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 In the presence of a notch LEFM is no longer valid.However, LEFM can still be applied supposing that, conservatively, sooner or laterat the tip of a notch a crack will initiate by fatigue or corrosion, in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

http://dx.doi.org/10.1007/978-88-470-2336-9_10

http://dx.doi.org/10.1007/978-88-470-2336-9_10

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

http://dx.doi.org/10.1007/978-88-470-2336-9_10

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


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


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


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)


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)


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


http://dx.doi.org/10.1007/978-88-470-2336-9_15

http://dx.doi.org/10.1007/978-88-470-2336-9_15

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


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.


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


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]


2 W

σm

σb

t

a

2c

t

2c

a

φ

A

Fig. A.20 Semi-elliptical surface crack with a [ c [8]


2 W

σm

t

2a

2c

t

2c

2a

φA

σm

d

Fig. A.21 Elliptical central crack [8]


Fig. A.22 � Ellipse corner crack with a c [8]


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]


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]


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)


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


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


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

Appendix Linear Elastic Fracture Mechanics. Compendium …978-88-470-2336-9/1.pdf · Appendix...

Documents

Transcript of Appendix Linear Elastic Fracture Mechanics. Compendium …978-88-470-2336-9/1.pdf · Appendix...