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Transcript of Appendix Linear Elastic Fracture Mechanics. Compendium …978-88-470-2336-9/1.pdf · Appendix...
AppendixLinear Elastic Fracture Mechanics.Compendium of Stress Intensity FactorsSolutions
A.1 Introduction
Linear elastic fracture mechanics (LEFM) studies the behavior of materials, workpieces and structures in which cracks are present. Actually, the term fracture refersand identifies those failures caused by the presence of a crack. A crack is definedas an extremely sharp structural discontinuity characterized by a root radius nolarger than 0.005 mm. Structural discontinuity having root radii larger than 0.005are classified as notches. In the presence of a notch LEFM is no longer valid.However, LEFM can still be applied supposing that, conservatively, sooner or laterat the tip of a notch a crack will initiate by fatigue or corrosion, in particular. Thefundamental result of LEFM is that ahead of a crack an elastic stress field existsthat is always self-similar (see Fig. 10.4). Its analytical expression for an infinitebody containing a through wall crack of length 2a under remote loading, known asGriffith crack, schematized in Fig. A.1 is given by the G. Irwin expression (see Eq.10.4)
rij ¼KIffiffiffiffiffiffiffiffi
2prp fijðhÞ
KI ¼ rffiffiffiffiffiffi
pap ðA:1Þ
in which f(h) is a non-dimensional factor that depends on the angle h, r is thedistance from the crack tip and a the semi-crack length, as schematized inFig. A.2. The elastic stress field presents a singularity of the type 1/Hr. Itsamplitude is given by the Irwin stress intensity factor KI.
The subscript I indicates that the stress intensity factor KI refers to the first ofthe three fundamentals mode of aperture of a crack, schematized in Fig. A.3. Anyother mode can be considered as a combination of two or more fundamentalmodes. For any real case in which the geometry is not infinite, loaded underwhatever conditions and the crack is not central, the expression of the stressintensity factor KI is always given by the second of Eq. (A.1) with the addition of amultiplying factor f(a)
P. P. Milella, Fatigue and Corrosion in Metals,DOI: 10.1007/978-88-470-2336-9, � Springer-Verlag Italia 2013
807
s
ss
s
Fig. A.1 Central through-wall crack of length 2a in aninfinite body remote loaded
x
y
z
r
σy
σx
σz
θcrack front
Fig. A.2 Polar coordinatesahead of a crack tip
x
z
y
x
z
y
MODE I MODE II MODE III
KI KII KIII
x
z
y
Fig. A.3 Schematic of the three modes of aperture of a crack
808 Appendix: Linear Elastic Fracture Mechanics
KI ¼ rffiffiffiffiffiffiffi
pa�p
f að Þ ðA:2Þ
The non-dimensional function f(a) depends uniquely on the geometry of thesystem and length a of the crack. One of the main objective of LEFM is theassessment of the function f(a) relative to the particular geometry under study.Once the f(a) function is known, the relative KI can be inferred via Eq. (A.2). OnKI depends either the FCGR, da/dN, through the Paris-Erdogan power law (10.10),or the occurrence of SCC when the applied KI becomes equal to the thresholdstress intensity factor KIscc. Also brittle fracture occurs when the applied KI
reaches the critical value of the toughness of the material KIc. Several solutionsrelative to simple, yet important geometries will be given in the next sections.
A.3 Fracture Mechanics Specimens with Increasing KI
Plain Uniaxial Specimens
Same simple geometries will be considered first. These are plane geometriesbelonging to the category of KI-increasing specimens with increasing crack length(see Fig. 10.7). The specimens considered in this section where the first to be usedin fracture mechanics applications and are shown in Fig. A.4. They have side or
2W
2a
4WW
/6
F
8 W
F
0.3-0.4 W
CC(T)
(a)
W/3
DEC(T) SEC(T)
(b) (c)
a a
0.15-0.2 W
F
2W
2a
2W
0.3-0.4 W
F
F
W/3
F
W/3
Fig. A.4 Geometries ofstandard fracture mechanicsplane specimens underremote force F
Appendix: Linear Elastic Fracture Mechanics 809
central notches fatigued to develop a crack at the tip and are subjected to a uniaxialstress state. The first geometry, Fig. A.4a, is the central crack panel CC(T) (the Tstands for traction). The second, Fig. A.4b, is the double edge crack panel orDEC(T). The third one, Fig. A.4c, is the single edge crack panel or SEC(T). Foreach geometry the relative f(a) or h(a) function are given, depending on whetherthe KI expression is given in terms of force F, Fig. A.4, or stress r, Fig. A.5 actingon the extremities of the specimen. Figure A.4 and A.5 also indicates the standarddimensions of the specimens.
For all the geometries considered the general expression of KI is
KI ¼F
sffiffiffiffi
wp � h a
w
� �
KI ¼ rffiffiffiffiffiffi
pap
� f a
w
� �
:
ðA:3Þ
The f(a) and h(a) functions, that in the specific geometries considered are f(a/w)and h(a/w) functions, are:
2W
2a
0.3-0.4 W
CC(T)
(a)
DEC(T) SEC(T)
(b) (c)
a a
0.15-0.2 W
2W
2a
2W
0.3-0.4 W
σ σ σ
σ σ σ
Fig. A.5 Geometries of standard fracture mechanics plane specimens under remote stress r
810 Appendix: Linear Elastic Fracture Mechanics
CC(T) PANEL [1, 2]
ha
w
� �
¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
pa
4wsec
pa
2w
r
� 1� 0:025 � a
w
� �2þ0:06 � a
w
� �4� �
fa
w
� �
¼ffiffiffiffiffiffiffiffiffiffiffiffiffi
secpa
2w
r
� 1� 0:25 � a
w
� �2þ0:06 � a
w
� �4� �
:
ðA:4Þ
The functions given by Eq. (A.4) are shown in Fig. A.6
DEC(T) PANEL [1, 2]
ha
w
� �
¼ffiffiffiffiffiffiffiffiffiffiffi
pa2w
1� aw
s
1:122� 0:561a
w
� �
� 0:205a
w
� �2þ0:471
a
w
� �3þ0:190
a
w
� �4� �
fa
w
� �
¼ 1:122� 0:561 � a=wð Þ�0:205 � a=wð Þ2þ0:471 � a=wð Þ3�0:190 � a=wð Þ4ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1� a=wp
ðA:5ÞGraphically they are shown in Fig. A.7.
SEC(T) PANEL [1, 3]
ha
w
� �
¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2tan pa2w
p
cos pa2w
0:752þ 2:02a
w
� �
þ 0:37 1� sinpa
2w
� �3� �
fa
w
� �
¼ 1:12� 0:231 � a
w
� �
þ 10:55 � a
w
� �2�21:72 � a
w
� �3þ30:39 � a
w
� �4:
ðA:6Þ
.Graphically the two functions are shown in Fig. A.8.
Fig. A.6 Diagram of the f(a/w) and h(a/w) functions for a CC(T) panel
Appendix: Linear Elastic Fracture Mechanics 811
For this last geometries the expression are valid only for a \ 0.6w because forlarger a value a non-negligible bending component must be taken intoconsideration.
Biaxial Specimens
Soon after the introduction of CC(T) and DEC(T) panels the attention of fracturemechanics researchers focused on a particular specimen that could introduce acertain degree of biaxial stresses. This was due to the fact that in the early 060 s, inparticular, concerns were arising about the triaxial or plain strain state on thetoughness of materials. A material that under uniaxial stress state exhibited largeductility and, therefore, had an apparent high toughness could become ratherbrittle under a plain strain state condition. Concerns were arising from the high
Fig. A.7 Diagram of the f(a/w) and h(a/w) functions for a DEC(T) panel
Fig. A.8 Diagram of the f(a/w) and h(a/w) functions for a SEC(T) panel
812 Appendix: Linear Elastic Fracture Mechanics
fatigue pre-crack
WOL Type X
WOL Type T
fatigue pre-crack
dialgage
Compact C(T)
fatigue pre-crack
side groove
(c)
(b)
(a)
Fig. A.9 Fracture mechanics specimens type WOL-X, WOL-T and compact C(T)
Appendix: Linear Elastic Fracture Mechanics 813
pressure industries and, in particular, from the nuclear industry that built heavysection steel pressure vessels that were subjected to high pressure and biaxial stressstate. It was an engineer of the nuclear industry, Manjoine [4] that at WestinghouseNuclear introduced the historical WOL (wedge opening load) type X specimenshown in Fig. A.9a.
