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Effects of shape and size of artificially introduced alumina particles on 1.5Ni–Cr–Mo (En24) steel
Effects of shape and size of artificially introduced alumina particles on 1.5NiCrMo (En24) steel
10
From the discussions in previous chapters, we can understand that the shape of defects and inclusions, that is spherical or angular, does not have a crucial influence on the fatigue limit. Comparisons between a hole and a crack (Section 5.5), or cracked and uncracked carbides, are good examples for understanding this problem. As long ago as 1963, Duckworth and Ineson studied the effects of the geometry and size of alumina particles on the fatigue strength of En24 steel [1]. They artificially introduced alumina particles into steels produced in a laboratory furnace, and conducted fatigue tests on specimens prepared from the steels. In their study, all fatigue tests, rotating bending tests and tension compression tests, were conducted at the same nominal stress amplitude. However, the results showed that very large scatter in fatigue lives depending on the size and location of the inclusions from which fatigue failure initiated. That is, it was found that individual specimens behaved in different ways under the same stress amplitude. Thus, the existence of nonmetallic inclusions causes different fatigue behaviours in individual specimens, and increases the difficulty of quantitative evaluation of fatigue strength. In this chapter, the study by Duckworth and Ineson [1] is introduced. They tried to clarify directly the effect of inclusion shape, and their large amount of data is reanalysed by the method explained in previous chapters [2]. The reanalysis of their data gives us a unified understanding of their data scatter and clarifies the factors influencing the effects of inclusions. Although Araki and colleagues [3] conducted similar experiments to those of Duckworth and Ineson, the influence of artificially added alumina particles did not appear clearly, probably because of the low hardness of the material they used.
10.1
Artificially introduced alumina particles with controlled sizes and shapes, specimens and test stress
As the fatigue behaviour of 1.5NiCrMo steels is well known En24 steel was adopted as the test material. In some ingots, alumina particles (0.0200.250 mm Metal Fatigue. DOI: https://doi.org/10.1016/B978-0-12-813876-2.00010-8 © 2019 Elsevier Ltd. All rights reserved.
228
Metal Fatigue
Table 10.1 Cast numbers and chemical composition Analysis (wt.%) Cast no.
Mean size of particles added (µm)
C
Si
Commercial En24 cast JK None 0.40 0.30 Laboratory En24 cast 1 None 0.42 0.26 Laboratory En24 casts with angular alumina particles added 55 73 0.45 0.38 56 65 0.45 0.46 61 65 0.47 0.23 63 40 0.47 0.33 78 30 0.41 0.16 76 20 0.44 0.23 77 10 0.46 0.24 84 73 0.43 0.26 119 63 0.41 0.47 118 45 0.43 0.43 117 28 0.43 0.42 116 19 0.41 0.37 115 9 0.39 0.29 Laboratory En24 casts with spherical alumina particles added S11 73 0.37 0.31 S2 63 0.39 0.23 S4 45 0.36 0.25 S7 34 0.42 0.35 S6 20 0.35 0.21 S8 10 0.35 0.26
Mn
S
P
Ni
Cr
Mo
0.56
0.012
0.015
1.46
1.06
0.21
0.65
0.022
0.035
1.46
1.16
0.32
0.69 0.68 0.69 0.70 0.54 0.69 0.68 0.66 0.66 0.67 0.67 0.67 0.69
0.022 0.022 0.021 0.022 0.011 0.017 0.011 0.014 0.013 0.011 0.015 0.017 0.011
0.024 0.024 0.023 0.023 0.014 0.012 0.017 0.011 0.019 0.016 0.017 0.015 0.014
1.55 1.59 1.51 1.54 1.66 1.60 1.56 1.66 1.56 1.56 1.51 1.61 1.56
1.28 1.42 1.30 1.11 1.02 1.06 1.02 1.19 1.13 1.16 1.17 1.20 1.23
0.34 0.31 0.30 0.36 0.33 0.33 0.33 0.37 0.32 0.34 0.31 0.36 0.35
0.57 0.56 0.54 0.61 0.49 0.53
0.021 0.012 0.012 0.013 0.012 0.017
0.033 0.019 0.016 0.015 0.016 0.015
1.63 1.76 1.74 1.64 1.62 1.53
1.28 1.27 1.31 1.27 1.25 1.25
0.30 0.32 0.30 0.33 0.30 0.33
Source: From Y. Murakami, K. Kawakami, W.E. Duckworth, Quantitative evaluation of effects of shape and size of artificially introduced alumina particles on the fatigue strength of 1.5Ni-Cr-Mo (En24) steel, Int. J. Fatigue 13 (6) (1991) 489499.
size) were added, and for comparison, an ingot with no added alumina particles was also produced. Table 10.1 shows the cast number, the nominal size of the added alumina particles, and the results of chemical analysis of the ingots. Particles of two shapes were added, angular and spherical. Angular particles were added to casts numbers 55, 56, 61, 63, 7678, 84 and 115119, and spherical particles to casts numbers S2, S4, S6S8 and S11. All ingots were forged and rolled to a 19.05-mm diameter bar. All test piece blanks were annealed before machining by heating at 650 C for 4 h. They were then rough machined to 0.76 mm oversize in all dimensions. Subsequent heat treatment was heating at 850 C for 1 h, followed by oil quenching and tempering at 200 C for 8 h. The hardness of each specimen was checked on a Vickers hardness testing machine, and specimens were then finally ground to the appropriate final dimensions shown in Fig. 10.1. Therefore, the measured value of hardness may be a little higher ( 10%) than that in the final state of the specimens [4]. The purpose of the tests carried out by Duckworth and Ineson was to investigate the effects of the artificially introduced alumina particles on the initiation of fatigue. Therefore, all tests were conducted at a constant stress level, above the fatigue limit, at which the majority of the test pieces would be expected to fail.
Effects of shape and size of artificially introduced alumina particles on 1.5NiCrMo (En24) steel 229
Figure 10.1 Specimen geometry. (a) Rotating bending beam specimen. (b) Tension compression specimen. Dimensions in millimetres. Source: From Y. Murakami, K. Kawakami and W.E. Duckworth, Quantitative evaluation of effects of shape and size of artificially introduced alumina particles on the fatigue strength of 1.5Ni-Cr-Mo (En24) steel, Int. J. Fatigue 13 (6) (1991) 489499.
