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Utilized fiber optic chords to measure strain in composite material and derive mechanical properties while validating the feasibility of the fiber optic sensors.
Cross-flow turbines (CFTs) are inherently unsteady devices with regards to operating principle and loading. By improving our understanding of the dynamic loading on these turbines, we hope to better inform CFT design, improve survivability, and reduce overall costs. The University of New Hampshire (UNH) and the National Renewable Energy Laboratory (NREL) collaborated on a project to instrument and test a four-bladed New Energy Corp. vertical axis cross-flow turbine in a real tidal flow. One blade from the 3.2 m diameter x 1.7 m height turbine was instrumented with eight full-bridge strain gauges along the span of the blade. The turbine was then deployed at the UNH-Atlantic Marine Energy Center (AMEC) Tidal Energy Test Site in Portsmouth, NH. Time-synchronized measurements of blade strain, inflow, thrust, rotational speed, and electrical output were obtained to characterize blade loading under various conditions. The blade strain was examined to assess the dynamic loading and conduct a fatigue analysis on the device.
Pumping tests with sinusoidal variation in pumping rate have been proposed as a method for improving aquifer characterization. These tests can interrogate a larger aquifer volume than slug tests and they can be more sensitive to small variations in drawdown. Current methods of using sinusoidal variations of rate are based on measuring pressure signals from the reservoir or aquifer, which requires access to monitoring wells. An alternative approach has been developed that measures the strain in the vadose zone instead of pressure in the reservoir. An instrument has been developed at Clemson University that can measure small strains using optical fiber sensors, and we propose that it can be used to measure strain during sinusoidal pumping tests. The objective of this project is to evaluate the feasibility of measuring and interpreting the vertical strain in the vadose zone generated during a sinusoidal rate pumping tests to estimate aquifer and/or overburden properties. Pumping tests were performed at a site with a water table at 9 m and saturated saprolite from 9 to 30m depth. Sinusoidal pumping tests in the saprolite used different pumping amplitudes and periods while pressure was measured at three piezometers and vertical strain was measured in the vadose zone from 1 to 7 m depth. The delay time of the pressure increased linearly with distance, and it increased with the square root of the period, while the amplitude of the pressure decreased with distance and increased with amplitude. Vertical strain in the vadose zone varied with the same period as the pumping rate and the delay times were similar to those for pressures measured at similar radial distances. Delay times for the strain increased with an increasing propagation of the strain field. The hydraulic diffusivity was estimated using delay times for pressure and strain, and the results were compared with the values estimated from a constant-rate pumping test. The hydraulic diffusivity from the constant rate test was 0.039 m2/sec, whereas it was 0.053 (±0.05) m2/sec and 0.035 (±0.03) m2/sec from the pressure data and 0.08 (±0.022) m2/sec and 0.035 (±0.001) m2/sec from the strain data from sinusoidal tests of various periods and amplitudes. There is no statistical difference among these values. This study indicates that strain measurements in the vadose zone can be used to estimate aquifer properties during sinusoidal pumping tests.
We describe an upgraded fiber-optic sensor system and its performance in measuring the dynamic strains in a mercury target of the Spallation Neutron Source (SNS). Strains result from dynamic pressure waves in the stainless-steel mercury target induced by short (~700 ns), intense (up to 23.3 kJ), high-energy (~1 GeV) proton pulses. In the upgraded sensor system, the output of each sensor head is interrogated with a compact, all-fiber based Faraday Michelson interferometer, which generates interference signals with a steady phase shift. Strain waveforms are recovered from the phase-shifted interference signals using a high-speed digital signal processing procedure developed in our previous work. We demonstrate successful measurements of dynamic strain pulses, e.g., 400με over 190μs , on a recently installed SNS target using the upgraded sensor system. The measured strain waveforms are analyzed for more than 20 sensor locations and/or orientations, and provide information regarding the temporal structure of strain profiles and dependence of the strain magnitude on the proton powers of 200 – 1400 kW. The new interrogator also measures the radiation-induced-attenuation (RIA) in the optical fiber, enabling experimental investigations of RIA profiles induced by a 700-ns radiation pulse. The radiation effects on the strain measurement performance are discussed over a radiation dose range of up to 4×10 8 Gy and an RIA compensation method is proposed. The measurements allow insight into the response of this unique piece of equipment and can be used for validation of simulations.
