A probabilistic mesomechanical crack nucleation model is proposed to link the microstructural material heterogeneities to the statistical scatter in the macro structural response. The macrostructure is modeled as an ensemble of microelements. Cracks nucleate within the microelements and grow from the microelements to final fracture. Variations of the microelement properties are defined using statistical parameters. A micromechanical slip band decohesion model along with a Paris law crack growth model are used with first order reliability methods and Monte Carlo simulation to determine the distribution of fatigue life for the macrostructure. The modeled response is compared to trends in experimental observations from the literature.

1.
Halford, G. R., “Evolution of Creep-Fatigue Life Prediction Models,” Creep-Fatigue Interactions at High Temperatures, AD-Vol. 21, ed., Haritos, G. K., Ochoa, O. O., ASME, 1991, pp. 43–57.
2.
Schijve
J.
, “
Fatigue Predictions and Scatter
,”
Fat. Fract. Eng. Mat. Struct.
, Vol.
17
, No.
4
,
1994
, pp.
381
396
.
3.
Sasaki
S.
,
Ochi
Y.
,
Ishii
A.
,
Hirofuml
A.
, “
Effects of Material Structures on Statistical Scatter in Initiation and Growth Lives of Surface Cracks and Failure Life in Fatigue
,”
JSME Inter. J.
, Series I, Vol.
32
, No.
1
,
1989
, pp.
155
161
.
4.
Bastenaire, F. A., “New Method for the Statistical Evaluation of Constant Stress Amplitude Fatigue-Test Results,” Probabilistic Aspects of Fatigue, ed., Heller, R. A., ASTM STP 511, 1972, pp. 3–28.
5.
Axelrad, D. R., “The Mechanics of Discrete Media,” Continuum Models of Discrete Systems (CMDS3), ed., Kro¨ner, E., Anthony, K.-H., Univ. Waterloo, 1980, pp. 3–34.
6.
Haritos
G. K.
,
Hager
A. K.
,
Salkind
M. J.
,
Wang
A. S. D.
, “
Mesomechanics: The Microstructure-Mechanics Connection
,”
Int. J. Sol. Struct.
, Vol.
24
, No.
11
,
1988
, pp.
1081
1096
.
7.
Tanaka
K.
,
Mura
T.
, “
A Dislocation Model for Fatigue Crack Initiation
,”
ASME Journal of Applied Mechanics
, Vol.
48
,
1981
, pp.
97
103
.
8.
Mura, T., Tanaka, K., “Dislocation Dipole Models for Fatigue Crack Initiation,” Mechanics of Fatigue, AMD-Vol. 47, ASME, 1981, pp. 111–132.
9.
Taira, S., Tanaka, K., Hoshina, M., “Grain Size Effect on Crack Nucleation and Growth in Long-Life Fatigue of Low-Carbon Steel,” Fatigue Mechanisms, ASTM STP 675, 1979, pp. 135–173.
10.
Floreen, S., “High Temperature Crack Growth Structure Property Relationships in Nickel Base Superalloys,” Creep-Fatigue-Environment Interactions, ed., Pelloux, R., Slotoff, N., Metallurgical Soc., 1980, pp. 121–128.
11.
Tokaja
K.
,
Ogawa
T.
,
Ohya
K.
, “
The Effect of Grain Size on Small Fatigue Crack Growth in Pure Titanium
,”
Fatigue
, Vol.
16
,
1994
, pp.
571
578
.
12.
Gayda
J.
,
Miner
R.
, “
Fatigue Crack Initiation and Propagation in Several Nickel-Based Superalloys at 650°C
,”
Int. J. Fat.
, Vol.
5
, No.
3
,
1983
, pp.
135
143
.
13.
Lerch, B., “Microstructural Effects on the Room and Elevated Temperature Low Cycle Fatigue Behavior of Waspaloy,” NASA CR 165 497, 1982.
14.
Forsyth, P., The Physical Basis of Metal Fatigue, American Elsevier Publ., 1969.
15.