Thus, a nominal stress of 710 MPa was used. Most of the fatigue tests were performed in two-point loading using Wo¨hler-type rotating bending fatigue testing machines. Tension compression fatigue tests were carried out at zero mean stress (R 5 1) in a Losenhausen universal fatigue testing machine, model UHW6, having a maximum capacity of 29.9 kN. After fatigue testing, all the fractured specimens were examined, using an optical microscope, at magnifications of 3 35 and 3 100. In every case, the fracture appearance of the test specimens containing added alumina particles was different from that observed on the specimens without artificial inclusions. In the former, a circular area of lighter colour than the remainder of the fracture surface, the socalled fish eye, was usually observed, and in the centre of this fish eye, an inclusion very often remained in one half of a specimen. In some cases, the inclusion had fractured, leaving part in each half, and in the few remaining situations, the inclusion had completely shattered, leaving a hole in both fracture surfaces.
230
10.2
Metal Fatigue
Rotating bending fatigue tests without shot peening
Table 10.2 shows the fatigue test results. Fig. 10.2 shows a comparison between the ratio of the applied stress, σ0 , at an inclusion to the calculated fatigue limit, σ0w , with the number of cycles to failure, Nf. In this figure, the symbols x, Δ and & indicate the location of inclusions. There are no data points located below σ0 =σ0w 5 0:9, showing the high accuracy of the evaluation method. pffiffiffiffiffiffiffiffiffi Fig. 10.3 shows the relationship between area and the number of cycles to failure for specimens fractured from a surface or a subsurface inclusion. The data trend
Table 10.2 Rotating bending fatigue test results, angular particles in specimens not shot peened
Specimen no.
Cycles to failure, Nf
Cast no. 55, HV 5 606 A1 1.05 3 106 A3 1.57 3 107 A5 4.80 3 104 A6 6.56 3 104 A9 1.01 3 106 A12 2.83 3 106 Cast no. 56, HV 5 614 A1 4.33 3 106 A4 1.41 3 105 A6 7.11 3 104 A7 1.96 3 105 A9 7.02 3 104 A10 8.16 3 104 A12 3.58 3 104 A13 1.95 3 105 A14 9.76 3 104 A15 6.47 3 106 Cast no. 61, HV 5 610 A9 5.97 3 105
Inclusion size, pffiffiffiffiffiffiffiffiffi area (µm)
Distance from surface, h (µm)
Nominal stress at inclusion, σ0 (MPa)
Fatigue limit predicted by Eqs. (6.1), (6.2), (6.3), σ0w ðMPaÞ
σ 0 /σ0 w
77.9 88.8 31.4 30.1 55.5 65.2
290 327 0 15 103 122
656 649 710 707 691 687
548 (6.3) 536 (6.3) 584 (6.1) 580 (6.2) 580 (6.3) 565 (6.3)
1.20 1.21 1.22 1.22 1.19 1.22
47.6 35.9 62.0 51.0 51.7 66.8 53.2 77.7 56.2 51.4
118 40 0 30 41 71 32 45 50 219
688 703 710 704 702 697 704 702 701 669
601 (6.3) 630 (6.3) 528 (6.1) 537 (6.2) 593 (6.3) 568 (6.3) 534 (6.2) 501 (6.2) 585 (6.3) 594 (6.3)
1.14 1.11 1.35 1.31 1.18 1.23 1.32 1.40 1.20 1.13
20.4
Just breaks free surface Just breaks free surface 134 48 59
710
623 (6.2)
1.14
710
559 (6.2)
1.27
685 701 699
619 (6.3) 617 (6.3) 569 (6.3)
1.11 1.14 1.23
A10
1.56 3 105
38.9
A12 A13 A14
7.84 3 106 8.50 3 106 3.31 3 105
38.8 39.6 64.2
(Continued)
Effects of shape and size of artificially introduced alumina particles on 1.5NiCrMo (En24) steel 231
Table 10.2 (Continued) Inclusion size, pffiffiffiffiffiffiffiffiffi area (µm)
Distance from surface, h (µm)
Nominal stress at inclusion, σ0 (MPa)
Fatigue limit predicted by Eqs. (6.1), (6.2), (6.3), σ0w ðMPaÞ
σ 0 /σ0 w
15.7 14.7 29.5 30.2 24.1 26.6 28.0
710 710 706 699 710 699 710
660 (6.1) 667 (6.1) 586 (6.2) 645 (6.3) 614 (6.1) 659 (6.3) 591 (6.2)
1.08 1.06 1.21 1.08 1.16 1.06 1.20
14.6 19.7
0 0 20 58 0 58 Just breaks free surface 0 0
710 710
668 (6.1) 635 (6.1)
1.06 1.12
17.2 19.7 33.2 19.8 15.6 15.3 29.1 8.86 35.8
0 13 58 0 0 0 151 0 115
710 708 699 710 710 710 682 710 689
643 (6.1) 619 (6.2) 628 (6.3) 628 (6.1) 653 (6.1) 655 (6.1) 642 (6.3) 718 (6.1) 620 (6.3)
1.10 1.14 1.11 1.13 1.09 1.08 1.06 0.99 1.11
25.1 11.5 21.7 15.3
22 10 0 Breaks surface
706 708 710 710
662 (6.3) 754 (6.3) 622 (6.1) 650 (6.2)
1.07 0.94 1.14 1.09
Cast no. 77, HV 5 610 A3 7.86 3 106
14.3
710
661 (6.2)
1.07
A7
1.57 3 105
12.5
710
676 (6.2)
1.05
A8 A9
8.91 3 107 7.38 3 106
11.5 11.5
Break free surface Break free surface 20 15
706 707
758 (6.3) 758 (6.3)
0.93 0.93
Specimen no.
Cycles to failure, Nf
Cast no. 63, HV 5 610 A3 3.11 3 104 A4 1.29 3 105 A5 2.21 3 105 A6 4.57 3 107 A7 8.96 3 104 A8 4.52 3 107 A12 2.81 3 105 A15 6.20 3 104 A17 5.57 3 104 Cast no. 78, HV 5 602 A3 1.64 3 107 A5 4.68 3 104 A6 4.02 3 105 A7 7.21 3 104 A9 3.43 3 106 A12 4.07 3 104 A14 4.39 3 107 A15 5.34 3 106 A17 2.13 3 107 Cast no. 76, HV 5 606 A3 8.34 3 105 A7 6.71 3 106 A8 1.07 3 104 A10 1.42 3 106
pffiffiffiffiffiffiffiffiffi suggests that the larger the value of area, the shorter the p fatigue ffiffiffiffiffiffiffiffiffi life. This figure indirectly verifies the utility of the geometrical parameter, area. In this figure, the fracture data from internal inclusions were not plotted because the fatigue crack pffiffiffiffiffiffiffiffiffi propagation from an internal inclusion would cause a variation in the area 2 Nf relationship due to the difference in the location of the inclusions.