The reduced dimensions of these specimens were due to the limited spaceavailable in a nuclear power reactor in which they were introduced close to corefor neutron embrittlement surveillance programs. Type X specimen is carrying a Vshaped central notch extending at least to 40 % of the total length W fatigued todevelop a sharp crack (q B 0,005 mm). The specimen is loaded by a pin-clevissystem pulling the lower side of the hole while the upper face of the specimen isscrew-fixed to the loading cell. The stress state on the crack plane is equivalent tothe biaxial stress state existing in the wall of a pressure vessel. As shown inFig. A.10, on the A–A section of area S1 is acting a stress whose maximum valuer1 at the crack tip is given by the moment M1 = F�a plus traction F
r1 ¼ FaW1þ F
S1ðA:7Þ
On the B–B section of area S2 the maximum bending stress r2
r2 ¼ FaW2
ðA:8Þ
with W1 and W2 being the strength moduli of sections S1 and S2, respectively.Westinghouse gave a significant impulse to the development of this typeintroducing the WOL type T specimen of Fig. A.10b [5], which was larger and
A
A
A
B
B B
F
F
pD2t
t
σ2
σ1
pressure p
pD4t
S2
S1
a
BA
A
Fig. A.10 Analogy between the biaxial stress state in a pressure vessel wall and that existingahead of the crack tip in a WOL-X or WOL-T or compact C(T)
814 Appendix: Linear Elastic Fracture Mechanics
thicker so to overcome the excessive bending experienced by type X specimen.WOL Type T specimen is wedge bolt-loaded as shown in Fig. 15.19. Type X
specimen is no longer used. The development process continued till the intro-duction of the third type of specimen worldwide known as the Compact C(T)specimen of Fig. A.9c. Today the C(T) type specimen is the most used one infracture mechanics applications. However, WOL Type T specimen is still used inSCC applications for measuring the stress intensity threshold KIscc (see Sect. 15.5).The h(a/w) and V(a/w) functions for the calculation of the corresponding K and Dfor types WOL-T and C(T) specimens are listed in the following [6]. The symbolsrefer to Fig. A.9b and c for types WOL-T and C(T) specimens, respectively.D represents the crack mouth opening displacement (CMOD), i.e., the displace-ment measured at the notch opening on the specimen surface, as shown inFig. A.9.
COMPACT SPECIMEN C(T)
KI ¼F
sffiffiffiffi
wp h
a
w
� �
ha
w
� �
¼2þ a
w
� �
0:886þ 4:64 aw
� �
� 13:32 aw
� �2þ14:72 aw
� �3�5:6 aw
� �4h i
1� aw
� � 3=2
D ¼ F
E0sV
a
w
� �
Va
w
� �
¼ 1þ 0:25aw
� �
" #
1þ aw
� �
1� aw
� �
" #2
1:6137þ 12:678a
w
� �
� 14:231a
w
� �2�16:61
a
w
� �3þ35:05
a
w
� �4�14:494
a
w
� �5� �
:
ðA:9Þ
Functions h(a/w) and V(a/w) are graphically shown in Figs. A.11 and A.12,respectively (Fig. A.13, A.14).
Fig. A.11 Diagram of the function h(a/w) for compact C(T) specimen
Appendix: Linear Elastic Fracture Mechanics 815
Fig. A.12 Diagram of the function V(a/w) for compact C(T) specimen
Fig. A.13 Diagram of the function h(a/w) for WOL type T specimen
Fig. A.14 Diagram of the function V(a/w) for WOL type T specimen
816 Appendix: Linear Elastic Fracture Mechanics
KI ¼F
sffiffiffi
ap h
a
w
� �
ha
w
� �
¼ a
w
� �
30:96� 195:8a
w
� �
þ 730:6a
w
� �2�1186:3
a
w
� �3þ754:6
a
w
� �4� �
D ¼ F
E0sV
a
w
� �
Va
w
� �
¼ exp 4:495� 16:13a
w
� �
þ 63:838a
w
� �2�89:125
a
w
� �3þ46:815
a
w
� �4� �
ðA:10Þ
A.2.3 High Triaxiality Specimens
A particular citation deserve cylindrical specimens containing a circumferentialcrack and those in three point bending since they have a very high triaxiality, evenwith smaller thickness. This are the round notch bar in traction or RNB(T) ofFig. A.15 and the three point bending TP(B) or single edge crack in bending,SE(B) of Fig. A.17, respectively. Their calibration function h(a/w) are given in thefollowing [7] (Fig. A.16, A.18).
KI ¼FL
sw3=2h
a
w
� �
ha
w
� �
¼ 3 � a
w
� �1=21:99� aw
� �
1� aw
� �
2:15� 3:93 � awþ 2:7 � a
w
� �2h i
2 � 1þ 2 � aw
� �
1� aw
� �3=2
ðA:12Þ
V ¼ F � L
E0sw
� �
qa
w
� �
qa
w
� �
¼ 6 � a
w
� �
0:76� 2:28 � a
w
� �
þ 3:87 � a
w
� �2�2:04 � a
w
� �3þ 0:66
1� aw
� �2
" #
ðA:13Þ
A.3 Three-Dimensional Surface and Internal Cracks
Figures A.19, A.20, A.21 and A.22, A.23.
Appendix: Linear Elastic Fracture Mechanics 817
2R
b a
F
F
(A.11)
RNB(T) SPECIMEN
Fig. A.15 Cylindrical specimen with circumferential crack RNB(T)
Fig. A.16 Diagram of the function h(a/w) for RNB(T) specimen
F
TP(B) OR SE(B) SPECIMEN
t
L (=4W)
Wa
δ
Fig. A.17 Schematic ofSE(B) specimen
818 Appendix: Linear Elastic Fracture Mechanics
Fig. A.18 Diagram of the function h(a/w) for SE(B) specimen
2 W
σm
σb
t
a
2c
tφ
2 c
a
A
Fig. A.19 Semi-elliptical surface crack with a c [8]
Appendix: Linear Elastic Fracture Mechanics 819
2 W
σm
σb
t
a
2c
t
2c
a
φ
A
Fig. A.20 Semi-elliptical surface crack with a [ c [8]
820 Appendix: Linear Elastic Fracture Mechanics
2 W
σm
t
2a
2c
t
2c
2a
φA
σm
d
Fig. A.21 Elliptical central crack [8]
Appendix: Linear Elastic Fracture Mechanics 821
Fig. A.22 � Ellipse corner crack with a c [8]
822 Appendix: Linear Elastic Fracture Mechanics
A.4 Cylindrical Geometries Under Pressure
Figures A.24, A.25 and A.26.
W
σm
σb
t
a
c
t
a
c
φ
Aa
Fig. A.23 � Ellipse corner crack with a [ c [8]
R t
2a
Fig. A.24 Through-wall crack [9]
Appendix: Linear Elastic Fracture Mechanics 823
References
1. Tada, H., Paris, P.C., Irwin, G.R.: The Stress Analysis of Cracks Handbook. Del Research Co.,St Louis (1985)
2. Tada, H., Paris, P.C., Irwin, G.R.: The Stress Analysis of Cracks Handbook. Del Research Co.,Hellerton (1973)
3. Brown, W.F., Srawley, J.E.: Plain Strain Fracture Toughness Testing of High StrengthMetallic Materials. American Society for Testing and Materials, ASTM STP–410 (1967)
4. Manjoine, M.J.: Biaxial brittle fracture tests. J. Basic Eng. Trans. ASME 293–298 (1965)5. Wilson, W.K.: Optimization of WOL Brittle Fracture Test Specimen. Westinghouse Research
Report 66–B40–BTLFR–R1, January 4 (1966)6. E 399–90, Annual Book of ASTM Standards, Section 3, Metal Test Methods and Analytical
Procedures, 506–536 (1990)7. Benthem, J.P., Koiter, W.T.: Asymptotic approximation to crack problems. In: Sih, G.C. (ed.)
