Vibration Fatigue Damage Accumulation of Ti–6Al–4V under Constant and Sequenced Variable Loading Conditions
Abstract
:1. Introduction
2. Experiments
- In the CAV test, the maximum stress and the stress amplitude are constant (see Figure 3a), and the maximum stress is within the range of 420–570 MPa.
- The two-block loading test consists of the high-low (H-L) and the low-high (L-H) cases (Figure 3b,c). Three stress levels are used including 517 MPa, 595 MPa, and 647 MPa. The specimen is firstly loaded at one stress level for certain cycles and then loaded at another stress level until failure.
- The loading spectra of the two-level block loading test (Figure 3d) are composed of several loading blocks with different stress levels. The loading level within each block is the same, but the difference between loading levels and the cyclic ratio between blocks are variable. Therefore, two sorts of two-level block loading tests are studied: (a) variable loading difference of 23 and 153 MPa with the constant cyclic ratio of 1. and (b) variable cyclic ratio from 0.2 to 20 at the constant load difference of 59 MPa.
3. Damage Models
4. Results and Discussion
4.1. Constant Amplitude Loading Test
4.2. High-Low and Low-High Block Loading Test Results
4.3. Two-Level Repeated Block Loading Test Results
5. Conclusions
Author Contributions
Acknowledgments
Conflicts of Interest
References
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No. | finit/Hz | ffinal/Hz | 2A/mm | σmax/MPa | N/Cycles |
---|---|---|---|---|---|
1 | 82.65 | 81.41 | 32.4 | 736 | 15,000 |
2 | 83.43 | 82.57 | 31.7 | 719 | 42,000 |
3 | 79.68 | 77.28 | 29.0 | 647 | 41,800 |
4 | 81.69 | 79.52 | 29.0 | 647 | 40,900 |
5 | 77.23 | 76.40 | 29.0 | 647 | 28,900 |
6 | 76.55 | 75.45 | 27.0 | 595 | 86,500 |
7 | 75.81 | 74.86 | 27.0 | 595 | 51,100 |
8 | 81.60 | 79.83 | 26.0 | 569 | 50,400 |
9 | 80.24 | 77.43 | 26.0 | 569 | 79,500 |
10 | 80.64 | 79.52 | 24.0 | 517 | 89,700 |
11 | 81.10 | 80.13 | 24.0 | 517 | 111,000 |
12 | 79.55 | 78.54 | 24.0 | 517 | 230,232 |
13 | 81.60 | 80.78 | 23.6 | 506 | 195,000 |
14 | 80.94 | 80.14 | 23.0 | 490 | 209,000 |
15 | 80.10 | 79.00 | 22.5 | 477 | 1,333,900 |
16 | 80.56 | 79.83 | 22.0 | 463 | 3,540,000 |
17 | 81.09 | 80.18 | 21.0 | 438 | 7,330,000 |
18 | 80.66 | 79.68 | 20.5 | 425 | 33,100,000 |
Stress Level/MPa | Load Sequences | n1 | n1/N1 | n2 | n2/N2 | n1/N1 + n2/N2 | Predicted n2/N2 | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
LDR | DLDR | DCA | NLDR | NLCD | |||||||