232
Metal Fatigue
Figure 10.2 Comparison between failure stress and predicted fatigue strength for rotating bending specimens that were not shot peened.
Figure 10.3 Relationship between
10.3
pffiffiffiffiffiffiffiffiffi area of inclusions and number of cycles to failure.
Rotating bending fatigue tests on shot-peened specimens
The purpose of these experiments was to examine the effects of the shape of inclusions on fatigue strength. Fig. 10.4 shows typical spherical and angular alumina particles, as added to the ingots. The nominal size does not necessarily indicate the true size of each inclusion, because of variation in the sizes of inclusions of the same nominal size.
Figure 10.4 Typical alumina particles, as added to ingots. (A) Typical spherical alumina particles. (a) 73 µm nominal size. (b) 40 µm nominal size. (c) 10 µm nominal size. (B) Typical angular alumina particles. (a) 73 µm nominal size. (b) 40 µm nominal size. (c) 10 µm nominal size [1].
234
Metal Fatigue
pffiffiffiffiffiffiffiffiffi Figure 10.5 Histograms of area inclusions at fracture origins. (a) Spherical alumina particles. (b) Angular alumina particles.
After examining Fig. 10.4, a typical common answer to the question “Which is more detrimental, a spherical inclusion or an angular inclusion?” would be “An angular inclusion.” However, reality does not correspond to this answer. Since the sizes of the inclusions found on the fracture pffiffiffiffiffiffiffiffiffisurface have large scatter, all the results are classified separately in terms of area for p spherical ffiffiffiffiffiffiffiffiffi and angular inclusions at fracture origins. Fig. 10.5 shows histograms of area at the fracture surface pffiffiffiffiffiffiffiffiffi for (a) spherical alumina and (b) angular alumina. Although the values of area do show a larger scatter, there is no significant difference in the distribution pffiffiffiffiffiffiffiffiffi of area for spherical and angular inclusions. Fig. 10.6 shows the relationship between σ0 =σ0w and Nf in rotating bending fatigue for angular and spherical particles. All data points have values of σ0 =σ0w $ 0:89. The maximum evaluation error is approximately 10%, which may be caused by a higher estimate for HV than the actual value, as described above. Thus, the evaluation accuracy is sufficient for practical purposes, regardless of inclusion shape. If we look at the histograms of Fig. 10.5a and b from the viewpoint of, there is very little difference. This is the reason why the shape of inclusion is not significant pffiffiffiffiffiffiffiffiffi at lower stress levels in Fig. 10.6, rather it is area that is the crucial geometrical factor. Many researchers may find this conclusion difficult to accept if we concentrate our attention on ‘stress concentration factors’ of small defects and inclusions.
Effects of shape and size of artificially introduced alumina particles on 1.5NiCrMo (En24) steel 235
Figure 10.6 Comparison between failure stress and predicted fatigue strength for shotpeened rotating bending specimens and for shot-peened tension compression specimens.
If we try to solve a problem of this kind by stress concentration factors, we shall not be able to reach a complete solution. Although the angular shape of TiN inclusions has been thought to be the cause of their detrimental effect, we can understand from the experiments by Duckworth and Ineson that this widely accepted viewpoint is not correct with respect to fatigue limits. However, at higher stress levels the specimens fractured from angular alumina particles do tend to show slightly shorter fatigue lives compared with those fractured from spherical alumina particles, as shown in Fig. 10.6. The most likely reason is that cracks nucleate earlier from angular inclusions than from spherical inclusions, resulting in shorter fatigue lives at higher stress levels, although the fatigue limit is determined by the condition for nonpropagation of a crack emanating from an inclusion. Generally speaking, the compressive stress on the specimen surface produced by shot peening makes the effective distance, h, of the fatal inclusion from the surface deeper, as seen by comparing Tables 10.3 and 10.4 with Table 10.2. In shot-peened specimens, high compressive residual stresses exist on the surface, and tensile residual stresses exist in the interior. Therefore fractures, on the whole, initiate from internal inclusions or defects. The reason why some values of σ0 =σ0w in Fig. 10.6
236
Metal Fatigue
Table 10.3 Rotating bending fatigue test results, angular particles in shot-peened specimens
Cycles to failure, Nf
Inclusion pffiffiffiffiffiffiffiffiffi size, area (µm)
Cast no. 84, HV 5 581 1.16 3 106 52.0 1.57 3 106 68.0 6.97 3 106 56.0 6.02 3 105 93.0 1.45 3 106 79.4 7.67 3 105 74.2 8.96 3 105 90.8 2.55 3 105 93.4 4.12 3 105 69.1 4.01 3 105 97.0 3.04 3 105 87.9 Cast no. 119, HV 5 579 4.92 3 106 52.7 1.63 3 106 63.8 1.66 3 106 81.3 8.31 3 105 83.8 3.66 3 105 85.6 55.4 2.13 3 106 2.98 3 106 63.3 Cast no. 118, HV 5 581 2.80 3 106 56.7 6.84 3 106 53.9 2.43 3 106 63.9 1.05 3 107 44.2 3.68 3 106 73.1 1.56 3 107 57.1 2.62 3 106 56.7 Cast no. 117, HV 5 581 8.28 3 107 33.2 4.68 3 107 51.7 2.57 3 106 54.5 1.05 3 108 26.9 4.43 3 106 72.1 1.75 3 107 46.6 Cast no. 116, HV 5 574 9.08 3 107 36.2 4.78 3 105 125.9 1.61 3 107 37.6 9.04 3 105 116.0 5.24 3 107 33.6
Distance from surface, h (µm)
Nominal stress at inclusion, σ0 (MPa)
374 686 453 327 449 257 318 375 418 521 445
641 583 626 649 627 662 651 640 632 613 627