Method of Analysis and Solutions of Crack Problems, p. 131 (1973)
pR o
RiRt
a b
Fig. A.25 Internal longitudinal surface [9]
2 c
t
a
p
p
Fig. A.26 Finite surface internal longitudinal crack [9]
824 Appendix: Linear Elastic Fracture Mechanics
8. Newman, J.C., Raju I.S.: Stress Intensity Factors Equations for Cracks in Three-DimensionalFinite Bodies Subjected to Tension and Bending Loads. NASA Technical Memorandum85793. NASA Langley Research Center, Hampton (1984)
9. Zahoor, A.: Closed form expression for fracture mechanics analysis of cracked pipes. J. Press.Vessel Technol. 107, 203–205 (1985)
Appendix: Linear Elastic Fracture Mechanics 825
Author Index
AAchilles, R.D, 804Ackermann, F., 69Adelmann, J., 190Ahmad, J., 70Ahrensdorf, K., K., 421, 474Akiniwa, Y., 71, 403Aksoy, A.M., 189Albert, W.A.J., 2, 67, 69, 188Alden, T.H., 34Allen, N.P., 191Almen, J.O., 167, 190(2)Ambriz, R.R, 581, 650Ambrose, J.R., 687Amrouche, A, 581, 650Amzallag, C., 581, 622, 768, 804, 805(2)Andersen, P.L., 687Anderson T.L., 71Anderson, W.P., 521, 578Angeli, J.P., 623Ankab, K.M., 190Araki, S., 190Arii, M., 580, 805Ashworth, V., 686Athens, A., 727Atkinson, J.D., 727(2), 805(3)Atkinson, M., 189Austen, I.M., 1, 805(2)Azou, P., 728
BBackofen, W.A., 34, 69, 188Baker, R.G., 765Banford, W.H., 580, 805(2)Barker, H., 686Barnett, W.J., 728
Barsom, J.M., 579, 580(2), 622, 615, 618,771, 774, 784, 796, 804, 805(3)
Basquin, O.H., 2, 67, 257, 314, 307, 362Bastien, P., 728Bates, R.C., 539, 541(2), 579, 581Bathias, C., 363, 579, 622(2), 804Baxter, W.J., 68Bayerlein, M., 68Beachem, C.D., 107, 108(2), 728Beck, T.R., 805Becker, W, 108Beglet, J.A., 71, 579Begley, J.A., 531, 556Benhamena, A., 581, 650Benjamin, W.D., 741, 764Bennet, J. A., 804(2)Benoit, D., 622, 804Bensch, M.M., 727Benthem, J.P., 824Bernard, G.L., 805Bernard, J.L., 581, 805Bernard, P.J., 623, 608Bernasconi A., 518, 519Bernstein, I.M., 727, 728Betteridge, W., 191Beyer, W.H., 243, 307, 403(2)Bhongbhibhat, T., 519Bishop, N.V.M., 446, 447(2), 475(3)Black, P. H., 190(2)Blackburn, M.J., 805Blasarin, A., 323, 362Blatherwick, A.A., 307(2), 402Blom, A.E., 71Boettner, R.C., 107Bonora, N., 243, 363Borodii, M.V., 509, 510(2), 519(2)Bowker, P., 728
P. P. Milella, Fatigue and Corrosion in Metals,DOI: 10.1007/978-88-470-2336-9, � Springer-Verlag Italia 2013
827
B (cont.)Boyd, R.K., 189Bradley, W.W., 764Braithwaite, F., 1, 67Brazill, R.L., 579Brearly, 689Bridgman, P.W., 262, 307(2)Briggs, C.W., 189, 306Brock, G.W., 190, 307Broeker, D.E., 727Brose, W.R., 361(2)Brown, B.F., 686, 764Brown, C.W., 623Brown, M.J., 71, 191Brown, M.W., 500, 518, 519(2)Brown,W.F., 824Bucci, R.J., 580, 805Buch, A., 190(2)Buchanan, L.W., 727Buchheit, R.G., 765Bulloch, J.H., 727, 729, 804, 805(2)Bundy, R. W., 365, 518Burk, J.V., 363Bussa, S., 362
CCaine, T.A., 727Carpinteri A., 519Carreker, R. P.,Jr., 191Carter, C.S., 764Carter, G.F., 686Castro, D.E., 622Cazaud, R., 190, 191, 306, 518Ceschini, L.J., 579, 805(2)Chaboche, J.L., 435, 436, 475Chaung, H.E., 726Chen, G.S., 764Chen, N. K., 475Chen, N.H., 446Chevenard, P., 726Che-yu Li, P., 764Chiou, S., 805Cho, E.A., 765(2)Chodorowski, W.T, 189Choi, H., 687Chopra, O.K., 68, 729Chopra, O.K., 62Chornet, E., 761, 765Chrenko, R. M., 190Cicci, F., 579Cina, B.J., 107Clark, W.G., Jr., 68, 69, 70, 71, 359, 541(2),
578, 579(2), 580(2), 581, 622, 650
Clark, W.G., 646Clarke, W.L., 727Clement, P., 623Clerivet, A., 622Coffin, L.F. Jr., 188, 314, 362(3)Coffin, L.F, 264Combrade, P., 687Compton, K.G., 764Congleton, J., 189Connelly, F.M., 336, 363Conrad, H., 189Conserva, M., 726Cook, T.S., 623Corten, H.T., 424, 428, 474, 475(2)Cotterill, P.J., 610, 623Cottrell, A.H., 77, 107, 458Coudert, E.M., 243Coughlin, R., 761, 765Cox, A.F., 727Craig W.J., 40Crews, J.H. Jr., 362Crews, J.H., 330, 431Crompton, J.S., 622Crooker, T.W., 597, 622(2), 805Crossland, B., 495, 518Crugnola F., 474Cullen, W.H., 362, 580, 781, 805(2)Cummings, H.N., 134, 139, 189(2)Czegley, M., 580
DDaniels, C., 108Darken, L.S., 728Dautovic, P.D., 727Davidson, D.L, 107Davidson, R.M., 726Davis, D.C., 518Davis, E.A., 336, 363Davoli P., 518, 519Davy, H., 666, 686Dawson, D.B., 778, 805de Castro, J. T. P., 518De Cazinczy, F., 131, 189De los Rios, E.R., 61de Moivre, A., 197de Olivera Miranda, A. C., 518De Wit, J.H.W., 726DeBold, T., 726Diegle, R.B., 687Dillamore, I.L., 727Dirlik, T., 446, 475Dixon, W.J., 307, 446Dobbelaar, J.A.L., 726
828 Author Index
Dolan, T.J., 243, 367, 402, 424, 428,474(2), 475
Dowling, N.E., 71(2), 250, 307, 361,403, 474, 531, 556, 579
Downey, F.K., 764Duckworth, W.E., 189(2), 126, 129, 139Dugdale, D.S., 50, 54, 68, 70, 386, 403DuQuesnay, D.L., 307, 403
EEbert, J., 189, 306Edwards, L., 188Eid, N.M.A., 103, 189El Haddad, M.H., 403Elber, W., 7, 598, 600, 622, 623Emanuelson, R., 805(2)Emig, P.W., 679, 687Endo, M., 53, 132, 189(3), 248Endo, T., 306(2), 362, 474Engle, R.M., 579Enomoto, K., 190Erdogan, F., 521, 578Erickson, M.A., 306Ernst, H., 622Evans, E.B.., 143, 189, 190, 306Evans, U.R., 658, 673, 687Evans, W.P., 165Ewing, J.A., 74, 337
FFaraday, M., 666Faral, M., 108Farnehough, G.D, 650Fash, J.W., 362Fatemi, A., 323, 362, 501, 510, 518, 519(2)Faupel, J.H., 145, 190Feeney, J.A., 805Feltner C.E., 30, 32Ferro, A., 307Fessler, R.R., 729Filippini, M., 518, 519Findley, W.N., 189, 498, 518Finney, J.M., 307, 366, 402Fisher, F.E, 145Floreen, S., 727Fontana, M.G., 686(2), 727, 805Ford, F.P., 679, 683, 685, 687(7)Forman, R.G., 530, 579Forrest, J.E., 727, 729, 805Forrest, P. G., 40, 154, 190, 191(2), 307(2),
367, 402, 518Forsetti, P., 323, 362
Forsyth, P.J.E., 38, 75, 77, 79, 101,107(2), 108(3)
Franz., H.E., 190French, H. J., 50, 52Freudenthal, A.M., 475Frishmuth, R.E., 519Frith, P.H., 189Frost, N. E., 50, 52, 54, 107, 131, 143,
189(2), 386(2), 403(4), 518, 578, 804Fuchs, O.H., 159, 190Fuchsbauer, B., 190Fujita, F.E., 718, 729Futami, T., 190