When calculating residual strain via neutron or X-ray diffraction, uncertainties propagated from the peak fit are often inadequate to describe the true scatter of measurements about a singular strain state, such as one that should describe a macroscopic continuum. Because diffraction is inherently a selective process, orientation-dependent scatter arises from the sub-sampling of strong microstructure and strain gradients. This paper investigates the appropriateness of propagated uncertainties with reference to their original intention, i.e. noise about a mean value. Thirty-six unique orientations of strain measurements are taken at multiple locations within an additive friction-stir deposition component with fine-scale gradients (∼200 µm) of plastic strain, texture and residual elastic strain. Multiple strain and stress calculation pathways are compared: direct substitution of three measurements into Hooke's law, direct inversion of any six unique orientations into the strain state tensor and thirty-six measurement least-squares estimation. For the last two cases, the appropriateness of the uncertainty interval is statistically evaluated on the basis of a physical constraint: common agreement under the strain transformation law. For this sample, the direct inversion of six measurements retains a conservative estimate of the uncertainty. However, propagated uncertainties in the least-squares solution greatly underestimate the true experimental scatter. A simple pathway to estimate appropriate uncertainty intervals is suggested. These results demonstrate that the interpretation of uncertainty in residual strain is strongly dependent on intrinsic sample-dependent effects, and that oversampling orientations and statistical analysis can give more accurate results with realistic uncertainties.
This article demonstrates high-frequency dynamic strain measurements using fiber Bragg grating (FBG) sensors embedded in metal parts. Using an ultrasonic additive manufacturing (UAM) process, FBGs inscribed in polyimide coated optical fibers were embedded in aluminum parts. An electromagnetic shaker was used to exert dynamic events on the embedded FBG sensors with frequencies from 1 to 10 kHz. The high-speed interrogation of FBG sensors was accomplished using a tunable vertical-cavity surface-emitting laser (VCSEL) and a high-speed interrogation system sampling at 120 kHz. The strain response measured by the FBG sensors was compared with real-time measurements using a laser velocimeter. A finite-element analysis (FEA) was performed to simulate responses to both static strain and high-frequency dynamic strain. In conclusion, results show that strains as small as 2.5$με$ can be resolved at frequencies up to 10 kHz.
Strains occur at shallow depths in response to pressure changes during well tests in an underlying aquifer, and recent developments in instrumentation have made it feasible to measure essentially the full strain tensor. Simulations using poroelastic analyses indicate that shallow normal strains are approximately proportional to the logarithm of time when a well is injecting into or pumping from a deep aquifer or reservoir. The drawdown is also a linear function of log time, as shown by the classic Cooper-Jacob type-curve analysis. The time when the semilog straight line intercepts the zero-strain axis is similar to the time determined from the Cooper-Jacob pressure analysis, and it can be used to estimate hydraulic diffusivity, suggesting that horizontal strain data can be used directly to estimate aquifer properties. This approach was validated using measurements from shallow (30-m deep) borehole strainmeters during an injection test at a 530-m-deep sandstone aquifer/reservoir in Oklahoma. The results show intercept times for the shallow normal strain data are essentially the same as for deep pressure data from an equivalent radial distance. The slopes of the semilog plots of the pressure and the strain increase at the same time, suggesting that they both respond to a lateral aquifer boundary. Significantly, though, strain was measured at shallow depths while the pressure data were measured at 530-m depth. This suggests that strain data from shallow depths could be an effective way to improve the characterization of an underlying aquifer.
We report thermographic phosphors (TP) are combined with stereo digital image correlation (DIC) in a novel diagnostic, TP + DIC, to measure full-field surface strains and temperatures simultaneously. The TP + DIC method is presented, including corrections for nonlinear CMOS camera detectors and generation of pixel-wise calibration curves to relate the known temperature to the ratio of pixel intensities between two distinct wavelength bands. Additionally, DIC is employed not only for strain measurements but also for accurate image registration between the two cameras for the two-colour ratio method approach of phosphoric thermography. TP + DIC is applied to characterize the thermo-mechanical response of 304L stainless steel dog bones during tensile testing at different strain rates. The dog bones are patterned for DIC with Mg 3 F 2 GeO 4 :Mn (MFG) via aerosol deposition through a shadow mask. Temperatures up to 425°K (150°C) and strains up to 1.0 mm/mm are measured in the localized necking region, with conservative noise levels of 10°K and 0.01 mm/mm or less. Finally, TP + DIC is compared to the more established method of combining infrared (IR) thermography with DIC (IR + DIC), with results agreeing favourably. Three topics of continued research are identified, including cracking of the aerosol-deposited phosphor DIC features, incomplete illumination for pixels on the border of the phosphor features, and phosphor emission evolution as a function of applied substrate strain. This work demonstrates the combination of phosphor thermography and DIC and lays the foundation for further development of TP + DIC for testing in combined thermo-mechancial environments.