566 (6.3) 541 (6.3) 559 (6.3) 514 (6.3) 527 (6.3) 533 (6.3) 516 (6.3) 513 (6.3) 540 (6.3) 510 (6.3) 519 (6.3)
1.13 1.08 1.20 1.26 1.19 1.24 1.26 1.25 1.17 1.20 1.21
325 437 361 335 427 364 276
650 629 643 648 631 642 659
563 (6.3) 546 (6.3) 524 (6.3) 521 (6.3) 519 (6.3) 558 (6.3) 546 (6.3)
1.15 1.15 1.23 1.24 1.21 1.15 1.21
582 575 473 522 766 557 464
602 603 622 613 568 607 624
558 (6.3) 563 (6.3) 547 (6.3) 582 (6.3) 535 (6.3) 557 (6.3) 558 (6.3)
1.08 1.07 1.14 1.05 1.06 1.09 1.12
402 424 382 367 803 521
635 631 639 642 561 613
610 (6.3) 567 (6.3) 562 (6.3) 632 (6.3) 536 (6.3) 576 (6.3)
1.04 1.11 1.14 1.02 1.05 1.06
277 510 287 860 668
659 615 657 550 586
595 (6.3) 484 (6.3) 591 (6.3) 490 (6.3) 603 (6.3)
1.11 1.27 1.11 1.12 0.97
Fatigue limit predicted by Eqs. (6.1), (6.2) and (6.3), σ0w ðMPaÞ σ0=σ0w0
Effects of shape and size of artificially introduced alumina particles on 1.5NiCrMo (En24) steel 237
Table 10.4 Rotating bending fatigue test results, spherical particles in shot-peened specimens
Cycles to failure, Nf
Inclusion pffiffiffiffiffiffiffiffiffi size, area (µm)
Cast no. S11, HV 5 556 1.27 3 106 59.5 2.64 3 106 137.4 7.88 3 106 76.7 1.60 3 106 93.1 Cast no. S2, HV 5 560 6.77 3 107 47.8 6.21 3 107 57.6 2.85 3 107 49.2 Cast no. S4, HV 5 554 3.07 3 107 40.8 2.69 3 106 112.6 2.34 3 107 46.1 7.11 3 106 53.2 3.34 3 107 46.1 6.39 3 106 51.4 1.54 3 107 44.3 Cast no. S7, HV 5 566 55.8 3.06 3 107 3.07 3 107 34.1 6.58 3 107 33.8 2.34 3 107 41.7 Cast no. S8, HV 5 550 5.55 3 107 54.9 2.37 3 107 58.5 2.53 3 106 72.5 8.61 3 106 40.3 2.73 3 107 46.1 4.87 3 107 26.6
Distance from surface, h (µm)
Nominal stress at inclusion, σ0 (MPa)
Fatigue limit predicted by Eqs. (6.1), (6.2) and (6.3), σ 0w ðMPaÞ
σ 0 =σ0w0
341 1100 515 830
647 506 614 556
534 (6.3) 464 (6.3) 512 (6.3) 495 (6.3)
1.21 1.09 1.20 1.12
420 460 470
632 625 623
557 (6.3) 540 (6.3) 554 (6.3)
1.13 1.16 1.12
390 1300 375 470 450 357 675
638 469 640 623 626 644 585
567 (6.3) 478 (6.3) 555 (6.3) 542 (6.3) 555 (6.3) 545 (6.3) 559 (6.3)
1.13 0.98 1.15 1.15 1.13 1.18 1.05
1200 500 310 320
487 617 652 651
547 (6.3) 594 (6.3) 595 (6.3) 575 (6.3)
0.89 1.04 1.10 1.13
680 655 440 56 390 415
584 588 628 700 638 633
536 (6.3) 630 (6.3) 512 (6.3) 564 (6.3) 552 (6.3) 605 (6.3)
1.09 1.11 1.23 1.24 1.16 1.05
are a little lower than 1.0 may be the result of tensile residual stress in the interior, in addition to an overestimate of the hardness, HV, at a fracture origin. The method of evaluating the effects of residual stress on the fatigue strength was explained in Chapter 8, Spring steels. The method is not used in the present chapter because residual stress values are not included in the data of Duckworth and Ineson. If we assume the residual stress at the fracture origin to be σr 5 1200 MPa, then the fatigue strength, σ0w , predicted using Eqs. (6.3) and (6.4) is a 7% overestimate, and the ratio of σ0 =σ0w is underestimated by 7%. Thus, if we did consider the effect of residual stresses, then the evaluation error of σ0 =σ0w would be expected to decrease.
238
10.4
Metal Fatigue
Tension compression fatigue tests
In Fig. 10.6, the values σ0 =σ0w for tension compression fatigue (symbol K) are evidently larger than those for rotating bending fatigue (symbols Δ and x). We can easily understand the reason for this if we take into consideration the fact that all the fatigue tests were conducted at the same nominal stress. In tension compression, a greater volume of a specimen is subjected to high stress than in rotating bending pffiffiffiffiffiffiffiffiffi fatigue, with its concomitant stress gradient. Accordingly, the value of areamax of the maximum inclusion in tension compression is larger than that in rotating bending, reducing the fatigue limit, σ0w , for tension compression, or increasing the ratio pffiffiffiffiffiffiffiffiffi 0 0 σ =σw . Prediction of areamax for inclusions contained in a particular number of specimens can be made by the method based on extreme value statistics, as explained in previous chapters. pffiffiffiffiffiffiffiffiffi According to extreme value statistics, the expected value of areamax increases withpincreasing test volume, or number of specimens. For example, the mean values ffiffiffiffiffiffiffiffiffi of areamax of inclusions at the fracture origin are 34.6 μm for nonshot-peened specimens in rotating bending (Fig. 10.2), 62.6 μm for shot-peened specimens in rotating bending (Fig. 10.6), and 76.8 μm for tension compression (Fig. 10.6).
References [1] W.E. Duckworth, E. Ineson, The effects of externally introduced alumina particles on the fatigue life of En24 steel, Clean Steel Iron Steel Inst. Sp. Rep. 77 (1963) 87103. [2] Y. Murakami, K. Kawakami, W.E. Duckworth, Quantitative evaluation of effects of size and shape of artificially introduced alumina inclusions on the fatigue strength of Ni-CrMo steel, Tetsu to Hagane 77 (1) (1991) 163170. Y. Murakami, K. Kawakami, W.E. Duckworth, Quantitative evaluation of effects of shape and size of artificially introduced alumina particles on the fatigue strength of 1.5Ni-Cr-Mo (En24) steel, Int. J. Fatigue 13 (6) (1991) 489499. [3] M. Sumita, I. Uchiyama, T. Araki, A model experiment on relationship between fatigue properties of steel and size, shape, and distribution of inclusions, Tetsu to Hagane 57 (2) (1971) 335354. [4] Y. Murakami, H. Usuki, Prediction of fatigue strength of high-strength steels based on statistical evaluation of inclusion size, Trans. Jpn. Soc. Mech. Eng. A 55 (510) (1989) 213221.