GGaier, M., 115Gallagher, J.P., 622, 729, 805Galvani, L., 663Gangloff, R.P., 729(2), 765(2)Gao, M., 729, 764Garret, G.G., 579Garrison, W.M. Jr., 765Garwood, M.F., 248, 307Gary, D., 321, 362Gassner, E., 438, 475Gaugh, H.J., 307Gauss, C.F., 197Gerber, W.Z., 282, 307Gerberich, W.W., 728Germer, L.H., 728Glinka, G., 650Glynn, J., 3Gomez, M.P., 578, 622Gomez. G., 521Goodacre, R., 804Goodman, J., 282, 307Gordon, J.R., 650Gorla C., 518, 519Gosset, W.S., 204Goto, M., 190Gough, H.J, 8Gough, H.J., 2, 34, 246, 306, 479(2),
488(3), 517(2), 518Gouma, P.I., 765Gowda, C.V.B., 363Graville, B.A., 765Gray, R.A. Jr., 650(2)Green, J.A.S., 727(2)Greene, N.D., 686(2)Griffith, A.A., 583, 622, 728Griffiths, A.J., 727Grinberg, N., 95, 107(2)Groeneveld, T.P, 729
Author Index 829
G (cont.)Groover, R.E., 764Gross, T. S., 108, 189Grover, H.J., 307, 402, 403(2), 434, 475Gumbel, E.J., 224, 243Güngör, S., 188Gurney, T.R., 650Guthrie, E.C., 475
HHaangsen, P.J, 650Hackett, E.M., 581, 579Haibach, E., 264, 307Haigh, B.P., 282, 307, 479, 519, 308Halford, G. R., 321, 362, 434, 475(2), 493, 518Hall, E.O., 204, 307Hamada, S., 580Hanna, G.L., 579Hanninen, H., 729, 805(2)Hardie, D., 728Hardrath, H.F., 371, 403, 475, 623Härkegård, G., 243Harrison, T.C., 639, 650Hartman, E.C., 189Hawtorne, J.R., 650(2)Hayden, H.W., 727(2)Hayes, M., 190Heidenreich, R., 519Hellman, D., 579Hempel, M.R., 39, 186, 191, 307Hengell, H.J., 726Henky, D.L., 430, 475, 485Herman, E.C.M., 726Hertzberg, R.W., 538, 579, 580, 622,
623, 650Heuler, P., 363Hewing, J.A., 2Heywood, R.B., 189, 306, 366, 371,
380, 402, 403Hicks, M.A., 623Higuchi,M., 805Hirschberg, M.H. 362(2)Hirth, J.P., 728Hoar, T.P., 687(3)Hobson, P.D., 59, 63Holden, J., 189Hopkinns, S.W, 622Hoppe, W., 579Howell, F.M., 189, 307, 308Huang, W.C., 363Hull, D., 77, 107Humphrey, J.C., 3, 37, 74Hutchings, J., 106, 767, 804
Hutchinson, T. P., 243Hyler, W.S., 402
IIguchi, H., 459, 475Iida, K., 649, 650, 778, 805Ikegami, T., 190Imhof, E.J., 579(2), 580, 771, 804, 805Indig, M.E., 675, 687(2), 727(2)Ineson, E., 126, 129Innueber, J., 726Irvine, K.J., 805Irwin, G. R., 5, 524, 579, 586, 824(2)Issler, L., 519Itho, T., 505, 519(3)Itoh, F., 650Iwasaki, S., 190
JJacko, R.J., 805Jackson, L.R., 307, 402, 403(3)Jacobs, F.A., 441, 475Jacoby, G., 421, 474Jacques, H.E., 403James, L.A., 107, 579, 580(2), 581Jayaraman, N., 190Jernkont., 189Jewett, C.W., 727John, C.F.St., 727Johnson, H.H., 687, 727, 728, 764(2)Johnson, H.H., 741Johnson, M.J., 726Johnson, R. C., 188Johnston, T. L., 107Joice, J.A., 579Jones, D.A., 686Jones, J.W., 581Jones, R.H., 728Jones, R.L., 189Jones, R.V., 687Josephic, P.H., 728Joyce, J.A., 581Jung, J.Y., 363Juvinall, R.C., 188, 284, 306, 308
KKachanov, L.M., 435, 475Kado, S., 645, 650Kakuno, H., 495, 518Kameoka, M, 519Kanazawa, K., 505, 519(2)
830 Author Index
Kanazawa, T., 649Karry, R.W., 303Kassner, T.F., 726, 727Kaufman, R. P, 518Kaufman, R.P., 498Kawada, Y., 495, 518Kawaghishi, M., 107Kawagishi, M., 623Kawamoto, M., 479, 517, 519Kawasaki, T., 107Kearney, V.E., 579Keddam, M., 726Kemppainen, M., 729, 805Kemsley D.S., 16, 30Kerry, R.W., 367Kershaw, J., 579Keys, R.D., 191Khokhlov, S.F., 728Kida, S., 505, 519Kihara, H., 637, 638, 649, 650Kim, C.D., 765Kim, S., 608, 623Kitagawa, H., 44, 48, 53, 623Klesnil, M., 107, 531, 579, 590, 622Knott, J.F., 579(2), 619, 623(2)Kobayashi, M., 52, 232Kobayashi, H., 805Kodama, S., 265, 307Koh, S.K., 323, 362Koiter, W.T., 824Kommers, J.B., 518Kondo, T., 580(2), 805(2)Kondo, T., 773, 786Krauser, D.J., 622Kruger, J., 687Kuhlmann-Wilsdorf, D., 91, 107Kuhn, P., 371, 403(2)Kung, C.Y., 189Kunio, T., 40Kuniya, J., 580, 805Kunz, L., 403Kuribayashi, H., 623Kurihara, M., 580, 805Kusuda, T., 649Kwon, H.S., 765(2)
LLa Vecchia, G.M., 649Lai, G.Y., 727Laird, C., 16, 30, 31, 49, 91, 107Landes, J.D., 580, 741, 742, 764(3),
798, 800, 805(2), 803Landgraf, R.W., 361, 362(3)
Lange, E.A., 805Langer, B.F., 418, 474, 518Lankford, J., 59, 66, 107, 613, 623(5)Lanza, G., 479, 517Laplace, P.S., 197Latanision, R.M., 717, 728Lawrence, F.V.J., 69, 340, 403Laycock, N.J., 764Lazan, B.J., 307(2), 402Lee, S.B., 496, 518Lee, Y., 243Lees, D.J., 687Leger, J., 108Leis, B.N., 70, 363Lemaitre, J., 427, 435, 436, 475(2)Lempp, W., 519Leoni, M., 726Lesterlin, S., 804Li, 655Liao, C.M., 764Liaw, P.K., 107, 189Lieberman, G.J., 209, 243Light, M. C., 475Light, M.C., 445Liljeblad, R., 637, 650Lindley, T.C., 623Lipsitt, H.A., 68Lipson, C., 306, 403Lipzig, H.T.M., 190Liu, H.W., 524, 579(2)Liu, J., 519Liu, Y.C., 107López, V.H., 581, 650Loss, F.J., 580, 639, 650(3)Louat, N., 38, 69Love, R.J., 143, 189Low, A.C., 307Lowrence, F.V., 363Lu, M., 728, 729Lüdwick, P.Z., 335, 363Lukáš, P., 45, 69(2), 70(4), 403, 531,
579, 590, 622Lumsden J.B., 726Lutz, G.B., 188Lynch, S.P., 728Lyst, J. O., 190
MMa, B.T., 49Macrae, A.U., 728Maddox, S.J., 640, 650(3)Mager, T.R., 580(2) , 640, 805Maiya, P.S., 363
Author Index 831
M (cont.)Makhlouf, K, 581Malkin, V.I., 728Manjoine, M.J., 336, 363, 475, 824Mann, J.Y., 366, 402, 518Manson, S.S., 34, 314, 321, 362(4), 434,
475(2) , 475, 493, 518Manson, W., 479Marci, G., 622Marco, S.M., 474Maré, J., 306Marin, J., 475, 494, 518(2)Marissen, R., 622Marquis, G. B., 519Marry, R.W., 402Marsh, K. J., 189, 403, 518Martin, D.C., 635, 649Martin, J.F., 362Masing,G., 311, 312Mason, W., 517Masubuchi, K., 649(3)Masubuchi, T., 650Matake, T., 500, 518Mathur, P.N., 189Matocha,K., 490, 580Matsubuchi, K., 635Matsuda, K., 43, 69Matsuishi, M., 378, 474Matsumoto, T., 190Mattos, O.R., 726Maurer, 689Maxwell, 483May, M.J., 803, 806(3)Mayer, H.R., 580Mazzetti, P., 307McCabe, D.E., 650McCammon, R.D., 191McClintoc, F.A., 106, 579McCoy, R.A., 728(2)McDiarmid, D. L., 502, 518(2)McDonald, D., 675, 687McEvily, A.J., 531, 579, 623McGowan, J.J., 639, 650McGreevy, T.E., 251, 307McIntyre, P., 764McLuoghlin, V., 580, 805McMillan, J.C., 623McMinn, A., 580Medvedev, É.A., 728Meggiolaro, M. A., 518Mehl, R.F., 116, 189Mendizza, A., 764Mesmacque, G., 581, 650Meyers, M.A., 475
Mielke, S., 519Miki, K., 650Milella, P.P., 19, 29, 83, 95, 98, 101, 105, 115,
123, 134, 143, 181, 228, 311, 336, 366,367, 532, 553, 585, 587, 243, 362,363(3), 622(2)
