Mechanics of Materials
Lock-in Infrared Thermography for Fatigue Limit Estimation in Ti–6Al–4V Alloy
2021 Volume 62 Issue 6 Pages 738-743
Details
2021 Volume 62 Issue 6 Pages 738-743
Lock-in infrared thermography was used to estimate the fatigue limit for Ti–6Al–4V alloy at room temperature. The method detected infrared emitted from specimen during cyclic loading, i.e., temperature change related to frequency (f) of the loading. The temperature change contained reversible component and irreversible component, which related to thermos-elastic effect and plastic deformation, respectively. The latter component was divided from the former one by lock-in analysis to estimate fatigue limit. Estimated fatigue limits corresponded to those obtained from conventional fatigue tests at several stress ratios. A new assessment line was identified as σa = σw(1 − σm/σB)1/n, where σa represents the stress amplitude, σw signifies the fatigue limit, σm denotes mean stress, σB expresses tensile strength, and the n exponent for the alloy is about 2.3. The non-failure region of the new diagram was smaller than that of the modified Goodman diagram because of a reduced fatigue limit at near-zero stress ratios in the titanium alloy.
Ti–6Al–4V alloy has been widely applied for aerospace materials1) and for implant materials in human body2) because of its high strength-to-weight ratio, high corrosion resistance, and high biocompatibility. Its aerospace engineering applications include fuel tanks of scientific satellites,3) airframes, and fan blades as low-temperature components used at less than 573 K (T/Tm < 0.3). Irrespective of the status quo, the Ti alloy showed a characteristic fatigue property, a double fatigue limit, at stress ratios (R) of 0 and 0.3 at room temperature, as described in National Institute for Materials Science (NIMS) fatigue data sheet No. 111.4) Another fatigue limit appears at the giga cycle fatigue region (>109 cycles), signaling a decrease of allowable stress in design. However, assessments of the fatigue properties of materials used in industry are extremely time-consuming and expensive statistical processes. Because lock-in infrared thermography is anticipated as a simple method to estimate a fatigue limit using a single test,5–8) the time and cost of safety evaluation can be reduced drastically. Furthermore, because this method presents a failure location indicated as a high temperature area in an infrared image, product-level inspection is also anticipated.
To estimate a fatigue limit using thermography, an infrared camera detects an irreversible temperature change (TD) that is related to energy dissipation (q) in a coupled thermomechanical equation5,9) as
| \begin{equation} C\rho \dot{T} = r_{0} + K\nabla^{2}T + w + q, \end{equation} | (1) |
| \begin{equation} \nabla = \partial/\partial \mathrm{x} + \partial/\partial \mathrm{y} + \partial/\partial \mathrm{z}, \end{equation} | (2) |
| \begin{align} T(t) &= T_{\text{m}} + T_{\text{E}} \mathrm{e}^{2\pi i(ft+\phi)} + T_{\text{D}} \mathrm{e}^{2\pi i(2ft+\Phi)} \\ &\quad + (\text{higher harmonics}) + (\text{Noise}) \end{align} | (3) |
| \begin{equation} q = C\rho T_{\text{D}}. \end{equation} | (4) |
A sample in this study was the Ti–6Al–4V alloy (heat C) listed in the NIMS fatigue data sheet No. 111.4) The detailed chemical composition is presented in Table 1. Heat treatments were performed as follows: 1203 K for 3600 s for solution and 978 K for 3600 s for aging. After the heat treatments, sample was air cooled. Microstructure after the heat treatments was shown in Fig. 1. The alloy had α + β bimodal structure clearly and grain size was about 5 µm measured as intercept length. A plate-type specimen with 3 mm gauge thickness and 3 mm width was prepared for the thermography. Surfaces were polished using #600 emery paper. One surface was matte-coated for a pseudo-blackbody surface.
Microstructure of the sample after heat treatments. (a) Cross section and (b) longitudinal section.
Lock-in infrared thermography was conducted using an infrared camera (FLIR-A6751; FLIR Systems Inc.) and a hydraulic servo system as shown in Fig. 2. The infrared camera measured temperature change, T(t) in eq. (3), three times during the cyclic loading at each stress amplitude. Cyclic loading was applied for a specimen by the hydraulic servo system with frequency of 10 Hz for all tests. A sine wave loading cycle was applied. The frequency was influenced by a frame rate of an observation. Because the camera frame rate was 99 Hz and the shooting time was 30 s to obtain 3000 pictures in one measurement, frequency was about one-tenth of the frame rate. Then, the shooting time was selected as moderate value. Hayabusa et al. concluded that fatigue limit was not changed by shooting time up to 300 s.12) It is also reported a shorter time of 10 s is applied for the thermography, showing good agreement with a fatigue limit obtained by conventional fatigue tests.13) However, these tests were conducted at R = −1 where relatively large dissipated energy is observed. Because fatigue limits at several stress ratios were estimated, 30 s was chosen in this study.
Experimental setup of lock-in infrared thermography in this study.
To evaluate energy dissipation at each stress amplitude, incremental step loading tests were conducted (see Fig. 3). Stress amplitude increased step by step as shown in Fig. 3(a). Detailed procedure at a stress amplitude was shown in Fig. 3(b). Free running was done for 180 s at the beginning of the test to achieve stable loading. In addition, free running was set between the shooting times for lock-in analysis which was performed using a software (JFE Techno-Research Co., Japan) to separate TD from T(t). Here, lock-in signal was load signal obtained from testing machine. Although an inhomogeneous distribution of TD was detected in the specimen, the values were the averaged value in a fixed area for all evaluation. Then, the q value at each stress amplitude was calculated by eq. (4) with C of 0.565 J/g·K, ρ of 4.43 g/cm3 14) and TD.
