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An Article from the January 2003 JOM-e: A Web-Only Supplement to JOM
Jeongguk Kim and Peter K. Liaw are with the Department of Materials Science and Engineering at the University of Tennessee. H. Wang is with Oak Ridge National Laboratory. J.Y. Huang and R.C. Kuo are with the Institute of Nuclear Energy Research in Taiwan. J.G. Huang is with the Taiwan Power Company.
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In 1829, the first fatigue test was performed in Germany on steel
chains, which were subjected to 100,000 tension cycles at a frequency of ten
cycles per minute. Since then, a great amount of valuable research effort has
been devoted to studying the fatigue behavior of materials due to the irreplaceable
significance of this subject in the engineering world.1–8
In recent decades, fracture mechanics has become the dominant concept used in
describing and understanding fatigue behavior.
Although there is still interest in such concepts as fracture toughness and endurance limit, data scattering and time-consuming, costly experiments can cause difficulties during fatigue testing of industrial components and structures. Thus, increasing efforts have been focused on nondestructive evaluation (NDE) techniques for their critical importance in fatigue-life assessments, structural-integrity evaluations, failure prevention, and material savings. Several NDE methods have been applied to monitor mechanical damage, including ultrasonics, acoustic emission, eddy current, x-ray, and computed tomography,9–12 Relatively little work has been done to characterize fatigue behavior using thermographic infrared techniques.13–17
In this paper, a study has been conducted on the background and theory of thermography. Furthermore, an advanced high-speed and high-sensitivity infrared (IR) imaging system was used to monitor the temperature evolution of reactor pressure vessel steels subjected to 10 Hz, 20 Hz, and 1,000 Hz fatigue tests. Both thermodynamics and heat-conduction theories are applied to explain and model the observed temperature evolutions during fatigue and to predict the inelastic behavior.
What Is Thermography?
Thermography is a nondestructive evaluation (NDE) technique that monitors the target temperature change. Originally, the technique was used primarily in the military service to observe enemy movement at night and in hospitals to monitor the temperature change of organs and tissues. Later on, as the relationship between mechanical properties and temperature was better clarified and the technique became more advanced, thermography developed into an important nondestructive detection technique in the engineering world. The relationships between the materials temperature evolution and mechanical behaviors can be explained in light of three effects:
The History of Thermography in Materials Science
The relationship between temperature and material deformation was recognized in 1853 by Kelvin18 and then developed by Biot,19 Rocca, and Bever20 in the 1950s. In the 1960s, Dillon21 and Kratochvil22 developed the thermoplastic theory that directly relates the temperature with the material internal stress-strain state, which, in turn, controls the mechanical and fatigue behavior. In 1956, Belgen23 developed IR radiometric techniques for detecting temperature changes. These techniques calculated temperature change with stress by measuring the IR radiation emitted from the surface of solid materials. However, the limited sensitivity of the available instrumentation restrained the full development of thermography as a NDE technique until the 1980s, when rapid developments in electro-optical and signal processing techniques led to a more advanced IR imaging system, an IR camera.24–26 With a temperature resolution up to 10–3°C and a spatial resolution up to several micrometers, this new equipment makes possible the practical quantitative stress-strain analysis by temperature. Recent research has shown the potential of thermography in monitoring mechanical damage.27–40 However, detailed investigations and comprehensive analyses are needed to develop a more practical thermography method in characterizing the fatigue process.
The material used in fatigue tests is reactor pressure vessel (RPV) steel (SA533B1I2), which is composed of, in weight percent, 0.203C, 0.23Si, 1.34Mn, < 0.02P, 0.015S, 0.50Ni, 0.53Mo, 0.15Al, 0.005N, 0.01Cu, and balance, Fe. The steel plate was first solution-treated at 899°C for 1 h, then water-quenched to 40°C, and finally tempered at 670°C for 1 h. A tempered martensite was the final microstructure. The yielding strength of the RPV steel was 587 MPa, ultimate tensile strength was 716 MPa, and total elongation was 29% with a strain rate of 4 × 10–3/s and a gage length of 1.27 cm used in the tension test. A yielding-point phenomenon was observed in the test.40
Fatigue test samples are cylindrical bars with a gage length of 1.27 cm and a diameter of 0.508 cm at the gage section. The test samples are machined from the steel plate with the length direction parallel to the rolling direction and then polished in a sequence of 240, 400, 600, and 800 grit papers, followed by 9.5 mm, 1 mm, and 0.06 mm Al2O3 grit powders.