Critical state and continuum plasticity theories have been used in research and engineering practice in soil and rock mechanics for decades. These theories rely on postulated relationships between material stresses and strains. Some classical postulates include coaxiality between stress and strain rates, stress–dilatancy relationships, and kinematic assumptions in shear bands. Although numerical and experimental data have quantified the strains and grain kinematics in such experiments, little data quantifying grain stresses are available. Here, we report the first-known grain stress and local strain measurements in triaxial compression tests on synthetic quartz sands using synchrotron X-ray tomography and 3D X-ray diffraction. We use these data to examine the micromechanics of shear banding, with a focus on coaxiality, stress-dilatancy, and kinematics within bands. Our results indicate the following: 1) elevated deviatoric stress, strain, and stress ratios in shear bands throughout experiments; 2) coaxial principal compressive stresses and strains throughout samples; 3) significant contraction along shear bands; 4) vanishing volumetric strain but nonvanishing stress fluctuations throughout samples at all stages of deformation. Our results provide some of the first-known in situ stress and strain measurements able to aid in critically evaluating postulates employed in continuum plasticity and strain localization theories for sands.
Fracture injection/shut-in tests are commonly used to measure the state of stress. Injection creates a hydraulic fracture (or in some cases, opens a preexisting fracture), and then the pressure after shut-in is monitored to identify fracture closure. Different interpretation procedures have been proposed for estimating closure, and the procedures sometimes yield significantly different results. In this study, direct, in-situ strain measurements are used to observe fracture reopening and closure. The tests were performed as part of the EGS Collab project, a mesoscale project performed at 1.25 and 1.5 km depth at the Sanford Underground Research Facility. The tests were instrumented with the SIMFIP tool, a double-packer probe with a high-resolution three-dimensional borehole displacement sensor. The measurements provide a direct observation of the fracture closure signature, enabling a high-fidelity estimate of the fracture closure stress (ie, the normal stress on the fracture). In two of the four tests, injection created an opening mode fracture, and so the closure stress can be interpreted as the minimum principal stress. In the other two tests, injection probably opened preexisting natural fractures, and so the closure stress can be interpreted as the normal stress on the fractures. The strain measurements are compared against different proposed methods for estimating closure stress from pressure transients. The shut-in transients are analyzed with two techniques that are widely used in the field of petroleum engineering – the ‘tangent’ method and the ‘compliance’ method. In three of the four tests, the tangent method significantly underestimates the closure stress. The compliance method is reasonably accurate in all four tests. Closure stress is also interpreted using two other commonly-used methods – ‘first deviation from linearity’ and the method of Hayashi and Haimson. In comparison with the SIMFIP data, these methods tend to overestimate the closure stress, evidently because they identify closure from early-time transient effects, such as near-wellbore tortuosity. In two of the tests, microseismic imaging provides an independent estimate of the size of the fracture created by injection. When combined with a simple mass balance calculation, the SIMFIP stress measurements yield predictions of fracture size that are reasonably consistent with the estimates from microseismic. In conclusion, the calculations imply an apparent fracture toughness 2-3x higher than typical laboratory-derived values.