647/517 | High-low | 10,000 | 0.27 | 43,000 | 0.30 | 0.57 | 0.73 | 0.46 | 0.53 | 0.44 | 0.30 |
12,000 | 0.32 | 77,900 | 0.54 | 0.86 | 0.68 | 0.42 | 0.49 | 0.39 | 0.27 | ||
18,000 | 0.48 | 35,700 | 0.25 | 0.73 | 0.52 | 0.32 | 0.35 | 0.28 | 0.18 | ||
20,000 | 0.54 | 25,500 | 0.18 | 0.72 | 0.46 | 0.29 | 0.30 | 0.24 | 0.15 | ||
36,000 | 0.97 | 5400 | 0.04 | 1.01 | 0.03 | 0.02 | 0.02 | 0.01 | 0.01 | ||
Low-high | 20,000 | 0.14 | 41,800 | 1.12 | 1.26 | 0.86 | 0.93 | 0.97 | 0.99 | 1.00 | |
30,000 | 0.21 | 34,800 | 0.94 | 1.15 | 0.79 | 0.90 | 0.93 | 0.98 | 0.99 | ||
30,000 | 0.21 | 38,000 | 1.02 | 1.23 | 0.79 | 0.90 | 0.93 | 0.98 | 0.99 | ||
60,000 | 0.42 | 26,900 | 0.72 | 1.14 | 0.58 | 0.80 | 0.77 | 0.89 | 0.96 | ||
80,000 | 0.57 | 30,600 | 0.82 | 1.39 | 0.43 | 0.71 | 0.62 | 0.77 | 0.88 | ||
595/517 | High-low | 20,000 | 0.31 | 27,400 | 0.19 | 0.50 | 0.69 | 0.52 | 0.57 | 0.27 | 0.39 |
20,000 | 0.31 | 49,400 | 0.34 | 0.65 | 0.69 | 0.52 | 0.57 | 0.27 | 0.39 | ||
30,000 | 0.47 | 26,900 | 0.19 | 0.66 | 0.53 | 0.40 | 0.42 | 0.19 | 0.28 | ||
40,000 | 0.62 | 22,300 | 0.16 | 0.78 | 0.38 | 0.29 | 0.29 | 0.12 | 0.18 | ||
40,000 | 0.62 | 17,900 | 0.12 | 0.74 | 0.38 | 0.29 | 0.29 | 0.12 | 0.18 | ||
50,000 | 0.78 | 5800 | 0.04 | 0.82 | 0.22 | 0.18 | 0.17 | 0.07 | 0.10 | ||
Low-high | 30,000 | 0.21 | 63,800 | 0.99 | 1.20 | 0.79 | 0.89 | 0.88 | 0.90 | 0.98 | |
30,000 | 0.21 | 51,600 | 0.80 | 1.01 | 0.79 | 0.89 | 0.88 | 0.90 | 0.98 | ||
45,000 | 0.31 | 56,600 | 0.88 | 1.19 | 0.69 | 0.84 | 0.80 | 0.82 | 0.94 | ||
60,000 | 0.42 | 44,700 | 0.69 | 1.11 | 0.58 | 0.78 | 0.70 | 0.72 | 0.87 | ||
75,000 | 0.52 | 46,000 | 0.71 | 1.23 | 0.48 | 0.67 | 0.59 | 0.62 | 0.79 | ||
90,000 | 0.62 | 24,800 | 0.38 | 1.00 | 0.38 | 0.52 | 0.48 | 0.50 | 0.68 |
σH/MPa | σL/MPa | Δσ/MPa | nH | nL | nL/nH | Total nH | Total nL | Nf | |||
---|---|---|---|---|---|---|---|---|---|---|---|
Exp. | LDR | DCA | NLCD | ||||||||
663 | 626 | 37 | 2000 | 2000 | 1 | 18,000 | 17,360 | 35,360 | 37,346 | 37,033 | 36,362 |
663 | 600 | 63 | 2000 | 2000 | 1 | 22,640 | 22,000 | 44,640 | 41,032 | 40,384 | 38,606 |
663 | 578 | 85 | 2000 | 2000 | 1 | 16,830 | 16,000 | 32,830 | 44,308 | 42,851 | 40,173 |
663 | 545 | 118 | 2000 | 2000 | 1 | 24,000 | 23,560 | 47,560 | 48,531 | 46,263 | 41,573 |
663 | 510 | 153 | 2000 | 2000 | 1 | 28,800 | 28,000 | 56,800 | 52,556 | 49,636 | 41,647 |
626 | 603 | 23 | 3000 | 3000 | 1 | 18,000 | 17,700 | 35,700 | 49,632 | 49,346 | 48,792 |