10
From the discussions in previous chapters, we can understand that the shape of defects and inclusions, that is spherical or angular, does not have a crucial influence on the fatigue limit. Comparisons between a hole and a crack (Section 5.5), or cracked and uncracked carbides, are good examples for understanding this problem. As long ago as 1963, Duckworth and Ineson studied the effects of the geometry and size of alumina particles on the fatigue strength of En24 steel [1]. They artificially introduced alumina particles into steels produced in a laboratory furnace, and conducted fatigue tests on specimens prepared from the steels. In their study, all fatigue tests, rotating bending tests and tension compression tests, were conducted at the same nominal stress amplitude. However, the results showed that very large scatter in fatigue lives depending on the size and location of the inclusions from which fatigue failure initiated. That is, it was found that individual specimens behaved in different ways under the same stress amplitude. Thus, the existence of nonmetallic inclusions causes different fatigue behaviours in individual specimens, and increases the difficulty of quantitative evaluation of fatigue strength. In this chapter, the study by Duckworth and Ineson [1] is introduced. They tried to clarify directly the effect of inclusion shape, and their large amount of data is reanalysed by the method explained in previous chapters [2]. The reanalysis of their data gives us a unified understanding of their data scatter and clarifies the factors influencing the effects of inclusions. Although Araki and colleagues [3] conducted similar experiments to those of Duckworth and Ineson, the influence of artificially added alumina particles did not appear clearly, probably because of the low hardness of the material they used.
10.1
Artificially introduced alumina particles with controlled sizes and shapes, specimens and test stress
As the fatigue behaviour of 1.5NiCrMo steels is well known En24 steel was adopted as the test material. In some ingots, alumina particles (0.0200.250 mm Metal Fatigue. DOI: https://doi.org/10.1016/B978-0-12-813876-2.00010-8 © 2019 Elsevier Ltd. All rights reserved.
228
Metal Fatigue
Table 10.1 Cast numbers and chemical composition Analysis (wt.%) Cast no.
Mean size of particles added (µm)
C
Si
Commercial En24 cast JK None 0.40 0.30 Laboratory En24 cast 1 None 0.42 0.26 Laboratory En24 casts with angular alumina particles added 55 73 0.45 0.38 56 65 0.45 0.46 61 65 0.47 0.23 63 40 0.47 0.33 78 30 0.41 0.16 76 20 0.44 0.23 77 10 0.46 0.24 84 73 0.43 0.26 119 63 0.41 0.47 118 45 0.43 0.43 117 28 0.43 0.42 116 19 0.41 0.37 115 9 0.39 0.29 Laboratory En24 casts with spherical alumina particles added S11 73 0.37 0.31 S2 63 0.39 0.23 S4 45 0.36 0.25 S7 34 0.42 0.35 S6 20 0.35 0.21 S8 10 0.35 0.26
Mn
S
P
Ni
Cr
Mo
0.56
0.012
0.015
1.46
1.06
0.21
0.65
0.022
0.035
1.46
1.16
0.32
0.69 0.68 0.69 0.70 0.54 0.69 0.68 0.66 0.66 0.67 0.67 0.67 0.69
0.022 0.022 0.021 0.022 0.011 0.017 0.011 0.014 0.013 0.011 0.015 0.017 0.011
0.024 0.024 0.023 0.023 0.014 0.012 0.017 0.011 0.019 0.016 0.017 0.015 0.014
1.55 1.59 1.51 1.54 1.66 1.60 1.56 1.66 1.56 1.56 1.51 1.61 1.56
1.28 1.42 1.30 1.11 1.02 1.06 1.02 1.19 1.13 1.16 1.17 1.20 1.23
0.34 0.31 0.30 0.36 0.33 0.33 0.33 0.37 0.32 0.34 0.31 0.36 0.35
0.57 0.56 0.54 0.61 0.49 0.53
0.021 0.012 0.012 0.013 0.012 0.017
0.033 0.019 0.016 0.015 0.016 0.015
1.63 1.76 1.74 1.64 1.62 1.53
1.28 1.27 1.31 1.27 1.25 1.25
0.30 0.32 0.30 0.33 0.30 0.33
Source: From Y. Murakami, K. Kawakami, W.E. Duckworth, Quantitative evaluation of effects of shape and size of artificially introduced alumina particles on the fatigue strength of 1.5Ni-Cr-Mo (En24) steel, Int. J. Fatigue 13 (6) (1991) 489499.
size) were added, and for comparison, an ingot with no added alumina particles was also produced. Table 10.1 shows the cast number, the nominal size of the added alumina particles, and the results of chemical analysis of the ingots. Particles of two shapes were added, angular and spherical. Angular particles were added to casts numbers 55, 56, 61, 63, 7678, 84 and 115119, and spherical particles to casts numbers S2, S4, S6S8 and S11. All ingots were forged and rolled to a 19.05-mm diameter bar. All test piece blanks were annealed before machining by heating at 650 C for 4 h. They were then rough machined to 0.76 mm oversize in all dimensions. Subsequent heat treatment was heating at 850 C for 1 h, followed by oil quenching and tempering at 200 C for 8 h. The hardness of each specimen was checked on a Vickers hardness testing machine, and specimens were then finally ground to the appropriate final dimensions shown in Fig. 10.1. Therefore, the measured value of hardness may be a little higher ( 10%) than that in the final state of the specimens [4]. The purpose of the tests carried out by Duckworth and Ineson was to investigate the effects of the artificially introduced alumina particles on the initiation of fatigue. Therefore, all tests were conducted at a constant stress level, above the fatigue limit, at which the majority of the test pieces would be expected to fail.
Effects of shape and size of artificially introduced alumina particles on 1.5NiCrMo (En24) steel 229
Figure 10.1 Specimen geometry. (a) Rotating bending beam specimen. (b) Tension compression specimen. Dimensions in millimetres. Source: From Y. Murakami, K. Kawakami and W.E. Duckworth, Quantitative evaluation of effects of shape and size of artificially introduced alumina particles on the fatigue strength of 1.5Ni-Cr-Mo (En24) steel, Int. J. Fatigue 13 (6) (1991) 489499.