The goal of this project was to develop and demonstrate robust instrumentation to monitor the in-situ strain tensor in order to improve the reliability and security of CO 2 storage in geologic formations. We met the original goals of the project and the major overarching accomplishment is the advancement of strain tensor monitoring from an intriguing concept to a commercially available technology with a solid foundation of novel instruments supported by theoretical analyses and validation experiments. The main accomplishments of the project are summarized below. We designed, built and evaluated nine new optical fiber strainmeters and tiltmeters using Michelson interferometers to measure deformation with ultra-high resolution at both shallow and deep point locations in the subsurface. These are the robust strainmeters that motivated the title of the project. We designed, built and evaluated a novel method of measuring distributed strain in optical fibers with nanostrain resolution, and cm-scale location, and sampling into the seismic band. The new method is called Coherence-length-gated Microwave Photonics Interfereometry (CMPI). CMPI technology has advantages over existing commercial DAS and DSS methods. We developed and demonstrated capabilities to deploy instruments in the field and used them to measure strain caused by ambient signals like barometric pressure and tides, as well as induced signals like surface loading and pore pressure changes from pumping tests. We deployed a working strainmeter at 1,700 ft depth, slightly above an active reservoir. This is to our knowledge the greatest depth a strainmeter has been deployed and the techniques we used can readily be extended to greater depths. Optical fiber borehole tensor strainmeter techology was advanced from a TRL 4 at the start, to a TRL of 7 at the conclusion of the project. The project included advances in simulations and theoretical analyses. We developed and demonstrated a computational workflow that uses machine learning to reduce the computational requirements and make it practical to use Bayesian inversion to solve large numerical poroelastic analyses needed to interpret strain tensor field data. We evaluated the strain tensor fields and time series that would be caused by leaks of CO 2 or other fluids from reservoirs. These simulations demonstrated that signals from leaks could be measured with instruments developed for the project, opening a potentially new method for ensuring storage security. We showed that strains in caprock can be used to estimate pressure in a reservoir. This avoids the need to drill monitoring wells into the reservoir, and it expands the capabilities of monitoring in the caprock. The project includes a derivation and application of a novel analytical solution to the strains in the vicinity of a pressurized poroelastic inclusion. This solution explains field data measured during injeciton tests at the North Avant Field, and it will simplify future interpretation of strain tensor data. The project included a broad range of experiments, and of the most significant is the characterization of the strain tensor at an array three strainmeters during six injection tests at the North Avant Field, Oklahoma. This demonstrated repeatability of the strain signal measured by the new instruments developed for the project, and it showed similarities between the strain signal at shallow depths and pressure in the underlying reservoir. We also demonstrated that useful strain data can be measured at reservoir depths. This confirms that strain tensor data can be measured throughout the caprock over a reservoir. The project demonstrated the feasibility of using the strain tensor and distributed strain measured in caprock during a variety of different well tests where the pumping rate was constant, sinusoidal and positive, or a periodic square wave with zero net rate. This further strengthens the validity of using strain data to characterize reservoirs and aquifers. We also demonstrated that strain caused be fluctuations of air pressure and water pressure in the vadose zone can be measured and interpreted, suggesting that high resolution distributed strain measurements hold promise for monitoring the vadose zone. The project partially supported nine graduate students in the Environmental Engineering, Hydrogeology, Electrical Engineering programs at Clemson University. The research was described in nine journal papers, 23 talks and conference abstracts. Additional journal papers are in preparation. A new company called Tensora was started to provide strainmeter technology for commercial applications.
We discuss a simple statistical analysis which yields the precision, resolution, accuracy and trueness of diffraction-based lattice strain measurements. The procedure consists of measuring the thermal expansion induced in each component of an ideal, non-reacting, two-component, crystalline powder sample in situ. One component, with a high coefficient of thermal expansion (CTE), serves as an internal thermometer. The quantities of interest are obtained by determining the smallest, statistically significant, thermal lattice strain which can be detected through diffraction analysis in the second, low CTE, component in response to controlled temperature changes. This procedure also provides a robust check of the alignment of the diffraction system and is able to reveal the presence of systematic errors. The application of this technique to a time-of-flight engineering diffractometer/strain scanner is presented.
