20:
363:
is typically 0.4 times the ultimate tensile strength. Maximum typical values for irons are 170 MPa (24 ksi), aluminums 130 MPa (19 ksi), and coppers 97 MPa (14 ksi). Note that these values are for smooth "un-notched" test specimens. The endurance limit for notched
367:
For polymeric materials, the fatigue limit has been shown to reflect the intrinsic strength of the covalent bonds in polymer chains that must be ruptured in order to extend a crack. So long as other thermo chemical processes do not break the polymer chain (i.e. ageing or
301:, for the stress at which failure occurs after a specified number of loading cycles, such as 500 million, as in the case of aluminium. Other authors do not differentiate between the expressions even if they do differentiate between the two types of materials.
990:. However, recent research suggests that endurance limits do not exist for metallic materials, that if enough stress cycles are performed, even the smallest stress will eventually produce fatigue failure.
717:
1004:
833:
503:
972:
937:
902:
653:
583:
137:
1455:
867:
618:
450:
774:
745:
540:
420:
361:
334:
299:
260:
222:
195:
164:
1015:
387:
The fatigue limit of a machine component, Se, is influenced by a series of elements named modifying factors. Some of these factors are listed below.
1483:
83:
the maximum value of completely reversed bending stress that a material can withstand for a specified number of cycles without a fatigue failure
336:) for steels are one half the ultimate tensile strength, to a maximum of 290 MPa (42 ksi). For iron, aluminium, and copper alloys,
1086:
1009:
262:, for the stress below which failure never occurs, even for an indefinitely large number of loading cycles, as in the case of
228:, the stress value below which the material will withstand many load cycles, but implies that it is similar to fatigue limit.
1368:
1343:
1318:
1293:
1265:
1232:
1165:
1138:
1067:
1466:
73:
do not and will eventually fail even from small stress amplitudes. Where materials do not have a distinct limit the term
668:
1570:
1560:
372:), a polymer may operate indefinitely without crack growth when loads are kept below the intrinsic strength.
515:
Besides taking into account the surface finish, it is also important to consider the size gradient factor
1565:
1494:
542:. When it comes to bending and torsional loading, the gradient factor is also taken into consideration.
789:
457:
53:
level below which an infinite number of loading cycles can be applied to a material without causing
944:
909:
874:
625:
555:
1257:
1059:
375:
The concept of fatigue limit, and thus standards based on a fatigue limit such as ISO 281:2007
108:
1224:
1090:
839:
590:
1249:
1216:
425:
1420:
1020:
752:
723:
518:
398:
339:
312:
277:
238:
200:
173:
142:
8:
507:
Where factor a and exponent b present in the equation are related to the surface finish.
1424:
1436:
1155:
1052:
999:
98:
54:
50:
1540:
1440:
1364:
1339:
1314:
1289:
1261:
1250:
1228:
1217:
1161:
1134:
1063:
1536:
1428:
1393:
1197:
1515:
987:
364:
specimens (and thus for many practical design situations) is significantly lower.
1157:
The
Fatigue Threshold of Rubber and Its Characterization Using the Cutting Method
376:
1413:
Proceedings of the Royal
Society of London A: Mathematical and Physical Sciences
1527:
Bathias, C. (1999). "There is no infinite fatigue life in metallic materials".
1397:
1047:
369:
1411:
Lake, G. J.; A. G. Thomas (1967). "The strength of highly elastic materials".
1384:
Lake, G. J.; P. B. Lindley (1965). "The mechanical fatigue limit for rubber".
1201:
1554:
1432:
1126:
85:. For polymeric materials, the fatigue limit is also commonly known as the
66:
1456:"In search of a fatigue limit: A critique of ISO standard 281:2007"
452:, of the material and the surface finish of the machine component.
62:
58:
1529:
Fatigue & Fracture of
Engineering Materials & Structures
379:
lifetime prediction, remains controversial, at least in the US.
23:
Representative curves of applied stress vs number of cycles for
70:
197:, as "the limiting value of stress at which failure occurs as
263:
19:
1188:
Bhowmick, A. K. (1988). "Threshold fracture of elastomers".
1154:
Robertson, C.G.; Stocek, R.; Mars, W.V. (27 November 2020).
1115:(Wiley International ed.). John Wiley & Sons, Inc.