Miller, J.L., 307(2)Miller, K.J., 189, 500, 518, 519(2), 580Miller, M.S., 622Mills, W. J., 579, 580Miner, M. A., 418, 474(2)Mirdamadi, M., 518Mitchell, L.D., 32, 145, 190Mitchell, M.R., 68Mittemeijer, E.J., 190Miyamoto, T., 189Mizumo, I., 687Montague, W.G., 727Montalenti, G., 307Mood, A.M., 264Mood, D.M., 307, 579, 580Moody, N.R., 765Moon, D.M., 805(2)Moore, H.F., 145, 190, 518Mori, T., 475(2)Morrison, J.L., 307Morrow, J.D., 68(2), 263, 287, 307,
308, 315, 320, 362(6), 363Mott, N.T., 78Mughrabi, H., 69Munse, W.H., 188Munz, D., 622Murakami, Y., 53, 69, 70(2), 130, 132, 134,
189(5), 243(3), 248, 307(2), 580Muramatsu, T., 189
NNakajima, H., 580Nakanishi, S., 107Nakayama, H., 475(4)Nakazawa, H., 52, 70, 132, 265, 307Natsume, 130Natsume, Y., 189Naumann, E.C., 441, 475Navarro, A., 71Nelson, D.V., 165, 190Nelson, H.G, 108, 765Nernst, W., 654Neuber, H., 3, 67, 331, 363(2), 366,
367, 369, 371(2), 376, 402Neugebauer, J., 514, 519Neumann, P., 70, 188Newbegin, R.L., 764
832 Author Index
Newman, J.C., Jr., 531, 579, 602,623(2), 824
Newman, J.F., 687(2)Newmann, R.C., 764Newmark, N.M., 474(2)Nichols, F.A., 727Nichols, R.W., 637, 650Nine, H.D., 91Nishiara, T., 479Nishihara, T., 517, 519Nisitani, H., 69Niu, X., 650Nordberg, H., 650Nose, H., 475Novak, S.R., 764(2)Nowak, H., 622
OO’Conner, H.C., 307O’Connor, B.P.D., 475Oba, H., 649Oba, H., 650Obataya, Y., 519Ogawa, T., 71(2), 622Ohgi, G., 518, 495Ohnami, M., 519(2)Ohya,K., 622Okabe, N., 475(2)Opperhauser, H., 728Oriani, R.A., 728(2)Ortiz, K., 446, 475Osage, D.A., 71Osako, S., 71Osgood, C.C., 190Osozawa, K., 726Overbeeke, J.L., 190
PPalmgren, A. Z., 418, 474Palusamy, S.S, 189Pao, P.S., 728, 805(2)Papadopulos, I. V., 492, 496, 518(2), 519Paris, P.C., 5, 521(2), 527, 538, 578(2), 579(2),
580(2), 687, 727, 764, 824(2)Parkins, R.N., 687Parry, M., 650Paxton, H.W., 765Pearson, S., 623Pednekar, S.P., 687Pelilli, G., 362Pelloux, R.M.N., 108(4), 579, 580,
623, 106, 778, 805
Persoz, L., 190Petch, N.J., 43, 189, 307, 713Petch, N.O., 728Peterson, M.H., 764Peterson, R.E., 68, 308, 367, 369(2),
371, 376, 402(2), 403(2)Petit, J., 804Petrone, N., 474Phelps, E.H., 729Phillips, C.E, 51, 189, 366, 402Pickard, A.C., 579Pineau, A., 610, 623Piper, D.E., 764Plantema, F.J., 474Plumtree, A., 427, 475(2)Pokidyshev, V.V., 728Polakowski, N.H., 20Pollard, H.V., 517Pollok, W.J., 727Pomp, A., 307Pompetzki, M. A., 307Poncelet, 1Pook, L. P., 107, 189, 403, 518Portevin, A., 726Pourbaix, M., 653, 686Powell, D.T., 728Prevéy, P.S., 190Procter, R.P.M, 76
RRabbe, P., 581, 622, 804Radaj, D., 517Raj, R., 728Raju, I.S., 824Rankine, W.J.M., 3, 67, 365, 402Ranson, J.T., 147, 189Rau, C.A., Jr., 622Raymond, M.H., 188Reemsnyder, H.S., 340, 363Reightler, C.L., 191Ren, W., 189Rice, J.R., 603, 623Rice, R.C., 107Richard, C.E., 623Richart, F.E., 474(2)Richter, I., 519Ricklefs, R.V., 165, 190Riecke, R.M., 727Rilly, J.T., 243Ritchie, R.O., 579(2), 603, 623Roberts, R., 623Roberts, W.T., 727Robertson, W.D., 728
Author Index 833
R (cont.)Robinson, S.L., 765Roe, C., 581Rolfe, S.T., 580, 622, 764, 774Rone, J.W., 188Rosemberg, H.M., 191Rozendaal, H.C.F., 190Ruiz, A., 581, 650Rungta, R., 107Ruther, W.E., 727Rybicki, E.F., 650Ryder, D.A., 101
SSaanouni, K., 363Sakamoto, I., 475Sakane, M., 519Saraceni, M., 474Sarrazin-Baudoux, C., 804Sato, K., 579Savaidis, G., 491, 518Schaffer, J., 107Schijve, J., 107(2), 307, 403, 441,
474, 475(3), 622(5)Schneider, C.S., 579Schottky, H., 726Schulte, W. C., 189(2), 308Schütz, W., 293Schwalbe, K.H., 579Schwartzberg, F.R., 191Scott. P.M., 71, 727, 805(2)Scully, J.C., 728, 687Searles, J.L., 765Seeger, T., 341, 363, 491, 518Shack, W.J., 729Shahinian, P., 580Shamsaei, N, 507, 519(3), 510(2)Sheldon, G.P., 623Sherratt, F., 447, 475Shigley, J.E., 145, 190Shih, T.T., 500Shimizu, T., 190Shimokava, H., 643Shimokawa, H., 650Shimuzu, M., 41Shiram, S., 108Shives, T.R., 804Shnol, E.M., 728Shoesmith, D.W., 687Shoji, T., 687Shukaev, S.M., 510, 519Shulte, K., 622
Shulte, O.E., 190Siebel, E., 188, 403Siebel, E., 115, 372Siegl, J., 580Sims, C.E., 728Sinclair, G.M., 40, 190, 243, 307,
362, 474, 638, 805Sines, G., 403, 518(3)Slama, G., 581, 805(2)Smalowska, Z., 687Smith, G.C., 69Smith, H.H., 580Smith, H.R., 7, 738, 764Smith, I.O., 727Smith, K.N., 322, 362, 501Smith, R.N., 69, 362, 518Smith, W.F., 686Smith,G.C., 45Snow, A.L., 518Socie D. F., 362, 518, 519(4)Soderberg, C.R., 282, 307Solonen, S., 729Sonsino, C. M., 517Soppet, W.K., 726Sovak, J.F., 805Spagnoli A., 519Speidel, M.O., 805Spitzer, R., 475Sprowls, D.O., 804Srawley,J.E., 824Srivatsan, T.S., 108Stables, P., 713, 728Stadnick, S.J., 362Staehle, R.W., 686, 726, 727Stallmeyer, J.E., 188Stanzl, S.E., 580Starke, E.A. Jr., 68(2)Starkey, W.L., 474Steigerwald, E.A., 579, 741, 764(2)Stephens, R.I., 68, 159, 190, 323,
362, 519Stickler, R., 70(2), 71, 403, 726Stieler, M., 372, 403Stirling, 225Stonesifer, R.B., 650Strauss, B., 689, 691, 726Stubbington, C.A., 38, 68, 69, 77, 107(2)Student (Gosset, W. S.), 243Stulen, F. B., 189(2)Suresh,S., 603, 623Susei, S., 649Svensson, T., 247, 307Swanson, S.R., 527, 579
834 Author Index
Sylvestrowicz, W., 307Szclarska-Smialovska, Z., 726
TTada, H., 824(2)Tai, W., 623Taira, S., 41, 475Takahashi, S., 44Takaku, H., 580, 805Takena, K., 650Takenouti, H., 726Takeuchi, N., 623Talda, P.M., 579, 764Tanaka, K., 403, 475, 622Tanaka, K., 589Tanaka, S., 190Tanaka, T., 475(3)Tate, A.E.L., 40, 367, 402, 518Tavernelli, J.F., 362Taylor, D., 623Tedmon, C.S., Jr., 727Templin, R.L., 143, 189, 366, 402Terrell, J.B., 362Tetelman, A.J., 728(2)Thomason, P.F., 128, 189Thompson, A. W., 727, 728Thompson, N., 38, 55, 91, 107, 188Tice, D.R., 805Tien, J.K., 728Tillmann, H.E., 186, 191, 498Ting, J.C., 403Tippett, L.H.C.Tokaji,K., 622Tokimasa, K., 580Tomashou, N.D, 687Tonnessen, A., 188Topper, T.H., 307, 322, 332, 362(2), 363(2),
403(2), 501, 518(2)Toriyama, T., 189, 243Torronen, K., 729, 805(2)Toryiama, T., 130Traficante, M., 362Traswell, A.E., 727Trautmann, K.K., 622Troiano, A.R., 703, 713, 727, 728Troshehenko, V.T., 243Truchon, M., 622Trushon, M., 804Truswell, A.R., 805Tschegg, E.K., 580Tsuji, H., 580Tucker, L.E., 361, 362
UUmemoto, T, 190(2)Unocic, K.A., 726Usuki, H., 243