The 1,000 Hz fatigue tests were performed using an advanced high-frequency electrohydraulic Material Test System (MTS) machine (Model 1,000 Hz 810) with an R ratio of 0.2, where R = smin/smax, and smin and smax are the applied minimum and maximum stresses, respectively. The servovalves of the machine were activated by voice coils, which provide the necessary frequency of 1,000 Hz. The machine has a maximum loading capability of ±25 KN. The test samples were fastened to the machine by specially designed mechanical grips. To avoid the testing noise at 1,000 Hz, the machine was situated in a well-designed soundproof room equipped with a heat pump that offered the cooling capability to prevent the overheating of servovalves.
For 10 Hz and 20 Hz fatigue experiments in air, the specimens were loaded on a MTS machine (Model 810) at R = 0.2. A load control mode was used, and different maximum stress levels ranging from 500 MPa to 650 MPa were applied. During fatigue testing, an extensometer, which was connected with the data-acquisition system of the MTS machine, was fixed on the gage-length section of the specimen. The strain values of the gage length, measured by the extensometer, could then be recorded directly into the MTS system for further analyses.
In addition, the tensile properties of the RPV steel were determined using a plate sample that was 10 mm in width, 35 mm in length, and 5 mm in thickness of the gage-length section. The tensile test was performed at a strain rate of 5 × 10–4/s.
Thermography detection was conducted using a state-of-the-art Raytheon Galileo thermographic IR imaging system with a 320 × 256 pixel focal-plane array InSb detector that is sensitive to a radiation wavelength of 3 mm to 5 mm. The temperature sensitivity is 0.015°C at 23°C, while the spatial resolution can be as small as 5.4 mm. The system’s maximum-speed data acquisition capability is 120 Hz at a full frame of 320 × 256 pixels and 50,000 Hz at 16 × 16 pixels. During fatigue testing, a thin sub-micrometer graphite coating was applied on the specimen gage-length section to decrease the surface-heat reflection.
A thermocouple was attached to the sample to calibrate the IR camera at the beginning of each test. During calibration, the specimen was heated to a high temperature with a heat gun, then air cooled. The temperature of the specimen was recorded from the thermocouple at different times, and the intensity of the IR camera was calibrated to the corresponding temperature. A fully automated software system was employed to acquire the data of temperature distributions of the test samples during fatigue experiments. The IR camera was used at low speeds of 0.1 Hz and 0.2 Hz, and a high speed of 120 Hz.
Figure 1 exhibits the IR images of RPV steels at a maximum stress of 600 MPa, R-ratio of 0.2, and test frequency of 1,000 Hz, which were taken at an IR camera speed of 1 Hz. Figure 1a presents a temperature profile of the fatigued sample at 280,000 cycles, while Figure 1b shows a temperature profile at 285,000 cycles. In both Figure 1a and 1b, the highest temperature region is located in the gage-length section of the specimen, as represented in red color. Subtracting the temperature distribution at 280,000 cycles from that at 285,000 cycles indicates the occurrence of cracking (Figure 1c). The red color in the subtraction image (Figure 1c) identifies the presence of a single hot spot. This is believed to be located at a crack tip, where the heat generation is the greatest. In that location, a significant amount of plastic deformation occurs, which becomes the heat source. Similar results can be found at 20 Hz. Thus, thermography can be used to identify the presence of crack initiation and propagation during fatigue testing.
Figure 1. IR images of RPV specimen high-cycle, fatigue-tested at 1,000 Hz, smax = 600 MPa, and R = 0.2.
Animation 1. A movie depicting the Lüders band evolution process of RPV specimen during 10 Hz fatigue testing.
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Figure 2. A temperature line profile of a RPV specimen during 1,000 Hz fatigue testing.
Figure 2 exhibits the average
temperature distribution along the gage-length (1.27 cm) direction of the specimen
corresponding to different cycles at a maximum stress of 620 MPa, R-ratio of
0.2, and test frequency of 1,000 Hz, taken at an IR camera speed of 1 Hz. Positions
0 and 1.27 on the x axis represent the two ends of specimen gage-length section.
The temperature was generally found to be the highest at the midpoint of the
sample. The temperature rises rapidly at first from 10,000 cycles to 100,000
cycles, and becomes stable after 100,000 cycles, then goes up sharply and quickly
to failure after 250,000 cycles. Near the center of the specimen, the temperature
can rise from about 40°C to 250°C depending on the cycles. The temperature
distribution curve at 260,000 cycles shows the temperature variation immediately
after the specimen breaks, which rises abruptly in the last 5,000 cycles, relative
to that at 255,000 cycles. At 260,000 cycles, the specimen fractures and separates,
which results in a temperature drop in the specimen gage-length section between
0.6 cm and 0.8 cm (i.e., the specimen separates between 0.6 cm and 0.8 cm in
the gage-length section).