1046:
784:
We can calculate the reliability factor using the equation
1484:"ISO 281:2007 bearing life standard – and the answer is?"
1283:
139:, as "the value of stress at which failure occurs after
1313:(5th ed.). Pearson Education, Inc. p. 110.
947:
912:
877:
842:
792:
755:
726:
671:
628:
593:
558:
521:
460:
428:
401:
382:
342:
315:
280:
241:
203:
176:
145:
111:
65:
alloys have a distinct limit, whereas others such as
1223:(2nd ed.). John Wiley & Sons, Inc. p.
1153:
1051:
966:
931:
896:
861:
827:
768:
739:
711:
647:
612:
577:
534:
497:
444:
414:
355:
328:
293:
254:
216:
189:
158:
131:
1453:
1383:
1338:(2nd ed.). Printice-Hall, Inc. p. 365.
1552:
1410:
16:Maximum stress that won't cause fatigue failure
1447:
1284:Askeland, Donald R.; Pradeep P. Phule (2003).
1113:Nature and Properties of Engineering Materials
1252:Advanced Strength and Applied Stress Analysis
747:is tensile strength at operating temperature
1476:
712:{\displaystyle k_{T}={\frac {S_{o}}{S_{r}}}}
550:Load modifying factor can be identified as.
1377:
1256:(2nd ed.). McGraw-Hill, Inc. pp.
1110:
1014:, a diagram by British mechanical engineer
422:, is related to both the tensile strength,
1404:
1288:(4th ed.). Brooks/Cole. p. 248.
1279:
1277:
224:becomes very large". ASTM does not define
1510:W. Schutz (1996). A history of fatigue.
1308:
1302:
1286:The Science and Engineering of Materials
1214:
1187:
1081:
1079:
1058:(2 ed.). McGraw-Hill, Inc. p.
776:is tensile strength at room temperature
663:The temperature factor is calculated as
18:
1526:
1520:
1333:
1327:
1274:
1247:
1208:
1119:
1042:
1040:
1038:
30:steel (showing an endurance limit) and
1553:
1504:
1491:Tribology & Lubrication Technology
1463:Tribology & Lubrication Technology
1358:
1352:
1241:
1125:
1076:
779:
658:
1035:
1361:Intermediate Mechanics of Materials
13:
1493:: 34–43. July 2010. Archived from
1386:Journal of Applied Polymer Science
1050:; E. Russell Johnston Jr. (1992).
510:
383:Modifying factors of fatigue limit
37:aluminium (showing no such limit).
14:
1582:
1454:Erwin V. Zaretsky (August 2010).
828:{\displaystyle k_{R}=1-0.08Z_{a}}
498:{\displaystyle k_{S}=aS_{ut}^{b}}
390:
304:
1541:10.1046/j.1460-2695.1999.00183.x
1336:Mechanical Behavior of Materials
1512:Engineering Fracture Mechanics
1181:
1147:
1133:. Cambridge University Press.
1104:
1005:Smith fatigue strength diagram
545:
395:The surface modifying factor,
92:
1:
1087:"Metal Fatigue and Endurance"
1028:
309:Typical values of the limit (
57:failure. Some metals such as
1248:Budynas, Richard G. (1999).
1219:Metal Fatigue in Engineering
1160:. Springer. pp. 57–83.
7:
1363:. McGraw-Hill. p. 65.
1334:Dowling, Norman E. (1998).
1215:Stephens, Ralph I. (2001).
993:
967:{\displaystyle z_{a}=2.326}
932:{\displaystyle z_{a}=1.645}
897:{\displaystyle z_{a}=1.288}
10:
1587:
1398:10.1002/app.1965.070090405
986:was introduced in 1870 by
977:
648:{\displaystyle k_{L}=0.59}
578:{\displaystyle k_{L}=0.85}
81:is used and is defined as
1202:10.1080/15583728808085379
132:{\displaystyle S_{N_{f}}}
1309:Hibbeler, R. C. (2003).
1111:Jastrzebski, D. (1959).
1465:: 30–40. Archived from
862:{\displaystyle z_{a}=0}
613:{\displaystyle k_{L}=1}
1433:10.1098/rspa.1967.0160
1359:Barber, J. R. (2001).