VVan der Sluys, W.A., 728, 781, 803, 805, 805Van Wiggen, P.C., 190Varadan, V.K., 728Vašek, A., 70Vassilaros, M.G., 579Vazquez, J., 622Vecchio, R.S., 622Verastinina, L.P., 687Vermilyea D.A., 687(2), 727(3)Vinckier, A., 726Volta, A., 663Von Euw, E.F.J., 623von Mises, R.E., 483Vosikovsky, O., 805
WWadman, B., 306Wadsworth, N. J., 38, 55, 69, 70, 91,
106, 107, 188, 804Wahl, A.M., 308, 402Waisman, J.L., 403, 518Walcher, J., 321, 362Walker, E.F., 805(3)Walker, E.K., 340, 363, 590, 593, 622, 803Wan, K.C., 764Watkinson, F., 765Watson, H.E., 580(2)Watson, P., 322, 362, 501, 518Weber, J.E., 687Weertman, J., 531, 579Wei, R.P., 188, 579(2), 729(3), 741, 742, 743,
764(3), 765(2), 798, 800, 803, 805(4)Wei, W., 805(2)Weibull, W., 212, 243, 524, 579Weiderhorn, S., 764Weir, T.W., 728Weiss, B., 70(2), 71, 403Wener, T., 362Wessel, E.T., 580, 622Wetzel, R.M., 332, 362, 363(2)Wheeler, O.E., 606, 623, 697Whener, T., 323Wilde, B.E., 765Wilkowski, G.M., 71Wilks, T.P., 189
Author Index 835
W (cont.)Williams, C.R., 209, 243Williams, D.P., 764, 765Willner, A.M., 741, 764Wilson, D.V., 727Wilson, I.L.W., 805Wilson, J.S., 282, 308Wilson, W.K., 361, 363, 824Wirsching, P.H., 445, 475Wöhler, A.Z., 2, 67, 280, 307Wood, W.A., 307Work, C.E., 474Wozniak,J., 580Wright, J.C., 727Wulpi, D. J., 107
YYamada, K., 42Yano, T., 475
Yates, J.R., 580Yeom, K.A., 765Yokobori, T., 68, 107, 579, 623Yokoyama, N, 580You, B.R., 407, 518Yu, M. T., 307, 403Yuuki, R., 71
ZZahoor, A., 824Zamrik, S.Y., 493(2), 518, 519Zapffe, C.A., 728Zenner, H., 512, 519(2)Zhang, S., 601, 622Zhao, W., 71Zubko, A.M., 728Zurburg, H.H., 307
836 Author Index
Subject Index
AActivation energy in SCC, 263Almen test, 167, 169Anodic dissolutionAluminum alloy
type 2017-T4, 538type 2023-T3, 601type 2024-T3, 19, 255, 280, 538type 2219-T851, 597type 2618-T651, 588type 5454-0, 16type 5456/H321, 551type 6060-T6, 769type 6061-T6, 258, 648type 6061-T651, 7, 16, 33, 103type 6082-T6, 118type 7022, 33type 7075-T6, 7, 16, 19, 59, 159, 255, 295,
551, 774type 7079-T651, 752type 7475-T7531, 601, 603
Anisotropyeffect on fatigue, 142, 173, 478
anodic dissolution model. See Passive filmrupture
Athermal flow stress component, 182Austenite hardening, 20austenitic stainless steel. See Stainless steel
BBaking-out of hydrogen, 567, 703, 705, 762Basquin line, 257, 273Basquin’s exponent. See Fatigue strength
exponentBeach marcks, 81, 87, 88Bridgman equivalent stress, 262
Bifurcation. See BranchingBlue brittleness.See Dynamic strain agingBluing
corrosion resistance, 722Branching
effect on crack growth, 626Burnishing. See cold-rolling
CCarburizing, 174Cast iron
traction and fatigue strength, 481, 488Cathodic protection, 666Cementite, 123Central tendency, 196CERT test. See Corrosion measurementsChi-square function, 209CMOD. See Crack mouth opening
desplacementCoating. See PlatingCOD. See Crack opening desplacementCoining
effect on fatigue, 161Cold cracking, 629Cold-rolling. See Cold workingCold-working
effect on fatigue, 159, 160Hydrogen embrittlement, 712
sensitization, 697Cold work anodic hardening, 665Confidence level, 201corrective coefficient in fatigue. See Fatigue
corrective coefficientCorrosion
anodic dissolution, 658anodic reaction, 659
P. P. Milella, Fatigue and Corrosion in Metals,DOI: 10.1007/978-88-470-2336-9, � Springer-Verlag Italia 2013
837
C (cont.)cathodic protection, 666crevice, 672generalized, 651localized, 651low potential SCC, 658redox reactions, 659threshold, 735
Corrosion measurementCERT method, 682, 692, 750potential pulsing method, 683
Corrosion assisted fatigueCottrell’s atmosphere
effect on yield strength, 458, 715Crack
bifurcation, 610closure, 597tunneling, 534ultrasonic monitoring
Crackingbead shape induced, 630cold, 629hot, 629hydrogen inducedin the HAZ, 627longitudinal, 627segregation induced, 629surface profile induced, 630tranverse, 627
Cracksat inclusions, 124, 126dormant. See Non-propagatingintergranular, 41longnon-propagating, 50small or short, 610surface, 43
Crack mouth opening displacement, 534Crack opening displacement, 534Crest factor in PSD, 452Crevice corrosion, 672Cross slip, 34Crystallographic planes. See Slip planesCumulative damage. See Miner ruleCumulative distribution function, 200Cumulative probability function, 197Cycle counting, 407
four-point, 411hysteresis loop, 415level crossing method, 407rainflow method, 415three-point method, 411
Cycle ratio. See DamageCyclic hardening, 5, 13, 18, 28, 33, 115
Cyclic softening, 5, 28, 33, 115Cyclic stress-strain curve, 17, 20
incremental step test, 18, 31multiple specimens, 17, 31
Cyclic strain hardening exponent, 311Cyclic strength coefficient, 311Cyclic strength modulus, 311Cyclic strength modulus, 311
effect on fatigue, 783
DDamage
cumulative, 416, 420critical curve, 46, 50cycle ratio, 418double linear rule, 433impact loads, 457line, 46linear, 430non-linear, 422, 427, 432nucleation, 35progression, 416, 420submicroscopic, 46
Decarburizingfatigue life reduction, 21, 33
defects (see also Inclusions)maximum expected, 242
degrees of freedom of a population, 196Deviatoric stressDimple rupture, 57, 123, 124direct current potential drop. See Potential
dropDislocation
Cottrell’s atmosphere, 458, 715movement, effect on yielding, 458forest, 33
Distortion strain energy, 483Driving force. See Energy release rateDuctile cast iron, 32
cyclic curve, 19, 32fatigue strength, 249
Ductile fracture, 57, 79, 82Dynamic loads. See Impact loadsDynamic strain aging, 182
EEffective stress intensity factor, 594–604Electrochemical potential, 653, 663, 666Energy absorption rate, 583energy release rate, 583Endurance limit.seeFatigue limitEquivalent elastic stress, 10, 18, 382
838 Subject Index
Equivalent spectrum method, 456Equivalent stress
multiaxial fatigue, 480maximum shear stress theory orTresca
theory, 152, 482von Mises theory, 152, 483
Error function, 200Euler’s function. see Gamma function
extrusion, 77, 116Evans diagram
corrosion potential, 669Exchange current
at electrode potential, 669
FFailure theories
maximum normal stress, 481Coulomb-Mohr, 481modified Mohr theory, 481Tresca or maximum shear stress, 482distortion strain energy, 483triaxiality factor, 492
Faraday constant, 679Fatigue