Figure 3 shows the temperature evolution, at the mid-point of the specimen gage-length section, plotted on a log scale of fatigue cycles for the 20 Hz fatigue test with a R ratio of 0.2 and maximum stress level of 640 MPa. The specimen temperature at the midpoint of the gage-length section initially increases from 23.7°C to 28.5°C with fatigue cycling, followed by a temperature decrease (i.e., a temperature hump) in the first 100 cycles. After that, the temperature approaches a steady state of about 27°C and then increases abruptly to 49°C until the specimen fails. A detailed analysis of the temperature profile has been provided in previous work.35,36,38,40
In Figure 4, the dashed line represents the amplified hump in Figure 3. In Figure 4, at the very beginning stage, a slight temperature decrease within the first 0.7 s was due to the thermoelastic effect, as discussed later. Then, the temperature rose rapidly from the first fatigue cycle at approximately 0.7 seconds and a temperature of 23.7°C, and reached a maximum of 28.5°C in about 2 s. After that, the temperature decreased gradually to a relatively constant value. However, if the test was stopped after the temperature became stable, and then, restarted, no temperature hump was observed. The corresponding results are plotted as a solid line in Figure 4. Note that in both tests shown by the dashed and solid lines, temperature oscillations within the range of approximately less than 0.6°C were observed within each fatigue cycle.
Since the mean temperature variation is closely related to the plastic deformation,21,22 a reasonable explanation of the presence of the temperature hump can be obtained from the stress-strain curve in Figure 5. This is a typical stress-strain curve for the tension-tension fatigue test. Corresponding to the temperature rise from approximately 0.7 s to 2 s in Figure 4, the stress-strain curve in Figure 5 moves from the first cycle to the 26th cycle, and the plastic strain increases from 0 to nearly the saturated value of about 4.7%. In this period, a great amount of heat is generated from the large plastic deformation and the temperature of the sample increases quickly. Moreover, the yielding-point phenomenon of RPV steels is observed in the uniaxial tensile test, which contributes to large plastic strains (Figure 5) and, in turn, more heat is generated.
However, after the first 26 cycles, relatively little plastic strain occurs due to the strain-hardening effect in Figure 5, and the temperature decreases when the heat inside the sample is conducted to the environment, finally reaching a relatively constant value due to the heat equilibrium between the heat generation of the specimen subjected to cyclic loading and the environment. Note that, in Figure 5, the maximum stress level is lower than 640 MPa for the first several cycles. This trend results from the fact that the fatigue machine needs some time to reach a stabilized stress level at the beginning of fatigue testing.
Figure 3. The specimen temperature evolution of reactor pressure vessel steel during 20 Hz fatigue testing, taken at an IR camera speed of 120 Hz.
Figure 4. The temperature-versus-time evolutions of reactor pressure vessel steel tested at 20 Hz, taken at an IR camera speed of 120 Hz.
Figure 5. The stress-versus-strain result of reactor pressure vessel steel tested at 20 Hz, smax = 640 MPa.
If the fatigue test is terminated and restarted, little heat will be generated from the plastic deformation since the plastic strain has already saturated. Thus, there will be no rapid temperature rise in the first 100 cycles, as indicated by the solid lines in Figure 4. The stress-strain curve of the restarted test is exhibited in Figure 6, which presents much less plastic deformation as compared to Figure 5, resulting in a much smaller temperature rise shown in the solid line, relative to the dashed line in Figure 4. Thus, there is a good correspondence between the temperature evolutions and the stress-strain characteristics during fatigue.
Figure 6. The stress-versus-strain profiles of reactor pressure vessel steel tested at 20 Hz, smax = 640 MPa.
This project is supported by the Taiwan Power Company. The authors are also very grateful for the financial support of the National Science Foundation (DMI-9724476, EEC-9527527, and DGE-998-7548) with D.R. Durham, M.F. Poats, W. Jennings, and L. Goldberg as contract monitors, respectively, and the Tennessee Advanced Materials Laboratory with E.W. Plummer as the director. A portion of the work was sponsored by the U.S. Department of Energy Secretary for Energy Efficiency and Renewable Energy, Office of Transportation Technologies, as part of the High Temperature Materials Laboratory User Program under contract DE-AC05-96OR22464, managed by the UT-Battelle.
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For more information, contact P.K. Liaw, University of Tennessee, Department of Materials Science and Engineering, 427-B Dougherty Engineering Building, Knoxville, TN 37996-2200; e-mail firstname.lastname@example.org.
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