Thus, a nominal stress of 710 MPa was used. Most of the fatigue tests were performed in two-point loading using Wo¨hler-type rotating bending fatigue testing machines. Tension compression fatigue tests were carried out at zero mean stress (R 5 1) in a Losenhausen universal fatigue testing machine, model UHW6, having a maximum capacity of 29.9 kN. After fatigue testing, all the fractured specimens were examined, using an optical microscope, at magnifications of 3 35 and 3 100. In every case, the fracture appearance of the test specimens containing added alumina particles was different from that observed on the specimens without artificial inclusions. In the former, a circular area of lighter colour than the remainder of the fracture surface, the socalled fish eye, was usually observed, and in the centre of this fish eye, an inclusion very often remained in one half of a specimen. In some cases, the inclusion had fractured, leaving part in each half, and in the few remaining situations, the inclusion had completely shattered, leaving a hole in both fracture surfaces.
230
10.2
Metal Fatigue
Rotating bending fatigue tests without shot peening
Table 10.2 shows the fatigue test results. Fig. 10.2 shows a comparison between the ratio of the applied stress, σ0 , at an inclusion to the calculated fatigue limit, σ0w , with the number of cycles to failure, Nf. In this figure, the symbols x, Δ and & indicate the location of inclusions. There are no data points located below σ0 =σ0w 5 0:9, showing the high accuracy of the evaluation method. pffiffiffiffiffiffiffiffiffi Fig. 10.3 shows the relationship between area and the number of cycles to failure for specimens fractured from a surface or a subsurface inclusion. The data trend
Table 10.2 Rotating bending fatigue test results, angular particles in specimens not shot peened
Specimen no.
Cycles to failure, Nf
Cast no. 55, HV 5 606 A1 1.05 3 106 A3 1.57 3 107 A5 4.80 3 104 A6 6.56 3 104 A9 1.01 3 106 A12 2.83 3 106 Cast no. 56, HV 5 614 A1 4.33 3 106 A4 1.41 3 105 A6 7.11 3 104 A7 1.96 3 105 A9 7.02 3 104 A10 8.16 3 104 A12 3.58 3 104 A13 1.95 3 105 A14 9.76 3 104 A15 6.47 3 106 Cast no. 61, HV 5 610 A9 5.97 3 105
Inclusion size, pffiffiffiffiffiffiffiffiffi area (µm)
Distance from surface, h (µm)
Nominal stress at inclusion, σ0 (MPa)
Fatigue limit predicted by Eqs. (6.1), (6.2), (6.3), σ0w ðMPaÞ
σ 0 /σ0 w
77.9 88.8 31.4 30.1 55.5 65.2
290 327 0 15 103 122
656 649 710 707 691 687
548 (6.3) 536 (6.3) 584 (6.1) 580 (6.2) 580 (6.3) 565 (6.3)
1.20 1.21 1.22 1.22 1.19 1.22
47.6 35.9 62.0 51.0 51.7 66.8 53.2 77.7 56.2 51.4
118 40 0 30 41 71 32 45 50 219
688 703 710 704 702 697 704 702 701 669
601 (6.3) 630 (6.3) 528 (6.1) 537 (6.2) 593 (6.3) 568 (6.3) 534 (6.2) 501 (6.2) 585 (6.3) 594 (6.3)
1.14 1.11 1.35 1.31 1.18 1.23 1.32 1.40 1.20 1.13
20.4
Just breaks free surface Just breaks free surface 134 48 59
710
623 (6.2)
1.14
710
559 (6.2)
1.27
685 701 699
619 (6.3) 617 (6.3) 569 (6.3)
1.11 1.14 1.23
A10
1.56 3 105
38.9
A12 A13 A14
7.84 3 106 8.50 3 106 3.31 3 105
38.8 39.6 64.2
(Continued)
Effects of shape and size of artificially introduced alumina particles on 1.5NiCrMo (En24) steel 231
Table 10.2 (Continued) Inclusion size, pffiffiffiffiffiffiffiffiffi area (µm)
Distance from surface, h (µm)
Nominal stress at inclusion, σ0 (MPa)
Fatigue limit predicted by Eqs. (6.1), (6.2), (6.3), σ0w ðMPaÞ
σ 0 /σ0 w
15.7 14.7 29.5 30.2 24.1 26.6 28.0
710 710 706 699 710 699 710
660 (6.1) 667 (6.1) 586 (6.2) 645 (6.3) 614 (6.1) 659 (6.3) 591 (6.2)
1.08 1.06 1.21 1.08 1.16 1.06 1.20
14.6 19.7
0 0 20 58 0 58 Just breaks free surface 0 0
710 710
668 (6.1) 635 (6.1)
1.06 1.12
17.2 19.7 33.2 19.8 15.6 15.3 29.1 8.86 35.8
0 13 58 0 0 0 151 0 115
710 708 699 710 710 710 682 710 689
643 (6.1) 619 (6.2) 628 (6.3) 628 (6.1) 653 (6.1) 655 (6.1) 642 (6.3) 718 (6.1) 620 (6.3)
1.10 1.14 1.11 1.13 1.09 1.08 1.06 0.99 1.11
25.1 11.5 21.7 15.3
22 10 0 Breaks surface
706 708 710 710
662 (6.3) 754 (6.3) 622 (6.1) 650 (6.2)
1.07 0.94 1.14 1.09
Cast no. 77, HV 5 610 A3 7.86 3 106
14.3
710
661 (6.2)
1.07
A7
1.57 3 105
12.5
710
676 (6.2)
1.05
A8 A9
8.91 3 107 7.38 3 106
11.5 11.5
Break free surface Break free surface 20 15
706 707
758 (6.3) 758 (6.3)
0.93 0.93
Specimen no.
Cycles to failure, Nf
Cast no. 63, HV 5 610 A3 3.11 3 104 A4 1.29 3 105 A5 2.21 3 105 A6 4.57 3 107 A7 8.96 3 104 A8 4.52 3 107 A12 2.81 3 105 A15 6.20 3 104 A17 5.57 3 104 Cast no. 78, HV 5 602 A3 1.64 3 107 A5 4.68 3 104 A6 4.02 3 105 A7 7.21 3 104 A9 3.43 3 106 A12 4.07 3 104 A14 4.39 3 107 A15 5.34 3 106 A17 2.13 3 107 Cast no. 76, HV 5 606 A3 8.34 3 105 A7 6.71 3 106 A8 1.07 3 104 A10 1.42 3 106
pffiffiffiffiffiffiffiffiffi suggests that the larger the value of area, the shorter the p fatigue ffiffiffiffiffiffiffiffiffi life. This figure indirectly verifies the utility of the geometrical parameter, area. In this figure, the fracture data from internal inclusions were not plotted because the fatigue crack pffiffiffiffiffiffiffiffiffi propagation from an internal inclusion would cause a variation in the area 2 Nf relationship due to the difference in the location of the inclusions.