Francois, D., “The Influence of the Microstructure on Fatigue,” Advances in Fatigue Science and Technology, ed., Moura Branco, C., Guerra Rosa, L., Kluwer Academic Publ., 1989, pp. 23–76.
16.
Provan
J.
,
Zhai
Z.
, “
Fatigue Crack Initiation and Stage-I Propagation in Polycrystalline Materials. I: Micromechanics
,”
Int. J. Fat.
, Vol.
13
, No.
2
,
1991
, pp.
99
109
.
17.
Bruckner-Foit, A., Jackels, H., Lahodny, H., and Mu¨nz, D., “Fatigue Reliability of Components Containing Microstructural Flaws,” Proceedings of ICOSSAR ’89, 1989, pp. 1499–1506.
18.
Davidson
D. L.
,
Chan
K. S.
, “
The Crystallography of Fatigue Crack Initiation In Coarse Grained Astroloy At 20°C
,”
A. Metall.
, Vol.
37
, No.
4
,
1989
, pp.
1089
1097
.
19.
Sasaki
S.
,
Ochi
Y.
, “
Some Experimental Studies of Fatigue Slip Bands and Persistent Slip Bands During Fatigue Process of Low-Carbon Steel
,”
Eng. Fract. Mech.
, Vol.
12
,
1979
, pp.
531
540
.
20.
Tanaka, T., Kosugi, M., “Crystallographic Study of the Fatigue Crack Nucleation Mechanism in Pure Iron,” Basic Questions in Fatigue, Vol. 1, ASTM STP 924, 1988, pp. 98–119.
21.
Schimd
E.
,
Z. Eledtrodhem.
, Vol.
37
,
1931
, pp.
447
447
.
22.
Backofen, W. A., Deformation Processing, Addison-Wesley, 1972, pp. 72–82.
23.
Smith, C. S., A Search for Structure, MIT Press, Cambridge, 1981.
24.
Kurtz
S. K.
,
Carpay
F. M. A.
, “
Microstructure and Normal Grain Growth in Metals and Ceramics. Part I. Theory
,”
J. Appl. Phys.
, Vol.
51
, No.
11
,
1980
, pp.
5725
5744
.
25.
Gokhale, A. B., Rhimes, F. N., “Effect of Grain Volume Distribution on the Plastic Properties of High Purity Aluminum,” Microstructural Science, Vol. 11, Ed., DeHoff, R., Braum, J., McCall, J., Elsevier, 1983, pp. 3–11.
26.
Tryon
R. G.
,
Cruse
T. A.
,
Mahadevan
S.
, “
Development of a Reliability-Based Fatigue Life Model for Gas Turbine Engine Structures
,”
Engr. Frac. Mech.
, Vol.
53
, No.
3
,
1996
, pp.
807
828
.
27.
Wu
Y-T.
,
Millwater
H. R.
,
Cruse
T. A.
, “
Advanced Probabilistic Structural Analysis Method for Implicit Performance Functions
,”
AIAA Journal
, Vol.
28
, No.
9
,
1990
, pp.
1663
1669
.
28.
Dieter, G. E., Mechanical Metallurgy, McGraw-Hill, Third Edition, 1986.
29.
Weibull, W., Fatigue Testing and Analysis of Results, Pergamon Press, 1961.
30.
Trantina
G.
, “
Statistical Fatigue Failure Analysis
,”
J. of Test. Eval.
, Vol.
9
, No.
1
,
1981
, pp.
44
49
.
31.
Ang, A. H.-S., and Tang, W. H., Probability Concepts in Engineering Planning and Design, Vol. 2, John Wiley, 1984, pp. 191–202.
32.
Brown
C.
,
King
J.
,
Hicks
M.
, “
Effects of Microstructure on Long and Short Crack Growth in Nickel Based Superalloys
,”
Met. Sci.
, Vol.
18
,
1984
, pp.
374
380
.
33.
Ransom, J., General Discussion, Symposium on Statistical Aspects of Fatigue, ASTM STP 121, 1952, pp. 59–62.
This content is only available via PDF.
You do not currently have access to this content.