626 | 569 | 57 | 3000 | 3000 | 1 | 22,600 | 21,000 | 43,600 | 56,413 | 55,617 | 53,200 |
626 | 539 | 87 | 3000 | 3000 | 1 | 33,000 | 31,260 | 64,260 | 62,330 | 60,972 | 55,577 |
626 | 510 | 116 | 3000 | 3000 | 1 | 30,000 | 29,200 | 59,200 | 67,869 | 65,903 | 56,054 |
598 | 563 | 35 | 5000 | 5000 | 1 | 40,840 | 40,000 | 80,840 | 68,403 | 67,424 | 65,604 |
598 | 524 | 74 | 5000 | 5000 | 1 | 41,600 | 40,000 | 81,600 | 79,852 | 76,631 | 69,960 |
598 | 510 | 88 | 5000 | 5000 | 1 | 30,000 | 27,560 | 57,560 | 82,637 | 80,052 | 70,202 |
569 | 539 | 30 | 5000 | 5000 | 1 | 50,000 | 47,600 | 97,600 | 90,172 | 89,124 | 86,583 |
569 | 510 | 59 | 5000 | 5000 | 1 | 45,000 | 43,300 | 88,300 | 101,519 | 99,484 | 90,577 |
σH/MPa | σL/MPa | Δσ/MPa | nH | nL | nL/nH | Total nH | Total nL | Nf | |||
---|---|---|---|---|---|---|---|---|---|---|---|
Exp. | LDR | DCA | NLCD | ||||||||
569 | 510 | 59 | 1000 | 20,000 | 20 | 9000 | 167,880 | 176,880 | 140,818 | 139,554 | 124,749 |
569 | 510 | 59 | 1000 | 20,000 | 20 | 7000 | 126,820 | 133,820 | 140,818 | 139,554 | 124,749 |
569 | 510 | 59 | 1000 | 10,000 | 10 | 15,000 | 148,180 | 163,180 | 135,527 | 135.587 | 111,827 |
569 | 510 | 59 | 1000 | 10,000 | 10 | 14,000 | 136,450 | 150,450 | 135,527 | 135.587 | 111,827 |
569 | 510 | 59 | 2000 | 10,000 | 5 | 28,000 | 132,800 | 160,800 | 127,584 | 126,351 | 110,039 |
569 | 510 | 59 | 2000 | 10,000 | 5 | 22,000 | 109,160 | 131,160 | 127,584 | 126,351 | 110,039 |
569 | 510 | 59 | 5000 | 5000 | 1 | 45,000 | 43,300 | 88,300 | 101,519 | 101,007 | 90,577 |
569 | 510 | 59 | 5000 | 5000 | 1 | 55,000 | 52,660 | 107,660 | 101,519 | 101,007 | 90,577 |
569 | 510 | 59 | 10,000 | 2000 | 0.2 | 70,000 | 13,830 | 83,830 | 84,639 | 84,099 | 81,180 |
569 | 510 | 59 | 10,000 | 2000 | 0.2 | 60,000 | 11,600 | 71,600 | 84,639 | 84,099 | 81,180 |
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Lin, J.; Li, W.; Yang, S.; Zhang, J. Vibration Fatigue Damage Accumulation of Ti–6Al–4V under Constant and Sequenced Variable Loading Conditions. Metals 2018, 8, 296. https://doi.org/10.3390/met8050296
Lin J, Li W, Yang S, Zhang J. Vibration Fatigue Damage Accumulation of Ti–6Al–4V under Constant and Sequenced Variable Loading Conditions. Metals. 2018; 8(5):296. https://doi.org/10.3390/met8050296
Chicago/Turabian StyleLin, Jiewei, Weidong Li, Shuo Yang, and Junhong Zhang. 2018. "Vibration Fatigue Damage Accumulation of Ti–6Al–4V under Constant and Sequenced Variable Loading Conditions" Metals 8, no. 5: 296. https://doi.org/10.3390/met8050296