corrective coefficients, 110delayed retardation, 608Haibach correction, 268, 468initiation, 55in vacuo, 105, 768limit, 6, 14, 33, 43, 118overload retardation, 604sigmoidal curve, 529stage I, 53, 62stage II, 55, 62stage III, 57time dependent life, 14
Fatigue appearancefactory roof, 106, 544intergranular, 41, 83saw-tooth, 544transgranular, 41, 83
Fatigue crack growth measurementultrasonic monitoring, 533potential drop technique, 535specimen compliance, 533
Fatigue ductility coefficient, 314Fatigue ductility exponent, 259Fatigue crack growth
aluminum alloys, 550carbon steels, 546ductile cast iron, 553martensitic steels, 545stainless steels, 549
titanium alloys, 552Fatigue specimens, 114Fracture mechanics specimens, 533, 809
central crack panel, 809double edge crack panel, 809single edge crack panel, 809type WOL, 813
Fatigue strength coefficient, 257Fatigue strength exponent, 257Fatigue tests, 111
alternate torsion, 111equivalent specimen method, 323reverse bending, 111rotational bending, 111staircase method, 264, 273tension-compression, 111tension-tension, 111
Fibersprocess volume, 145, 217
Finite population correction, 199Fillet weld
concave profiles, 630convex profile, 630
Fish eye defect, 177Flow stress
athermal component, 182plastic collapse, 563thermally activated component, 182
Fourier analysis, 447autocorrelation function, 449forward transform, 449inverse transform, 449
French’s curve, 49, 420Frequency
effect on corrosion fatigue, 773
GGalvanic cell, 663geometrical discontinuities. see Structural
notchesGerber parabola
effect of mean stress, 282Goodman line
effect of mean stress, 282Gamma function, 205Gauss’ law of errors distribution. see
NormaldistributionGaussian distribution. see Normal
distributionGibbs free energy, 654Grain boundaries
Persistent, 402size effect on fatigue limit, 144
Subject Index 839
G (cont.)Graphite in cast iron
degenerated, 123, 125Griffith theory, 583Grinding sensitization, 697, 699Gumbel distribution, 224, 242
HHaibach correction
S-N diagram, 264Haigh diagram, 289, 294Hall-Petch equation, 251Hall-Petch-Murakami model, 251HAZ. see Heat affected zoneHeat affected zone, 508, 513Heat treatments, 139high cycle fatigue, 13Hot cracking, 630Hydrogen
outgassing, 631Hydrogen baking-out. see Hydrogen
outgassingHydrogen
absorption or chemisorption, 711, 714,718, 756, 761
embrittlement, 630, 701, 711, 722external, 702, 705internal, 702low potential stress corrosion, 656
Hydrostatic stress, 484hysteresis loop, 310
IIHSI.see Induction heating stress
improvementImpact fatigue, 457Impact factor, 457Inclusions, 65
alumina, 125effect on fatigue, 122, 126, 127, 136, 141effect on steel strength, 33effect on stress corrosion, 684, 693, 707,
718, 723manganise sulfide, 125, 131, 137, 139, 630,
707, 723, 734probability of existence, 138rating method by statistics of extreme, 242
Incremental stress test, 17, 31Incubation time
stress corrosion, 741Induction heating stress improvement, 169Initiation curve, 47
Intergranular stress corrosion cracking, 692interstitial atoms (see also Cottrell’s
atmosphere)dislocation locking, 715
IRMSE. see Inclusion rating methodby statistic ofextreme
Irregularity factor, 408, 445Irwin plastic zone. see Plastic zone
KKitagawa-Takahashi diagram, 44, 53, 124, 128knee of fatigue diagram, 13, 33, 256
LLieberman factors, 209, 230limit load. see Plastic instabilityLoad type
effect on fatigue, 150, 222Load spectra
equivalent spectrum, 456irregularity factor, 408, 445narrow band, 409, 442representation and counting, 407variable, 437wide band, 409, 442, 445
Log-normal distribution, 201, 226, 232Low-cycle fatigue, 6, 13Lower confidence limit, 203Low plasticity burnishing, 162low rising test. see CERT testLPB. See Low plasticity burnishing
MManson-Coffin relationship, 314Magnesium
type ZK 60A-T5 alloy, 797Martensite plates, 42, 124, 175Masing hypothesis, 312Master curve, 295Mean stress effect, 280, 319, 383Mean stress sensitivity factor, 287Mean (statistics)
arithmetic, 195, 197, 226true, 196
Mean rank, 216Median rank, 216Median value, 197Memory effect
in fatigue, 325Mechanically small cracks, 29, 45, 61Metallurgical variability. See Process volume
840 Subject Index
Microcrack density, 48, 52, 58Miner rule, 328, 418Miller’s index, 37Mirror-polished finish, 116Modal value, 197Mode. See Modal valueModified Goodman diagram, 305Morrow correction, 320Morrow line, 288Morrow M factor. See Mean stress
sensitivity factorMSC. See Mechanically small cracksMoments of power spectral density, 452Multiaxial fatigue, 477
proportional loading. See In-phase loadingIn-phase loading, 477Out-of-phase loading, 477, 503Failure theories, 479
Murakami-Endo equation, 134
NNarrow-band random process, 409Necking
In traction test, 260Nernst equation, 654Neuber’s constant, 332Neuber’s rule, 330, 334Nickel alloy
type Astroloy, 588type X750, 538, 541, 552type 600, 552waspaloy, 19
Nitriding, 174Non-metallic phases, 33Non-proportional hardening, 505
coefficient, 505exponent, 505
non-proportional loads. See Multiaxial fatigueNormal distribution, 197Normalizing, 172Notch factor, 366Notch sensitivity index, 368Notch effect on S-N curve, 380Notch effect saturation, 386Notch strain hardening, 390NP factor FNP, 505Number of peaks in sample, 339
OOne-sided tolerance limit, 207Outgasing (hydrogen), 567Out-of-phase loads. see non-proportional loads
Overheatingeffect on fatigue, 172
Overloadeffect on fatigue strength, 328, 604
Oxidation potential, 660Owen factors, 209
PParis-Erdogan equation, 529Passivation
to corrosion, 671Palmgren-Miner rule. See Miner’s rulePassive film rupture, 674, 678, 689, 706, 733Peak value. See Modal valuePearlite, 123, 125Petch equation, 136Phase difference
effect on fatigue, 512Pitting, 733Plain strain condition, 334Plain stress condition, 334Planar slip, 28, 34, 78Plastic constraint factor, 586Plastic instability, 460, 467Plastic modulus, 311Plastic relaxation, 91Plastic wake
on crack flanks, 592Plastic zone
at crack tip, 592, 605, 607Plating
effect on fatigue, 178Polarization diagram, 668Potentio-dynamic polarization method, 690,