1311:Mechanics of Materials
1054:Mechanics of Materials
968:
933:
898:
863:
829:
770:
741:
713:
649:
614:
579:
536:
499:
446:
445:{\displaystyle S_{ut}}
416:
357:
330:
295:
256:
218:
191:
160:
133:
38:
1571:Materials degradation
969:
934:
899:
864:
830:
771:
769:{\displaystyle S_{r}}
742:
740:{\displaystyle S_{o}}
714:
650:
615:
580:
537:
535:{\displaystyle k_{G}}
500:
447:
417:
415:{\displaystyle k_{S}}
358:
356:{\displaystyle S_{e}}
331:
329:{\displaystyle S_{e}}
296:
294:{\displaystyle S_{f}}
257:
255:{\displaystyle S_{e}}
219:
217:{\displaystyle N_{f}}
192:
190:{\displaystyle S_{f}}
161:
159:{\displaystyle N_{f}}
134:
22:
1561:Elasticity (physics)
1131:Fatigue of Materials
974:for 99% reliability
945:
939:for 95% reliability
910:
904:for 90% reliability
875:
869:for 50% reliability
840:
790:
753:
724:
669:
626:
591:
556:
519:
458:
426:
399:
340:
313:
278:
239:
201:
174:
143:
109:
1425:1967RSPSA.300..108L
494:
1566:Fracture mechanics
1048:Beer, Ferdinand P.
1000:Fatigue (material)
964:
929:
894:
859:
825:
780:Reliability factor
766:
737:
709:
659:Temperature factor
645:
610:
575:
532:
495:
477:
442:
412:
353:
326:
291:
252:
214:
187:
156:
129:
87:intrinsic strength
79:endurance strength
39:
1419:(1460): 108–119.
1370:978-0-07-232519-5
1345:978-0-13-905720-5
1320:978-0-13-008181-0
1295:978-0-534-95373-7
1267:978-0-07-008985-3
1234:978-0-471-51059-8
1167:978-3-030-68920-9
1140:978-0-521-57046-6
1069:978-0-07-837340-4
1016:James Henry Smith
707:
655:for pure torsion
231:Some authors use
1578:
1545:
1544:
1524:
1518:
1508:
1502:
1501:
1499:
1488:
1480:
1474:
1473:
1471:
1460:
1451:
1445:
1444:
1408:
1402:
1401:
1392:(4): 1233–1251.
1381:
1375:
1374:
1356:
1350:
1349:
1331:
1325:
1324:
1306:
1300:
1299:
1281:
1272:
1271:
1255:
1245:
1239:
1238:
1222:
1212:
1206:
1205:
1196:(3–4): 339–370.
1185:
1179:
1178:
1176:
1174:
1151:
1145:
1144:
1123:
1117:
1116:
1108:
1102:
1101:
1099:
1098:
1089:. Archived from
1083:
1074:
1073:
1057:
1044:
1024:
1013:
973:
971:
970:
965:
957:
956:
938:
936:
935:
930:
922:
921:
903:
901:
900:
895:
887:
886:
868:
866:
865:
860:
852:
851:
834:
832:
831:
826:
824:
823:
802:
801:
775:
773:
772:
767:
765:
764:
746:
744:
743:
738:
736:
735:
718:
716:
715:
710:
708:
706:
705:
696:
695:
686:
681:
680:
654:
652:
651:
646:
638:
637:
619:
617:
616:
611:
603:
602:
584:
582:
581:
576:
568:
567:
541:
539:
538:
533:
531:
530:
504:
502:
501:
496:
493:
488:
470:
469:
451:
449:
448:
443:
441:
440:
421:
419:
418:
413:
411:
410:
362:
360:
359:
354:
352:
351:
335:
333:
332:
327:
325:
324:
300:
298:
297:
292:
290:
289:
272:fatigue strength
261:
259:
258:
253:
251:
250:
223:
221:
220:
215:
213:
212:
196:
194:
193:
188:
186:
185:
165:
163:
162:
157:
155:
154:
138:
136:
135:
130:
128:
127:
126:
125:
103:fatigue strength
75:fatigue strength
36:
33:
29:
26:
1586:
1585:
1581:
1580:
1579:
1577:
1576:
1575:
1551:
1550:
1549:
1548:
1525:
1521:
1509:
1505:
1497:
1486:
1482:
1481:
1477:
1469:
1458:
1452:
1448:
1409:
1405:
1382:
1378:
1371:
1357:
1353:
1346:
1332:
1328:
1321:
1307:
1303:
1296:
1282:
1275:
1268:
1246:
1242:
1235:
1213:
1209:
1190:Polymer Reviews
1186:
1182:
1172:
1170:
1168:
1152:
1148:
1141:
1124:
1120:
1109:
1105:
1096:
1094:
1085:
1084:
1077:
1070:
1045:
1036:
1031:
1018:
1007:
996:
984:endurance limit
982:The concept of
980:
952:
948:
946:
943:
942:
917:
913:
911:
908:
907:
882:
878:
876:
873:
872:
847:
843:
841:
838:
837:
819:
815:
797:
793:
791:
788:
787:
782:
760:
756:
754:
751:
750:
731:
727:
725:
722:
721:
701:
697:
691:
687:
685:
676:
672:
670:
667:
666:
661:
633:
629:
627:
624:
623:
598:
594:
592:
589:
588:
563:
559:
557:
554:
553:
548:
526:
522:
520:
517:
516:
513:
511:Gradient factor
489:
481:
465:
461:
459:
456:
455:
433:
429:
427:
424:
423:
406:
402:
400:
397:
396:
393:
385:
377:rolling bearing
347:
343:
341:
338:
337:
320:
316:
314:
311:
310:
307:
285:
281:
279:
276:
275:
246:
242:
240:
237:
236:
233:endurance limit
226:endurance limit
208:
204:
202:
199:
198:
181:
177:
175:
172:
171:
150:
146:
144:
141:
140:
121:
117:
116:
112:
110:
107:
106:
95:
47:endurance limit
34:
31:
27:
24:
17:
12:
11:
5:
1584:
1574:
1573:
1568:
1563:
1547:
1546:
1535:(7): 559–565.
1519:
1503:
1500:on 2013-10-24.
1475:
1472:on 2015-05-18.
1446:
1403:
1376:
1369:
1351:
1344:
1326:
1319:
1301:
1294:
1273:
1266:
1240:
1233:
1207:
1180:
1166:
1146:
1139:
1118:
1103:
1075:
1068:
1033:
1032:
1030:
1027:
1026:
1025:
1002:
995:
992:
979:
976:
963:
960:
955:
951:
928:
925:
920:
916:
893:
890:
885:
881:
858:
855:
850:
846:
822:
818:
814:
811:
808:
805:
800:
796:
781:
778:
763:
759:
734:
730:
704:
700:
694:
690:
684:
679:
675:
660:
657:
644:
641:
636:
632:
609:
606:
601:
597:
574:
571:
566:
562:
547:
544:
529:
525:
512:
509:
492:
487:
484:
480:
476:
473:
468:
464:
439:
436:
432:
409:
405:
392:
391:Surface factor
389:
384:
381:
350:
346:
323:
319:
306:
305:Typical values
303:
288:
284:
249:
245:
211:
207:
184:
180:
153:
149:
124:
120:
115:
94:
91:
15:
9:
6:
4:
3:
2:
1583:
1572:
1569:
1567:
1564:
1562:
1559:
1558:
1556:
1542:
1538:
1534:
1530:
1523:
1517:
1514:54: 263-300.
