectangular steel insert inside a surrounding rectangular epoxy sheath was used to model an extreme case of the torsional and bending components of hip joint load. The axial component of joint load was modelled using an axisymmetric finite element model of a tapered shaft. The finite element results were used to determine suitable positions for embedding gauges in the experimental model. Results showed that the finite element analysis failed to adequately model the close sliding fit between the steel insert and epoxy. Altering the experimental model to artificially replicate the finite element contact conditions produced good correlation in bending, with experimental strains agreeing with simple bending theory to within 6%. Satisfactory correlation under torsional loading was not obtained, but strain magnitudes were low. Predicted positions for embedding gauges give conservative results, lessening the possibility of strain gradient induced error in the large scale model test of the cement mantle and prosthesis.     

Embedded Strain Gauges: Effect of the Stress Normal to the Grid

Abstract:  In general, a strain gauge embedded in a model is subjected to a stress normal to the grid, whereas a gauge on the external surface is free from such a stress. This paper concerns the effect of the stress normal to the grid on the output of the strain gauge; usually, the influence of such a stress has a negligible effect, however, in some cases a notable influence has been noted. Therefore, the output of the strain gauge is determined in function of the strains in the plane of the gauge, ɛ _l and ɛ _t, and of the stress, σ _n, normal to the grid. The analysis shows that the output of the strain gauge is influenced by the coupled effect of transverse sensitivity and pressure sensitivity of the strain gauge. In particular, the analysis shows that, for Constantan gauges compensated for steel, the influence of the transverse sensitivity is in general prevailing on that one due to the pressure sensitivity. The results reported in this paper explain the experimental data obtained by various researchers.     

A Probabilistic Evaluation of the Least Squares Strain Tensor Derived from a Three-Dimensional Modular Strain Rosette Using the Monte-Carlo Technique

Abstract:  Strain gradients give rise to a number of problems in the field of embedded three-dimensional strain measurement. In order to avoid these problems a modular type three-dimensional strain rosette was embedded into known strain fields and the data from the individual gauges compared with theoretical predictions. Finally, the least squares strain tensor was predicted from experimental data analysed using the Monte-Carlo technique and the theoretical results forecast from finite element data taking into account the mechanical properties of the carrier, plug and prismatic bar. Some of the experimental results were found to correlate well with the theoretical values but some values in the least squares strain tensor, in particular under compression and torsional loading, departed considerably from the theoretical values. It was found that the effect of the measurement errors in the individual gauges combined with the matrix operations in the least squares strain tensor were responsible for biasing the resultant tensor data. However, the modular technique provided a solution to the problem of strain gradients.     

Stiffness and Reinforcement Effect of Electrical Resistance Strain Gauges

Abstract:  The increasing use of low-modulus materials, on which the reinforcement effect of the electrical resistance strain gauge is not negligible, has re-opened the research interest into this issue. This study deals with the evaluation of stiffness, and of the strain gauge Young's modulus involved in the estimation of both the global and the local reinforcement effect; the relationship between the strain gauge stiffness and the local reinforcement effect is also analysed. In particular, the experimental technique used to determine the stiffness of some commercial strain gauges is described. The results show that the strain gauge stiffness alone does not permit an accurate evaluation of the local reinforcement effect.     

Interlaminar Stress Determination in Carbon Fibre Epoxy Composites with the Embedded Strain Gauge Technique

Abstract: In order to determine interlaminar stresses, strain gauges have been embedded in carbon fibre/epoxy composites. Insulation problems occurring because of the electrical conductivity of the carbon fibres were successfully resolved with the help of special foils. Measurements on unidirectional and angle‐ply laminates were in good agreement with calculations based on the classical laminate theory. Moreover, the laminate strength was not significantly affected by the embedded strain gauges. The technique may also be applied to residual stress determination in composite components.     

Strain Measurement on Composites: Errors due to Rosette Misalignment

Abstract: Electrical resistance strain gauges are increasingly used for the determination of the strain field in composite components. The effect of the angular misalignment of a strain gauge rosette on the determination of the strains in a composite material is investigated in this paper. The theoretical analysis shows that the strain error along the principal material directions depends on the difference of principal strains, on the angular misalignment of the rosette and on the angle between the maximum principal strain and the fibre direction. The paper also shows experimental evidence for the theoretical analysis.     

