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Evaluation of the Thermo-Elastic Behavior of a High-alloyed Steel by Fourier Transformation based Lock-In-Thermography
... Such peaks are not eliminated by averaging over the ROI, as shown comparing Fig. 3e and f, and are affected by leakage. Only a few works in the literature have reported similar whole-spectrum analyses, among which the works of Urbanek and Bar, [27,28], where similar peaks have been observed and explained as caused by aliasing or vibrations from the testing rig. Fig.s 3c,f show the power spectrum of the average signal from the central rectangular area of the sample, marked in Fig. 3a. ...
A low-cost Thermoelastic Stress Analysis (TSA) experimental setup is proposed which uses an ordinary micro-bolometer and in-house developed signal processing scripts. The setup is evaluated by analysing the thermoelastic signal from a tensile and a SENT specimen made of stainless steel AISI 304L, and the bolometer performances are compared with those of a state of the art photon detector. Signal processing is based on off-line cross-correlation, using a self-reference signal which is retrieved from the acquired thermal data. Procedures are in particular developed to recognise, quantify and correct errors due to spectral leakage and loss of streamed frames. The thermoelastic signal amplitude/phase, the thermoelastic constant and the Mode I Stress Intensity Factor (SIF) from the bolometer and photonic cameras are evaluated considering the influence of loading frequency, sampling frequency, detector array sub-windowing and acquisition interval duration. A camera-specific linear calibration procedure is applied to correct the thermoelastic signal obtained with the bolometer. The procedure is extended to correct also SIF values, finding a good match with the SIFs obtained by the photon detector. An automatic iterative algorithm, based on the least square fitting of Williams’ series functions, is proposed to identify the crack tip position. An estimation of processing times of the developed signal processing scripts has been carried out, finding that a full crack characterisation (TSA maps, crack tip position, SIF) can be performed with a data acquisition time of 10-20 s, a post-processing time of less than 2 s and an overall hardware cost under 10 k€.
Fatigue damage onset involves a transformation of mechanical energy. This is in part spent into work of plastic deformation and fracture and in part transformed into heat. Therefore, different thermomechanical heat sources are activated during a fatigue loading cycle, resulting in a temperature modulation that can be characterized by its frequency content. Several studies have monitored the temperature on samples undergoing high-cycle fatigue, measuring specific thermomechanical metrics which could serve as indicators of damage evolution. The present work evaluates the harmonic content of temperature, to investigate its correlation with the material dissipation. The harmonic terms investigated are the amplitude and phase of temperature at the loading frequency (First Harmonic) and at twice the loading frequency (Second Harmonic). The paper reviews the mechanisms linking the evolution of heat dissipation to changes in these four parameters. The theoretical analysis is supported by an experimental campaign carried out on C45 steel tensile specimen subject to R=−1 and R=0.1 loading ratios. The harmonic metrics are evaluated analyzing both their spatially averaged value and their spatial dispersion, to check for the formation of localized heat dissipation zones in early fatigue life. The study shows that the phase of the Second Harmonic signal has a peculiar bimodal distribution that can be correlated to either a thermoelastic or dissipative prevailing effect. This behavior evolves towards a unimodal dissipative behavior when the load amplitude is increased, thus proposing the Second Harmonic phase parameter as an effective indicator for monitoring internal intrinsic dissipation in the material.
Active thermography NDT are full field, non contact techniques used on steel, composites and ceramics for defect and damage detection. In this paper, thermal parameters and material responses of samples are investigated quantitatively by means of theoretical and experimental approaches. Free material response to thermal loading is investigated for two classes of materials for structural applications: steel and ceramic.
During fatigue crack propagation experiments on a high alloyed steel under fully reversed loading conditions lock-in thermography measurements have been undertaken. The E-phase images of the thermography measurements were used to determine the size of the plastic zone. As expected, the measured plastic zone sizes are increasing with the stress intensity factor and were found to be independent of the crack length. Surprisingly a decrease of the crack propagation rate in experiments performed with a constant stress intensity (Kmax=const. and ⊗K=const.) was observed. With increasing crack length the thermographic measurements showed an increase of the dissipated energies measured in front of the crack tip. These increasing dissipated energies in front of the crack tip seem to be responsible for the decrease of the crack propagation rate. The energies dissipated in front of the crack tip don’t directly correspond with the size of the plastic zone.
The existence of two different definitions for total har-monic distortion (one in comparison to the fundamental and one in comparison to the signal's root mean square) might cause am-biguity and misinterpretation of measured data. The difference between those definitions is stressed out in this letter. It is sug-gested that total harmonic distortion measurements in the context of power systems should always adopt the first definition and never the second.