232
Metal Fatigue
Figure 10.2 Comparison between failure stress and predicted fatigue strength for rotating bending specimens that were not shot peened.
Figure 10.3 Relationship between
10.3
pffiffiffiffiffiffiffiffiffi area of inclusions and number of cycles to failure.
Rotating bending fatigue tests on shot-peened specimens
The purpose of these experiments was to examine the effects of the shape of inclusions on fatigue strength. Fig. 10.4 shows typical spherical and angular alumina particles, as added to the ingots. The nominal size does not necessarily indicate the true size of each inclusion, because of variation in the sizes of inclusions of the same nominal size.
Figure 10.4 Typical alumina particles, as added to ingots. (A) Typical spherical alumina particles. (a) 73 µm nominal size. (b) 40 µm nominal size. (c) 10 µm nominal size. (B) Typical angular alumina particles. (a) 73 µm nominal size. (b) 40 µm nominal size. (c) 10 µm nominal size [1].
234
Metal Fatigue
pffiffiffiffiffiffiffiffiffi Figure 10.5 Histograms of area inclusions at fracture origins. (a) Spherical alumina particles. (b) Angular alumina particles.
After examining Fig. 10.4, a typical common answer to the question “Which is more detrimental, a spherical inclusion or an angular inclusion?” would be “An angular inclusion.” However, reality does not correspond to this answer. Since the sizes of the inclusions found on the fracture pffiffiffiffiffiffiffiffiffisurface have large scatter, all the results are classified separately in terms of area for p spherical ffiffiffiffiffiffiffiffiffi and angular inclusions at fracture origins. Fig. 10.5 shows histograms of area at the fracture surface pffiffiffiffiffiffiffiffiffi for (a) spherical alumina and (b) angular alumina. Although the values of area do show a larger scatter, there is no significant difference in the distribution pffiffiffiffiffiffiffiffiffi of area for spherical and angular inclusions. Fig. 10.6 shows the relationship between σ0 =σ0w and Nf in rotating bending fatigue for angular and spherical particles. All data points have values of σ0 =σ0w $ 0:89. The maximum evaluation error is approximately 10%, which may be caused by a higher estimate for HV than the actual value, as described above. Thus, the evaluation accuracy is sufficient for practical purposes, regardless of inclusion shape. If we look at the histograms of Fig. 10.5a and b from the viewpoint of, there is very little difference. This is the reason why the shape of inclusion is not significant pffiffiffiffiffiffiffiffiffi at lower stress levels in Fig. 10.6, rather it is area that is the crucial geometrical factor. Many researchers may find this conclusion difficult to accept if we concentrate our attention on ‘stress concentration factors’ of small defects and inclusions.
Effects of shape and size of artificially introduced alumina particles on 1.5NiCrMo (En24) steel 235
Figure 10.6 Comparison between failure stress and predicted fatigue strength for shotpeened rotating bending specimens and for shot-peened tension compression specimens.
If we try to solve a problem of this kind by stress concentration factors, we shall not be able to reach a complete solution. Although the angular shape of TiN inclusions has been thought to be the cause of their detrimental effect, we can understand from the experiments by Duckworth and Ineson that this widely accepted viewpoint is not correct with respect to fatigue limits. However, at higher stress levels the specimens fractured from angular alumina particles do tend to show slightly shorter fatigue lives compared with those fractured from spherical alumina particles, as shown in Fig. 10.6. The most likely reason is that cracks nucleate earlier from angular inclusions than from spherical inclusions, resulting in shorter fatigue lives at higher stress levels, although the fatigue limit is determined by the condition for nonpropagation of a crack emanating from an inclusion. Generally speaking, the compressive stress on the specimen surface produced by shot peening makes the effective distance, h, of the fatal inclusion from the surface deeper, as seen by comparing Tables 10.3 and 10.4 with Table 10.2. In shot-peened specimens, high compressive residual stresses exist on the surface, and tensile residual stresses exist in the interior. Therefore fractures, on the whole, initiate from internal inclusions or defects. The reason why some values of σ0 =σ0w in Fig. 10.6
236
Metal Fatigue
Table 10.3 Rotating bending fatigue test results, angular particles in shot-peened specimens
Cycles to failure, Nf
Inclusion pffiffiffiffiffiffiffiffiffi size, area (µm)
Cast no. 84, HV 5 581 1.16 3 106 52.0 1.57 3 106 68.0 6.97 3 106 56.0 6.02 3 105 93.0 1.45 3 106 79.4 7.67 3 105 74.2 8.96 3 105 90.8 2.55 3 105 93.4 4.12 3 105 69.1 4.01 3 105 97.0 3.04 3 105 87.9 Cast no. 119, HV 5 579 4.92 3 106 52.7 1.63 3 106 63.8 1.66 3 106 81.3 8.31 3 105 83.8 3.66 3 105 85.6 55.4 2.13 3 106 2.98 3 106 63.3 Cast no. 118, HV 5 581 2.80 3 106 56.7 6.84 3 106 53.9 2.43 3 106 63.9 1.05 3 107 44.2 3.68 3 106 73.1 1.56 3 107 57.1 2.62 3 106 56.7 Cast no. 117, HV 5 581 8.28 3 107 33.2 4.68 3 107 51.7 2.57 3 106 54.5 1.05 3 108 26.9 4.43 3 106 72.1 1.75 3 107 46.6 Cast no. 116, HV 5 574 9.08 3 107 36.2 4.78 3 105 125.9 1.61 3 107 37.6 9.04 3 105 116.0 5.24 3 107 33.6
Distance from surface, h (µm)
Nominal stress at inclusion, σ0 (MPa)
374 686 453 327 449 257 318 375 418 521 445
641 583 626 649 627 662 651 640 632 613 627