Background: Measuring the physical properties of shale is critical for optimizing engineering activities such as geothermal energy generation and hydraulic fracturing. Shale is a transversely isotropic material. Furthermore, this material can also include micro and macro cracks at different locations and orientations that cause it to behave differently under tensile or compressive loading. Objective: In this work, a combined experimental–numerical approach is proposed to evaluate the bi-modulus elastic properties of isotropic and transversely isotropic materials. Methods: Full-field strain measurements for a circular disk under diametral compression are integrated with a regression analysis technique to evaluate the elastic properties of bi-modulus materials subjected to tensile and compressive loads using two loading configurations on the same specimen. Digital Image Correlation (DIC) is used to measure the full-field strains. Subsequently, in the case of an isotropic material, a linear least-squares approach is utilized to process the experimentally determined strains in conjunction with analytical expressions of the stress fields (in terms of far-field loading) to determine the elastic modulus E, the shear modulus G, and the Poisson’s ratio $v$. In the case of a transversely isotopic material, such as shale, a finite element model is implemented to determine the stress fields (again in terms of far-field loading), which is followed by repeating the previous regression analysis in an iterative process to estimate the elastic parameters. Results: The results show that the proposed technique successfully provides a complete set of elastic properties as a function of both the loading condition and the principal material directions. The technique is validated by measurements on a known isotropic material and then applied to determine the properties of shale. Conclusion: In this work, the proposed approach is successfully used to calculate the bi-modulus elastic response of poly(methyl meth- acrylate) (PMMA) and shale. As expected, PMMA exhibits an isotropic response with no bi-modulus effect, however, shale exhibits both transverse isotropy and a bi-modulus effect. Therefore, this approach holds promise for investigating the elastic properties of materials like rocks and fiber-reinforced composite laminates as functions of the principal material directions and the loading conditions.
Dynamic elastic strain in ~1.8 and 1.0 m diameter containment vessels containing a high explosive detonation was measured using an array of fiber Bragg gratings. The all-optical method, called real-time localized strain measurement, recorded the strain for 10 ms after detonation with additional measurements being sequentially made at a rate of 1.7 MHz. A swept wavelength laser source provided the repetition rate necessary for such high-speed measurements while also providing enough signal strength and bandwidth to simultaneously measure 8 or more unique points on the vessel’s surface. The data presented here arethen compared with additional diagnostics consisting of a fast spectral interferometer and an optical backscatter reflectometer to show a comparison between the local and global changes in the vessel strain, both dynamically and statically to further characterize the performance of the localized strain measurement. The results are also compared with electrical resistive strain gauges and finite element analysis simulations.
Interpreting strain data measured during well testing requires inverting poroelastic forward models set up to represent an aquifer or reservoir. One approach is to use stochastic methods to conduct the inversion. Subsurface parameters such as elastic modulus, permeability, and geometry of heterogeneities are estimated by searching the parameter space. This is feasible, but cumbersome, requiring more than a week of computation using many hundreds of computer nodes in one of our earlier analyses. This motivated us to consider alternative methods, including an artificial neural network (ANN) as a surrogate model.
The nuclear industry is progressing toward microreactors that can be factory assembled and deployed to remote regions for reliable, scalable power generation. However, the reduced power output requires enhanced monitoring capabilities to reduce staffing and eventually move toward autonomous control to improve the economics of microreactors. The ability to embed sensors such as fiber-optics, which can provide spatially distributed temperature and strain measurements, within microreactor components for real-time health monitoring would be particularly advantageous. Recent advances in ultrasonic additive manufacturing (UAM) have demonstrated the successful embedding of fiber-optics in soft materials such as Al and Cu by placing the sensors in machined cavities and ultrasonically welding over the top with thin foils. This article reports the first successful embedment of fiber-optic sensors and thermocouples within a common nuclear reactor material, SS304, via UAM. UAM parameters were first explored with simple plate geometries before moving to more complex geometries, such as pipes and other test articles for heat pipe–based microreactors. Select samples were sectioned for microscopy to evaluate the sensor/foil and foil/foil interfaces from samples fabricated by using 100% SS304 foils vs. foils plated with a Ni coating to improve UAM bonding. Furthermore, embedding metal-coated, low-bend loss fibers resulted in greatly reduced signal attenuation and adequate compressive residual strain in the embedded region to ensure successful strain coupling. Pipe specimen functional testing was performed by monitoring temperature and strain during transient and steady-state thermal testing.
Open-water testing of marine renewable energy devices represents a significant milestone and hurdle for research teams and companies that seek to reduce the levelized cost of energy to allow these devices to compete in the open electrical generation market. For open-water testing of tidal energy converters (TECs), accurate measurements of loading characteristics on the blades and other structural components correlated with power performance metrics can be invaluable to further refine design principles and models, allowing continued improvement and cost reductions of new turbine designs. This paper will describe the modifications and additions made to a TEC system to achieve time-correlated blade strain measurements during full turbine operation along with a discussion on the overall impacts the required modifications had on the unmodified turbine.