695Polarization
in electrochemical reactions, 541Porosity, 626Potential drop test method, 535Power spectral density, 450Purbaix diagram, 653Postweld heat treatment, 636Prestressing
effect on fatigue, 155, 636Probability density function, 196Probability of failure, 200Probability of survival, 200Probability paper, 203Process volume
effect on fatigue, 110, 144, 150, 153, 195,216, 238, 240, 375
Push-pull. Seefatigue testtension-compression
Subject Index 841
RR-ratio (see also mean stress effect)
effect on fatigue, 280, 588, 591, 593, 598,602, 640, 785
Ratched marks, 88RMS. see root mean squareRamberg-Osgood power low, 221Rank
of a sample, 174Redox reaction. See corrosionReheating
effect on fatigue, 173Relative stress gradient
in notch sensitivity, 372Residual stresses
due to machining, 120due to notches, 136due to welds, 633effect on Neubr’s rule, 340
Resolved shearing stress, 36Root-mean-square method, 451Run out
in fatigue, 265
SSaturation frequency
in environmental fatigue, 783Scale factor, 212Scanning electron microscope, SEM, 73SCC. see stress corrosion crackingSchmid’s factor, 36Schmid’s law, 36Second phase particles, 122, 125
phasealumina, 125azide a, 182carbide e, 182carbides, 123effect on steel strength, 122hydride, 718manganise sulfide, 125, 137, 131, 139, 630,
707, 734oxides, 123phase e, 123phase g, 123phase c, 123silicates, 123sulfites, 123Titanium carbonitride, 1125, 123
Segregation induced cracking, 629Sensitization of metals, 690
by cold work, 697SFE. see stacking-fault energy
Shake-down effect, 156, 289Shape of corrosion pits, 591Shear lips, 57, 60Shieincage cavities in cast iron, 129Shot peening, 162Siebel and Stieler method, 322Silver (strength), 185Size effect. see process volume effectSlag inclusions, 631Slip bands, 26, 27
by cold-working, 697corrugated, 38cross slip, 38impact loads, 463intersecting, 38, 115persistent, 38segmentay, 25, 37
Slip direction, 36Slip lines, 25, 27
in austenitic stainless steel, 115persistent, 27planar, 23segmentary, 26wavy, 23, 29
Slip planes, 36interaction, 478
Slip systems, 24Small scale yielding, 525Smith diagram, 294Smith-Watson-Topper model, 322S-N fatigue curve, 5, 109
modified, 110Spectral power density, 442Spring back effect. See shacke-down effectSpring index, 302SSY. see small scale yieldingStacking-fault energy, 34, 506Stainless steel, 549
austenitic type, 304, 10, 20, 549austenitic type 304L., 664, 690austenitic type, 316, 549austenitic type, 321, 549austenitic type, 350, 549cast type, 351, 549ferritic type 18Cr/Nb, 549martensitic type, 403, 5499Cr1Mo, 607
Steel-carbontype A, 106, 15, 185type A 201, 9, 11type A, 302, 9type A, 333, 15type A, 508, 589, 772type A, 514, 647
842 Subject Index
type A, 533, 7, 15, 61, 589, 647, 772, 779,780, 786, 788
type AISI 1018, 546type Fe, 460, 491
Steel nickel-crome/cobalt-molibdenumNiCrMoV, 61110NiCrMoCo, 77512Ni5Cr3Mo, 777, 785, 79810Ni8Co1Mo, 546type, 106, 15, 185, 582
Steel high strength5Ni, 5469Ni, 54618Ni, 738, 763HY, 80, 546HY, 130, 546, 775NiMoV, 537Type 4130, 295, 384type, 4340, 11, 17, 19, 21, 31, 33, 120, 144,
188, 295, 537, 705, 749, 751, 763, 773,778
type 9Cr1Mo, 493Steel
type 18Mn-5Cr, 750type 835 M, 30, 749
Static fatigue. See stress corrosionStrain rate
for SCC, 752–757Strauss solution. see Strauss testStrauss test
sensitization of austenitic SS, 691Stress corrosion crackig, 7, 651, 731Standard deviation, 198Standard error, 198Strain
controlled S-N curves, 14hardening, 18cyclic, 15hardening exponent
static, 34softening
saturation, 29Strain aging
dynamic strain aging, 182Strain life curve, 314Strain rate hardening
effect on fatigue, 547Strength coefficient, 18Stress concentration factor, 366Stress controlled S-N curves, 8Stress intensity factor, 5
definition, 524Stress ratio, 281Stress relaxation
in fatigue, 319Stress corrosion
by anodic dissolution, 674, 678, 689by hydrogen embrittlement, 674threshold, 735, 746
Stress gradienteffect on fatigue, 150, 370, 373, 377
Stress intensity factorfatigue threshold, 529
Stretched-zone, 586, 587Striations, 79, 93, 538, 539
brittle, 97, 100–102, 792Structural notches, 304Student’s distribution, 204, 231Sulfide anions
effect on corrosion, 683, 684, 693, 707,718, 723, 734, 752
Surface energy, 583Surface finish
effect on fatigue strength, 33, 35,58, 115, 120
Surface hardness, 14SWT parameter
fatigue damage, 322
TTemperature
effect on fatigue, 179, 557, 771effect on mechanical properties, 179
Test methods. See fatigue test methodsThermal treatments
effect on fatigue, 172Thermo-mechanical treatments
effect on fatigue, 168Threshold stress intensity factor, 587TIG dressing, 644Time dependent life, 5Tire tracks mark, 96, 98Titanium alloy
type Ti-6Al-4V, 106, 598, 596, 771, 781type Ti-8Al-1Mo-1V, 19, 787
Transition point, 315Transition temperature, 39, 638Toughness (fracture)
effect on fatigue, 553, 587, 589effect on SCC, 744
Transmission electron microscope, TEM, 73Tresca theory. see failure theory, maximum
shear stressTriaxiality
effect on hydrogen embrittlement, 708effect on Neuber’s rule, 334effect on SCC, 710
Subject Index 843
T (cont.)Triaxiality factor, 336, 492True rupture stress, 257, 268True strain, 257, 268
UUniform dilatation, 259Uniform deformation, 259Upper confidence level, 203Up-and-down method. see fatigue test method-
stairCase
Upward crossing, 339
VVacuum
effect on fatigue, 105, 768Van’t Hoff equation, 653Variable amplitude loads, 437, 604, 615Void or cavities formation
mechanism, 38, 123Volume effect. See process volume effect
WWarm prestressing, 636Wavy-slip, 28, 34, 78
Weibull distribution, 212, 232, 235,238, 240
exponent, 212, 219Weld cracking, 627
centerline cracking, 626incomplete fusion, 626incomplete penetration, 626longitudinal crack in the HAZ, 626transverse crack, 626, 629undercladding cracks, 626
Weldingresidual stresses, 633
Weldsdendrites, 631fusion line, 632heat affected zone, HAZ, 626process volume, 627
Weakest link criterion, 217Whiskers. see fibersWide-band random process, 339Wöhler’s diagram, 5
ZZinc-mzgnesium-aluminumalloy, 256
844 Subject Index