566 (6.3) 541 (6.3) 559 (6.3) 514 (6.3) 527 (6.3) 533 (6.3) 516 (6.3) 513 (6.3) 540 (6.3) 510 (6.3) 519 (6.3)
1.13 1.08 1.20 1.26 1.19 1.24 1.26 1.25 1.17 1.20 1.21
325 437 361 335 427 364 276
650 629 643 648 631 642 659
563 (6.3) 546 (6.3) 524 (6.3) 521 (6.3) 519 (6.3) 558 (6.3) 546 (6.3)
1.15 1.15 1.23 1.24 1.21 1.15 1.21
582 575 473 522 766 557 464
602 603 622 613 568 607 624
558 (6.3) 563 (6.3) 547 (6.3) 582 (6.3) 535 (6.3) 557 (6.3) 558 (6.3)
1.08 1.07 1.14 1.05 1.06 1.09 1.12
402 424 382 367 803 521
635 631 639 642 561 613
610 (6.3) 567 (6.3) 562 (6.3) 632 (6.3) 536 (6.3) 576 (6.3)
1.04 1.11 1.14 1.02 1.05 1.06
277 510 287 860 668
659 615 657 550 586
595 (6.3) 484 (6.3) 591 (6.3) 490 (6.3) 603 (6.3)
1.11 1.27 1.11 1.12 0.97
Fatigue limit predicted by Eqs. (6.1), (6.2) and (6.3), σ0w ðMPaÞ σ0=σ0w0
Effects of shape and size of artificially introduced alumina particles on 1.5NiCrMo (En24) steel 237
Table 10.4 Rotating bending fatigue test results, spherical particles in shot-peened specimens
Cycles to failure, Nf
Inclusion pffiffiffiffiffiffiffiffiffi size, area (µm)
Cast no. S11, HV 5 556 1.27 3 106 59.5 2.64 3 106 137.4 7.88 3 106 76.7 1.60 3 106 93.1 Cast no. S2, HV 5 560 6.77 3 107 47.8 6.21 3 107 57.6 2.85 3 107 49.2 Cast no. S4, HV 5 554 3.07 3 107 40.8 2.69 3 106 112.6 2.34 3 107 46.1 7.11 3 106 53.2 3.34 3 107 46.1 6.39 3 106 51.4 1.54 3 107 44.3 Cast no. S7, HV 5 566 55.8 3.06 3 107 3.07 3 107 34.1 6.58 3 107 33.8 2.34 3 107 41.7 Cast no. S8, HV 5 550 5.55 3 107 54.9 2.37 3 107 58.5 2.53 3 106 72.5 8.61 3 106 40.3 2.73 3 107 46.1 4.87 3 107 26.6
Distance from surface, h (µm)
Nominal stress at inclusion, σ0 (MPa)
Fatigue limit predicted by Eqs. (6.1), (6.2) and (6.3), σ 0w ðMPaÞ
σ 0 =σ0w0
341 1100 515 830
647 506 614 556
534 (6.3) 464 (6.3) 512 (6.3) 495 (6.3)
1.21 1.09 1.20 1.12
420 460 470
632 625 623
557 (6.3) 540 (6.3) 554 (6.3)
1.13 1.16 1.12
390 1300 375 470 450 357 675
638 469 640 623 626 644 585
567 (6.3) 478 (6.3) 555 (6.3) 542 (6.3) 555 (6.3) 545 (6.3) 559 (6.3)
1.13 0.98 1.15 1.15 1.13 1.18 1.05
1200 500 310 320
487 617 652 651
547 (6.3) 594 (6.3) 595 (6.3) 575 (6.3)
0.89 1.04 1.10 1.13
680 655 440 56 390 415
584 588 628 700 638 633
536 (6.3) 630 (6.3) 512 (6.3) 564 (6.3) 552 (6.3) 605 (6.3)
1.09 1.11 1.23 1.24 1.16 1.05
are a little lower than 1.0 may be the result of tensile residual stress in the interior, in addition to an overestimate of the hardness, HV, at a fracture origin. The method of evaluating the effects of residual stress on the fatigue strength was explained in Chapter 8, Spring steels. The method is not used in the present chapter because residual stress values are not included in the data of Duckworth and Ineson. If we assume the residual stress at the fracture origin to be σr 5 1200 MPa, then the fatigue strength, σ0w , predicted using Eqs. (6.3) and (6.4) is a 7% overestimate, and the ratio of σ0 =σ0w is underestimated by 7%. Thus, if we did consider the effect of residual stresses, then the evaluation error of σ0 =σ0w would be expected to decrease.
238
10.4
Metal Fatigue
Tension compression fatigue tests
In Fig. 10.6, the values σ0 =σ0w for tension compression fatigue (symbol K) are evidently larger than those for rotating bending fatigue (symbols Δ and x). We can easily understand the reason for this if we take into consideration the fact that all the fatigue tests were conducted at the same nominal stress. In tension compression, a greater volume of a specimen is subjected to high stress than in rotating bending pffiffiffiffiffiffiffiffiffi fatigue, with its concomitant stress gradient. Accordingly, the value of areamax of the maximum inclusion in tension compression is larger than that in rotating bending, reducing the fatigue limit, σ0w , for tension compression, or increasing the ratio pffiffiffiffiffiffiffiffiffi 0 0 σ =σw . Prediction of areamax for inclusions contained in a particular number of specimens can be made by the method based on extreme value statistics, as explained in previous chapters. pffiffiffiffiffiffiffiffiffi According to extreme value statistics, the expected value of areamax increases withpincreasing test volume, or number of specimens. For example, the mean values ffiffiffiffiffiffiffiffiffi of areamax of inclusions at the fracture origin are 34.6 μm for nonshot-peened specimens in rotating bending (Fig. 10.2), 62.6 μm for shot-peened specimens in rotating bending (Fig. 10.6), and 76.8 μm for tension compression (Fig. 10.6).
References [1] W.E. Duckworth, E. Ineson, The effects of externally introduced alumina particles on the fatigue life of En24 steel, Clean Steel Iron Steel Inst. Sp. Rep. 77 (1963) 87103. [2] Y. Murakami, K. Kawakami, W.E. Duckworth, Quantitative evaluation of effects of size and shape of artificially introduced alumina inclusions on the fatigue strength of Ni-CrMo steel, Tetsu to Hagane 77 (1) (1991) 163170. Y. Murakami, K. Kawakami, W.E. Duckworth, Quantitative evaluation of effects of shape and size of artificially introduced alumina particles on the fatigue strength of 1.5Ni-Cr-Mo (En24) steel, Int. J. Fatigue 13 (6) (1991) 489499. [3] M. Sumita, I. Uchiyama, T. Araki, A model experiment on relationship between fatigue properties of steel and size, shape, and distribution of inclusions, Tetsu to Hagane 57 (2) (1971) 335354. [4] Y. Murakami, H. Usuki, Prediction of fatigue strength of high-strength steels based on statistical evaluation of inclusion size, Trans. Jpn. Soc. Mech. Eng. A 55 (510) (1989) 213221.