The existence of two different definitions for total harmonic distortion (one in comparison to the fundamental and one in comparison to the signal's root mean square) might cause ambiguity and misinterpretation of measured data. The difference between those definitions is stressed out in this letter. It is suggested that total harmonic distortion measurements in the context of power systems should always adopt the first definition and never the second.
Lock-in thermography measurements are influenced by rigid body motion of the specimen due to the mechanical loading. These motion affects asymmetries in the measured temperature fields in the vicinity of the crack. This effect can be eliminated by a motion compensation procedure. Unfortunately, the results of the lock-in thermography are affected by this procedure, too. In this work the influence of the motion compensation procedure on fatigue crack propagation experiments, its gains and disadvantages are studied in a qualitative and quantitative manner. A new method for an automatic determination of the crack length in thermographic measurements is introduced and compared with potential drop measurements. Beside the known thermoelastic and dissipative effects, higher harmonic responses in the discrete Fourier transformation are analyzed and discussed.
Sir Humphrey Davy, by his experiment of melting two pieces of ice by rubbing them together, established the following proposition:—“The phenomena of repulsion are not dependent on a peculiar elastic fluid for their existence, or caloric does not exist.” And he concludes that heat consists of a motion excited among the particles of bodies. “To distinguish this motion from others, and to signify the cause of our sensation of heat,” and of the expansion or expansive pressure produced in matter by heat, “the name repulsive motion has been adopted.”
Thermoelastic Stress Analysis (TSA) is based on the principle that under adiabatic and reversible conditions, a cyclically loaded structure experiences temperature variations that are proportional to the sum of the principal stresses. These temperature variations may be measured using a sensitive infra-red detector and thus the cyclic stress field on the surface of the structure may be obtained. In order to achieve the adiabatic and reversible conditions, the test specimen must be cyclically loaded at a high enough frequency to prevent heat transfer, which is not only dependent of the loading frequency, but also stress gradients in the specimen and the thermal conductivity of the material. TSA has been found to be an ideal method to study crack tip strain fields, due to its non-contacting, full-field, data collection capabilities, however the adiabatic assumption breaks down close to the crack tip due to the steep stress gradients. Hence the majority of crack tip studies have focussed on the determination of linear elastic parameters, where data are recorded from regions surrounding the crack tip where the adiabatic and reversible assumptions are valid.
More recently the non-adiabatic region close to the crack tip has been explored, with the aim of gaining a greater understanding of crack-tip plasticity. Infrared thermography has been used to correlate the energy dissipation at the crack tip to the plastic zone [1,2], whereas others [3,4,5] have explored using the TSA phase data to quantify the size and shape of the crack-tip plastic zone. The latter method allows the elastic and plastic strain field information to be recorded simultaneously, and thus has the potential for near real-time studies of fatigue crack growth. Thus far, the phase method has only been applied at fairly low frequencies on aluminium alloys. Since the method considers non-adiabatic effects at the crack tip and heat transfer is known to be dependent on material and frequency, it was decided to investigate the extent of plasticity at the tip of propagating fatigue cracks in two different aerospace materials at a range of frequencies.
In thermoelastic stress analysis (TSA) it is normal practice to coat metallic specimens with black paint to enhance and standardize the surface emissivity. It is assumed that the paint coating has no effect on the thermal emission from the specimen, but it is well known that the response is sensitive to paint coating thickness, particularly at higher frequencies. In this paper the effects of loading frequency and paint coating thickness on the thermoelastic response are investigated. The thermoelastic response is compared to theory, and optimum test conditions and coating characteristics are suggested. The motivation for the work is to develop a TSA-based means of residual stress assessment, where the measurement of much smaller temperature changes than those that are resolved in standard TSA is required; therefore the analysis is much more sensitive to the effects of the paint coating. However, the work presented in this paper is relevant to a wide range of TSA investigations and presents data that will be of interest to all practitioners of TSA.
New developments in Thermo Elastic Stress Analysis by Infrared Thermography
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Identification of plastic-zone based on double frequency lock-in thermographic temperature measurement
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Sakagami, T.; Kubo, S.; Tamura, E.; Nishimura, T.. Identification of plastic-zone based on double frequency
lock-in thermographic temperature measurement, In: ICF11 Italy, 2005
On the revised theory of the thermoelastic effect
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Physics and Chemistry of Solids 49, 395-400. DOI: 10.1016/0022-3697(88)90099-6
- W Breitenstein
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Breitenstein, W.;Warta, W. Langenkamp, M. Lock-In Thermography -Basics and Use for Evaluating Electronic
Devices And Materials. Springer Series in Advanced Microelectronics 10, 2010