(a) Schematic plot of incremental step loading tests in this study. (b) Thermography was performed three times at each stress amplitude.
Figure 4 presents examples of infrared images of energy dissipation (q) at several stress amplitudes at R = −1. Although energy dissipation was observed slightly in the low stress amplitude region, it increased sharply in the high stress amplitude region. The change is depicted as stress–amplitude dependency in Fig. 5(a). A transition point of the q value was observed at the stress amplitude of 534 MPa as shown in Fig. 5(a), which corresponds to the fatigue limit reported in the NIMS data sheet, i.e., 525 MPa.4) Although the data sheet showed that frequency dependency on the S-N curve at R = −1, the fatigue limit at 10 Hz might be same as that at 120 Hz. Because Takeuchi et al.15) reported that fatigue limits at f = 600 Hz and at f = 20 kHz are 586 MPa and 605 MPa, respectively, the fatigue limits do not linearly relate to frequency for the heat C. In addition, the result showed that two levels of fatigue limit exist in each frequency region, i.e., the low frequency region at f < 120 Hz and the high frequency region at f > 600 Hz. Therefore, the fatigue limit estimated by the thermography was valid for further discussion.
Series of energy dissipation at several stress amplitudes at (a) R = −1, (b) 0, (c) 0.3 and (d) 0.725. Energy dissipation is observed at the center of the specimen. Increasing the stress amplitude raises the energy dissipation.
Stress amplitude dependency of energy dissipation at R = (a) −1, (b) 0, (c) 0.3, and (d) 0.725. S-N curves in Ref. 4) are overlaid for each stress amplitude. Fatigue limits are represented as dotted lines in each condition, which corresponds to the transition points of the energy dissipation. IR denotes data obtained using infrared thermography in this study.
Energy dissipation changed in the similar way at the other conditions. In addition, transition points were also observed at R = 0, 0.3 and 0.725 as shown in Fig. 5(b)–(d). Although the data at R = 0.3 corresponded to fatigue limits obtained by NIMS fatigue data sheet4) as shown in Fig. 5(c), difference between fatigue limit in NIMS fatigue data sheet4) and that estimated by the thermography became 13% at R = 0. The number was slightly larger than those at other thermography tests, <10%.5,7,8,12,13) However, the fatigue limit in NIMS data sheet4) has been unclear because of only one data around the estimated fatigue limit, about 260 MPa, as shown in Fig. 5(b). It means that the comparison contains relatively large difference at R = 0 under the current condition. To make the difference small, revision of the NIMS fatigue data sheet4) is expected.
Then, fatigue limit was estimated at R = 0.725 by the thermography to make a detailed fatigue limit diagram of the Ti–6Al–4V alloy. The data was used to confirm that a fitting curve becomes a straight line or a curve line. Unfortunately, the S-N curve at R = 0.725 was not reported in the date sheet,4) only data from infrared thermography (IR) are reported in Fig. 5(d). Energy dissipation becomes a small value like 0.004 MJ/m3, which is about 10 times less than that observer at R = −1. A transition point was observer at σa ∼ 93 MPa, whose value is regarded as fatigue limit in this condition.
Figure 6 shows a fatigue limit diagram with data from cyclic fatigue tests (open circles) and from infrared thermography (solid circles). The diagram also includes data of heats A and B in the NIMS data sheet.4) The cyclic fatigue tests and the infrared thermography showed almost identical fatigue limits at R = −1, 0, and 0.3, as presented in Fig. 5. Although this figure includes lines estimated using conventional lines such as the modified Goodman line and the Soderberg line, the experimental data were deviated from both lines, especially at R = 0 and 0.3. Then, the deviation became smaller with the increasing stress ratio. The x intercept approached the tensile strength of the alloy. Depending on this trend, neither conventional equation adapts to reliability evaluation of the Ti–6Al–4V alloy, meaning that reliability has been overestimated. Therefore, a new assessment line is better to be used for the secure reliability evaluation.
Fatigue limit diagram for the Ti–6Al–4V alloy. Open circles represent data from the cyclic fatigue tests.4) Solid circles show those obtained using thermography. The new assessment line decreases the non-destructive area compared with the conventional lines.
Conventional lines have been expressed using the following equations for the modified Goodman line and the Soderberg line, respectively:
| \begin{equation} \sigma_{\text{a}} = \sigma_{\text{w}}(1-\sigma_{\text{m}}/\sigma_{\text{B}}), \end{equation} | (5) |
| \begin{equation} \sigma_{\text{a}} = \sigma_{\text{w}}(1-\sigma_{\text{m}}/\sigma_{\text{y}}). \end{equation} | (6) |
| \begin{equation} \sigma_{\text{a}} = \sigma_{\text{w}}(1-\sigma_{\text{m}}/\sigma_{\text{B}})^{1/n}, \end{equation} | (7) |
Finally, the authors noted damage during the incremental step loading test to estimate fatigue limit. Although one specimen suffered various stress amplitudes during the test, it was assumed that plastic deformation and cracks are not generated because stress level is below fatigue limit in giga cycle region. Therefore, deformation history might not affect estimation of fatigue limit by lock-in infrared thermography.
This study revealed the effectiveness of lock-in infrared thermography for Ti–6Al–4V alloy and proposed a new assessment line in fatigue limit diagram at room temperature. Details of the conclusions are explained below.
The authors gratefully appreciate beneficial support from Dr. K. Naito and Mr. T. Nojima (NIMS). We are also thankful for financial support from the Council for Science, Technology and Innovation (CSTI), Cross-ministerial Strategic Innovation Promotion Program (SIP), “Materials Integration for Revolutionary Design System of Structural Materials” (Funding agency: JST), and the Innovative Science and Technology Initiative for Security from the Acquisition, Technology & Logistics Agency (ATLA), Japan.
