Rapid Assessment of Ti-6Al-4V Fatigue Limit via Infrared Thermography
Abstract
1. Introduction
2. Materials and Methods
- -
- The initial stress amplitude . The thermographic literature suggests selecting this stress as 60–70% the expected fatigue limit [34], or 20–30% of the [42], in order to have sufficient data below the fatigue limit itself. Similarly, one can also select the initial maximum stress , considering that = 0.45 at R = −1. The selected values of and are as follows:
- ○
- for the unnotched S-specimens, 81 MPa and 180 MPa;
- ○
- for the notched N-specimens, 49.5 MPa and 110 MPa.
- -
- The step of the stress amplitude, , that is the stress increment with respect to the maximum stress. Reference [34] suggests using 10% as the expected fatigue limit; hence, the values of 9 MPa ( 20 MPa) and 6.75 MPa ( 15 MPa) are selected.
- -
- The number of cycles for each loading block. This choice depends on the possibility of reaching a stabilized temperature ( or corresponding to the equilibrium condition between generated and dissipated heat. On the other hand, should be selected to avoid accumulating excessive damage in each block, especially at high loads. For the considered alloy, 5000 cycles were sufficient based on some initial tests and the literature, which suggest a range between 1000 [43] and 20,000 [44] cycles.
3. Results
- (1)
- Calculate the average D-mode value for each ROI:
- (2)
- Plot as a function of the applied stress amplitude or of the maximum stress . Figure 4 shows the D-mode trends for S- and N-specimens at the different ROIs.
- (3)
- Fit the first three data points using a linear regression. This is the starting point of an iteration over the applied loading blocks. Let us consider that j is the variable spanning the loading blocks, e.g., ranging from 0 to n-3, where n is the total number of blocks. The initial value of j is 0.
- (4)
- Calculate the residuals, the standard deviation of the sample S, and the threshold value 6S, corresponding to extreme rare events. Specifically, 1S (one standard deviation) encompasses roughly 68% of the data, 2S captures about 95%, 3S includes around 99.7%, and 6S aims for near-perfect accuracy, with 99.9999998% of the data falling within its range [53];
- (5)
- If the j + 1 residual is equal or below the 6S threshold, repeat the iteration from Step 3, adding one additional data point to the fitting, e.g., j = j + 1. Else, if the j + 1 residual is above the 6S threshold, it is the thermographic estimation of the fatigue limit (or damage stress) .
4. Discussion
5. Conclusions
- -
- An advanced post-processing analysis of the surface temperature was necessary. Only the second harmonic signal provided a reliable means for identifying the threshold for irreversible thermal dissipation, which ultimately allowed for the thermographic estimation of the fatigue limit.
- -
- The estimated fatigue limit for unnotched specimens was consistent with data found in the literature. This limit was influenced by the roughness of the specimen, as highlighted by the analysis of fracture surfaces, where multiple cracks initiated and coalesced.
- -
- The presence of a notch, which created a stress gradient in the titanium alloy, made it more challenging to capture the thermal dissipation accurately. Despite the differing thermal behavior observed at the two sides of the notch due to surface imperfections, the identified fatigue limit, which is a material property, remained identical.
- -
- The fatigue strength reduction factor determined through thermographic methods aligned well with theoretical solutions.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
A | Elongation |
aN | Material constant according to Neuber’s formulation |
aP | Material constant according to Peterson’s formulation |
E | Elastic modulus |
EDM | Electrical Discharge Machining |
H | Specimen width |
IR | Infrared |
Kf | Fatigue strength reduction factor |
Ktn | Stress concentration factor |
N | Number of cycles |
NETD | Noise Equivalent Temperature Difference |
q | Notch sensitivity |
r | Root radius of the notch radius |
R | Fatigue stress ratio, e.g., σmin/σmax |
ROI | Region of interest |
S | Statistical standard deviation of the sample |
SEM | Scanning Electron Microscope |
T | Temperature |
t | Time |
UTS | Ultimate tensile strength |
YS | Yield stress |
ΔN | Number of cycles per loading block in stepwise fatigue tests |
Δσa | Step of stress amplitude in stepwise fatigue tests |
Δσmax | Step of maximum stress in stepwise fatigue tests |
σa | Stress semi-amplitude |
σa0 | Initial stress amplitude in stepwise fatigue tests |
σD | Damage stress or thermographic estimation of the fatigue limit |
σD,st | Damage stress, IR-estimated from static tests |
σmax | Maximum applied stress |
σmax0 | Initial maximum stress in stepwise fatigue tests |
Appendix A
Appendix B
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1st Regime | 2nd Regime | Identification | Reference |
---|---|---|---|
Linear | Linear | Two curves method (TCM) | Luong, 1995 [25] |
- | Linear | One curve method (OCM) or Risitano method | La Rosa, Risitano, 2000 [6] |
Linear | Linear | Iterative TCM | Curà, 2005 [26] |
Parabola | Power law | Modified TCM | Sesana, 2012 [27] |
Linear | - | Threshold method | De Finis, 2015 [28] |
Exponential law | - | Minimum curvature radius | Huang, 2017 [29] |
Power law | Exponential law | Sum of the two functions | Douellou, 2020 [30] |
Property | Symbol | Value |
---|---|---|
Elastic modulus | E | 70,958 MPa |
Yield stress | YS | 458 MPa |
Ultimate tensile strength | UTS | 488 MPa |
Elongation | A | 14.8% |
IR-estimated damage stress from static tests | σD,st | 278 MPa |
Thermographic Estimation of the Fatigue Limit (R = −1) | (MPa) | (MPa) |
---|---|---|
σD,S | 264 ± 5 | 119 ± 2 |
σD,N | 165 ± 35 | 74 ± 16 |
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Colombo, C.; Salerno, A.; Teyssiéras, A.; Biffi, C.A. Rapid Assessment of Ti-6Al-4V Fatigue Limit via Infrared Thermography. Metals 2025, 15, 825. https://doi.org/10.3390/met15080825
Colombo C, Salerno A, Teyssiéras A, Biffi CA. Rapid Assessment of Ti-6Al-4V Fatigue Limit via Infrared Thermography. Metals. 2025; 15(8):825. https://doi.org/10.3390/met15080825
Chicago/Turabian StyleColombo, Chiara, Antonio Salerno, Arthur Teyssiéras, and Carlo Alberto Biffi. 2025. "Rapid Assessment of Ti-6Al-4V Fatigue Limit via Infrared Thermography" Metals 15, no. 8: 825. https://doi.org/10.3390/met15080825
APA StyleColombo, C., Salerno, A., Teyssiéras, A., & Biffi, C. A. (2025). Rapid Assessment of Ti-6Al-4V Fatigue Limit via Infrared Thermography. Metals, 15(8), 825. https://doi.org/10.3390/met15080825