A temperature calibration of a temperature/strain transducer based on two strain gauges

The operation of a temperature/strain transducer, called “duplex gauge”, based on two electrical resistance strain gauges, that are temperature compensated for use on materials with different coefficients of linear expansion, was briefly recalled. Three steel specimens were equipped with “duplex gauges” and were subjected to temperature variations and no external loads were applied. The chosen experimental setup (i) to measure the outputs of the gauge temperature compensated for steel and titanium silicate and (ii) to impose known temperature, assured good accuracy and precision in evaluation of the temperature calibration curve. The obtained results showed that the strain differences could be considered, at least for the experimental arrangement examined, a linear function of temperature over the range of 20 to over 140°C. The prepared calibration chart, that allows the correction of temperature induced apparent strain, will be used in future research when generic temperature and strain fields are applied to specimens.     

In‐Plane Heterostructures Enable Internal Stress Assisted Strain Engineering in 2D Materials

Conventional methods to induce strain in 2D materials can hardly catch up with the sharp increase in requirements to design specific strain forms, such as the pseudomagnetic field proposed in graphene, funnel effect of excitons in MoS₂, and also the inverse funnel effect reported in black phosphorus. Therefore, a long‐standing challenge in 2D materials strain engineering is to find a feasible scheme that can be used to design given strain forms. In this article, combining the ability of experimentally synthetizing in‐plane heterostructures and elegant Eshelby inclusion theory, the possibility of designing strain fields in 2D materials to manipulate physical properties, which is called internal stress assisted strain engineering, is theoretically demonstrated. Particularly, through changing the inclusion's size, the stress or strain gradient can be controlled precisely, which is never achieved. By taking advantage of it, the pseudomagnetic field as well as the funnel effect can be accurately designed, which opens an avenue to practical applications for strain engineering in 2D materials.     

A Three-Dimensional Strain Gradient Plasticity Analysis of Particle Size Effect in Composite Materials

Recent experiments on particle-reinforced metal-matrix composite materials have shown particle size effects. Small particles tend to give larger plastic work hardening than large particles at the same particle volume fraction. Prior models used to study the particle size effect are based on the strain gradient plasticity theories, and these models are mainly axisymmetric models with vanishing lateral stress tractions in order to represent the uniaxial tension condition. However, the prior results fall short to agree with the experimental data. A three-dimensional (3D) unit-cell model is adopted in the present study. The periodic boundary conditions are imposed for the 3D unit cell to ensure the compatibility of the unit cell before and after the deformation. The particles are elastic, while the metal matrix is elastic-plastic and is characterized by the conventional theory of mechanism-based strain gradient plasticity, which is established from the Taylor dislocation model but does not involve the higher-order stress. It is shown that the 3D unit-cell model with the periodic boundary conditions gives better agreements with the experimental data than the unit-cell model with the traction-free boundary conditions on the lateral surfaces.     

An Analysis of the Factors Influencing the Data Derived from a Plug Type Three-Dimensional Strain Rosette under Compression and Torsion

Abstract:  The embedding of three-dimensional strain rosettes embedded into epoxy models provides an experimental technique for analysing complex structures; however, this technique has been known to produce data that were difficult to explain in terms of their physical significance. To gain a greater insight into the behaviour of a three-dimensional strain rosette used in this way, a three-dimensional strain rosette was embedded into each of two separate prismatic bars of square cross-section and subjected to fundamental tests of compression and torsion in standard commercial testing machines. In initial tests on a bar containing a three-dimensional strain rosette (Bar A) the data derived from the individual gauges sometimes departed from the theoretical values by more that 30  μ e. After critical evaluation of the procedures used for making and testing Bar A, further tests were carried out on Bar B, which led to a reduction in the difference between theoretical and experimental data to 14  μ e, acceptable for most practical purposes. The use of square plugs containing three-dimensional strain rosettes which are embedded into square cavities in the model, and the measurement of the actual direction cosines of the gauges on the square plug prior to embedment is a distinct advantage over the use of cylindrical plugs. In addition, the use of testing machines with a fixed base as opposed to a floating lower platen is recommended.     

Strain measurement standards—an outline

Strain measurement techniques are being used more frequently today to check that manufactured components are at a safe stress level in service. Designers are also requiring strain gauge tests on prototypes to confirm that the theoretical calculations are realistic and designs are economic.
Against this background the measurement engineer finds himself under pressure to produce test results quickly and sometimes to justify them. Strain measurement standards would have an important role in convincing customers that tests have been carried out in an approved manner and could be the measurement engineer's defence in the case of disputed results.
A suggested range of standards and codes of practice is described, from the anticipated BSI Standard on Strain Gauge Calibration to a proposed standard on strain gauge application and possible specifications on instrumentation for static and dynamic measurement. The need for strain measurement technician training and possible participationin the National Testing Laboratory Accreditation Scheme, NATLAS, is also discussed.     