1513:
1507:
1496:
1492:
1485:
1479:
1468:
1464:
1457:
1450:
1442:
1438:
1434:
1430:
1426:
1422:
1418:
1414:
1407:
1399:
1395:
1391:
1387:
1380:
1372:
1366:
1362:
1355:
1347:
1341:
1337:
1330:
1322:
1316:
1312:
1305:
1297:
1291:
1287:
1280:
1278:
1269:
1263:
1259:
1254:
1253:
1244:
1236:
1230:
1226:
1221:
1220:
1211:
1203:
1199:
1195:
1191:
1184:
1169:
1163:
1159:
1158:
1150:
1142:
1136:
1132:
1128:
1122:
1114:
1107:
1093:on 2012-04-15
1092:
1088:
1082:
1080:
1071:
1065:
1061:
1056:
1055:
1049:
1043:
1041:
1039:
1034:
1022:
1017:
1011:
1006:
1003:
1001:
998:
997:
991:
989:
988:August Wöhler
985:
975:
961:
958:
953:
949:
940:
926:
923:
918:
914:
905:
891:
888:
883:
879:
870:
856:
853:
848:
844:
835:
820:
816:
812:
809:
806:
803:
798:
794:
785:
777:
761:
757:
748:
732:
728:
719:
702:
698:
692:
688:
682:
677:
673:
664:
656:
642:
639:
634:
630:
621:
607:
604:
599:
595:
586:
572:
569:
564:
560:
551:
543:
527:
523:
508:
505:
490:
485:
482:
478:
474:
471:
466:
462:
453:
437:
434:
430:
407:
403:
388:
380:
378:
373:
371:
365:
348:
344:
321:
317:
302:
286:
282:
273:
269:
268:fatigue limit
265:
247:
243:
234:
229:
227:
209:
205:
182:
178:
169:
168:fatigue limit
166:cycles", and
151:
147:
122:
118:
113:
104:
100:
90:
88:
84:
80:
76:
72:
68:
64:
60:
56:
52:
48:
44:
43:fatigue limit
21:
1532:
1528:
1522:
1511:
1506:
1495:the original
1490:
1478:
1467:the original
1462:
1449:
1416:
1412:
1406:
1389:
1385:
1379:
1360:
1354:
1335:
1329:
1310:
1304:
1285:
1251:
1243:
1218:
1210:
1193:
1189:
1183:
1171:. Retrieved
1156:
1149:
1130:
1121:
1112:
1106:
1095:. Retrieved
1091:the original
1053:
983:
981:
941:
906:
871:
836:
786:
783:
749:
720:
665:
662:
622:
620:for bending
587:
552:
549:
514:
506:
454:
394:
386:
374:
370:ozone attack
366:
308:
271:
267:
232:
230:
225:
167:
102:
96:
86:
82:
78:
74:
46:
42:
40:
1019: [
1008: [
546:Load factor
93:Definitions
61:alloys and
1555:Categories
1127:Suresh, S.
1097:2008-04-18
1029:References
585:for axial
1441:138395281
810:−
67:aluminium
1129:(2004).
994:See also
101:defines
63:titanium
1421:Bibcode
1173:24 July
978:History
59:ferrous
55:fatigue
49:is the
1439:
1367:
1342:
1317:
1292:
1264:
1260:–533.
1231:
1164:
1137:
1066:
266:; and
71:copper
51:stress
35:
32:
28:
25:
1498:(PDF)
1487:(PDF)
1470:(PDF)
1459:(PDF)
1437:S2CID
1023:]
1012:]
962:2.326
927:1.645
892:1.288
264:steel
1365:ISBN
1340:ISBN
1315:ISBN
1290:ISBN
1262:ISBN
1229:ISBN
1175:2024
1162:ISBN
1135:ISBN
1064:ISBN
813:0.08
643:0.59
573:0.85
99:ASTM
97:The
69:and
41:The
1537:doi
1516:DOI
1429:doi
1417:300
1394:doi
1258:532
1198:doi
270:or
89:.
77:or
45:or
1557::
1533:22
1531:.
1489:.
1461:.
1435:.
1427:.
1415:.
1388:.
1276:^
1227:.
1225:69
1194:28
1192:.
1078:^
1062:.
1060:51
1037:^
1021:de
1010:de
274:,
235:,
170:,
105:,
1543:.
1539::
1443:.
1431::
1423::
1400:.
1396::
1390:9
1373:.
1348:.
1323:.
1298:.
1270:.
1237:.
1204:.
1200::
1177:.
1143:.
1100:.
1072:.
959:=
954:a
950:z
924:=
919:a
915:z
889:=
884:a
880:z
857:0
854:=
849:a
845:z
821:a
817:Z
807:1
804:=
799:R
795:k
762:r
758:S
733:o
729:S
703:r
699:S
693:o
689:S
683:=
678:T
674:k
640:=
635:L
631:k
608:1
605:=
600:L
596:k
570:=
565:L
561:k
528:G
524:k
491:b
486:t
483:u
479:S
475:a
472:=
467:S
463:k
438:t
435:u
431:S
408:S
404:k
349:e
345:S
322:e
318:S
287:f
283:S
248:e
244:S
210:f
206:N
183:f
179:S
152:f
148:N
123:f
119:N
114:S
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