Strain gauges in a nuclear environment

A short review is presented of the different degradation mechanisms of strain gauges under ionizing radiation, corresponding to the different types of application in nuclear environments. The available experimental results are summarized. Particular attention is given to the assessment work still needed for small bonded gauges to be used in accurate force sensors for remotely controlled manipulators used in maintenance and refurbishing operations.     

Strain Measurement in a Shape Memory Alloy with Strain Gauges

Abstract:  The recovery of shape due to temperature-induced martensite to austenite phase transformation in shape memory alloys (SMA), such as nickel titanium alloys, has been investigated and utilised in applications for many years. One of the problems in incorporating SMA in host materials, such as composites, is the poor bonding characteristics of the SMA. A closely related problem in experiments is the measurement of strains in SMA specimens; as thin wires have been used in many of the experimental investigations, strains have been deduced from length measurements. In the current work, electrical resistance strain gauges have been bonded on SMA strips. Tensile strains up to 8% during tensile loading as well as compressive strains during strain recovery due to subsequent heating have been measured. Strains determined by other methods, such as extensometer and length measurements, are also reported and compared. The major contribution of this work is the successful bonding of strain gauges on SMA and the measurement of large strains (up to 8%).     

The role of strain measurement technology in structural evaluation

This paper describes the importance of structural evaluation to the process of design assessment and outlines the significant role played by strain measurement technology in extending the scope of strain history data collection and facilitating strain monitoring of full-scale structures in the laboratory. After some general discussion of the various models of structural behaviour, it then proceeds to give a brief historical account and outlines the principles of thermoelastic stress analysis (TSA). A general desciption is provided of a specific TSA technique namely Stress Pattern Analysis by Thermal Emission (SPATE).
Despite the level of innovation and development in strain measurement technology, the use of bonded strain gauge elements is still by far the most commonly used strain measurement and monitoring technique in structural evaluation work at NEL. The paper highlights several recent test programmes carried out at NEL in the form of case studies which demonstrate different aspects of measuring, monitoring and validation of this and other strain measurement techniques; and verification of analytical models.     

Experimental analysis of acrylic models

Strain gauge application has been used to study the mechanical behaviour of shell models. Application has been made directly to acrylic devices designed by means of the homeostatic model technique. The testing procedure of one such model made with the aim of assessing the anticipated membrane status is detailed. This has resulted in an interesting experience of strain gauge application to this type of material.     

Numerical approach of cyclic behaviour of 316LN stainless steel based on a polycrystal modelling including strain gradients

A non-local polycrystal approach, taking into account strain gradients, is proposed to simulate the 316LN stainless steel fatigue life curve in the hardening stage. Material parameters identification is performed on tensile curves corresponding to several 316LN polycrystals presenting different grain sizes. Applied to an actual 3D aggregate of 316LN stainless steel of 1200 grains, this model leads to an accurate prediction of cyclic curves. Geometrical Necessary Dislocation densities related to the computed strain gradient are added to the micro-plasticity laws. Compared to standard models, this model predicts a decrease of the local stresses as well as a grain size effect.     

Determination of thermal stress in concrete pavements by means of measurement of in-situ strains

A new method of determining the thermal stress of concrete pavement in-situ has been developed and applied to engineering practice with success. It consists of three parts:
1. A system of theorems was established on the basis of mathematical modelisation that both temperature and thermal strain were sine functions of t, the time of observation, owing to the daily fluctuations of temperature and consequently the corresponding thermal strain. It was found that there exist a time phase and an angle of axes rotation between temperature and thermal strain.
2. A bridge circuit with a strain block and specially designed equipment 'free body' was introduced. The strain transducer for every test point consists of one strain gauge in the strain block and one in the 'free body', the former is used as the active gauge in the bridge circuit and the latter as the dummy. A temperature probe of resistance type was inserted nearby each of the gauges. Arrangement of observations and procedure of the data treatment were stated.     

The development of a model for the investigation of stresses in the cement layer underlying a tibial plateau

Tibial component loosening is a major problem associated with knee prostheses. Tensile stresses in the brittle cement immediately below the tibial plateau are likely to influence loosening. To establish the stresses at selected sites in the cement layer, a large model of a tibial plateau, underlying cement and bone was constructed and three dimensional strain rosettes were embedded into it. The mechanical properties of the model materials were evaluated and compared with properties of an actual knee. The construction of the model is described and different methods for embedding the three dimensional strain rosettes into the cement are evaluated.