A finite element model, which implements single crystal constitutive relationships, was used to simulate fatigue cracks growing at the microstructural level. Plastic deformation (slip) was allowed along two specified microscopic crystallographic planes. As the orientations of the slip systems were changed several crucial fatigue crack growth parameters, measured over all possible orientations, were found to vary: (1) crack tip forward slip band size, rp, 0.03 ≤ rp/(Kmaxo)2 ≤ 0.31 where λo is the critical resolved shear stress on a slip system, (2) crack opening displacement, δ, 1.2 ≤ δ/(Kmax2/Emσo) ≤ 7.8 where Em and σo are the elastic modulus and yield stress of a polycrystalline material with many randomly oriented double slip crystals, and(3) crack closure level, Sopen/Smax, 0.02 ≤ Sopen/Smax ≤ 0.35. Corresponding to these differences in crack growth parameters, crack growth laws were used to estimate the expected changes in crack growth rates when microstructurally short cracks grow through grains with different crystallographic orientations. The resulting predictions form approximate upper and lower bounds on crack growth rates for microstructurally short cracks. For several different materials, the crack growth rate variability predictions were in the range 7 ≤ (da/dN)(max)/(da/dN)(min) ≤ 37, which is consistent with experimentally measured variations.

1.
Asaro
Robert J.
,
1978
, “
Geometrical Effects in the Inhomogeneous Deformation of Ductile Single Crystals
,”
Acta Metallurgica
, Vol.
27
, pp.
445
453
.
2.
Asaro
Robert J.
,
1983
, “
Micromechanics of Crystals and Polycrystals
,”
Advances in Applied Mechanics
, Vol.
23
, pp.
1
115
. John W. Hutchinson.
3.
Asaro, Robert J., McHugh, P. E., Varias, A. G., Shih, C. F., 1991, “Computational Modeling of Microstructures,” Elsevier Science Publications, pp. 295–318.
4.
Chan, K. S., 1987, “Micromechanics of Small Fatigue Cracks: A Model,” Fatigue 87, Vol. 4, pp. 1802–1818.
5.
Chan, K. S., 1993, “Scaling Laws for Fatigue Crack Growth of Large Cracks in Steels,” Mett. Trans., Vol. 24A.
6.
Chan
K. S.
, and
Lankford
J.
,
1987
, “
The Role of Microstructural Dissimilitude in Fatigue and Fracture of Small Cracks
,”
Acta. Metall
, Vol.
36
, pp.
193
206
.
7.
Davidson
D. L.
,
1983
, “
A Model for Fatigue Crack Advance Based on Crack Tip Metallurgical and Mechanics Parameters
,”
Acta. Metall
, Vol.
32
, pp.
707
714
.
8.
Davidson
D. L.
, and
Lankford
J.
,
1985
, “
The effects of Aluminum Alloy Microstructure on Fatigue Crack Growth
,”
Materials Science and Engineering
, Vol.
74
, pp.
189
199
.
9.
Donahue
R. J.
,
Clark
H. McI.
,
Atanmo
P.
,
Kumble
R.
, and
McEvily
A. J.
,
1973
, “
Crack Opening Displacement and the Rate of Fatigue Crack Growth
,”
Inter. J. of Fract.
, Vol.
8
, pp.
209
219
.
10.
Gall
K.
,
Sehitoglu
H.
, and
Kadioglu
Y.
,
1991
, “
F.E.M. Study of Fatigue Crack Closure Under Double Slip
,”
Acta. Meta.
, Vol.
44
, pp.
3955
3965
.
11.
Gall, K., Sehitoglu, H., and Kadioglu, Y., 1996, “Plastic Zones and Fatigue Crack Closure Under Plane Strain Double Slip,” Vol. 27A, pp. 3491–3502. (1996-11).
12.
Koiter
W. T.
,
1953
, “
Stress-Strain Relations, Uniqueness and Variational Theorems for Elastic Plastic Materials With a Singular Yield Surface
,”
Quart. Appl. Math.
, Vol.
11
, p.
350
350
.
13.
Laird, C., 1967, “The Influence of Metallurgical Structure on the Mechanisms of Fatigue Crack Propagation,” ASTM STP 415, pp. 131–180.
14.
Lalor, P., and Sehitoglu, H., 1988, “Crack Closure Outside Small Scale Yielding Regime,” American Society for Testing and Materials, STP 982, pp. 342–360.
15.
Lankford
J.
,
1982
, “
The Growth of Small Fatigue Cracks in 7075-T6 Aluminum
,”
Fatigue of Engineering Materials and Structures
, Vol.
5
, pp.
233
248
.
16.
Larson, J. M., Williams, J. C., and Thompson, A. W., 1988, “Crack Closure Effects on the growth of Small Surface Cracks in Titanium-Aluminum Alloys,” Mechanics of Fatigue Crack Closure, ASTM STP 982, J. C. Newman, Jr. and W. Elber, eds., American Society for Testing and Materials, Philadelphia, pp. 149–167.
17.
Li
C.
,
Zhang
P.
, and
Zhang
T.
,
1994
, “
On Crystallographic Crack Transfer Across Interfaces in Four Types of Aluminum Bicrystal
,”
Materials Science and Engineering
, Vol.
A183
, pp.
23
30
.
18.
Li
C.
,
1990
, “
On the interaction among stage I short crack, slip band and grain boundary: a FEM analysis
,”
International Journal of Fatigue
, Vol.
43
, pp.
227
239
.
19.
Liaw, P. K., 1988, “Overview of Crack Closure at Near-Threshold Fatigue Crack Growth Levels,” Mechanics of Fatigue Crack Closure, ASTM STP 982, J. C., Newman, Jr. and W. Elber, eds., American Society for Testing and Materials, Philadelphia, pp. 62–92.
20.
Liu
H. W.
,
1989
, “
Fatigue Crack Growth by Crack Tip Cyclic Plastic Deformation: The Unzipping Model
,”
Inter. J. of Fract
, Vol.
39
, pp.
63
77
.
21.
McClung, R. C., and Torng, T. Y., 1986, “Analysis of Small Fatigue Cracks in HSLA-80 Steel,” Fatigue 86, PP. 337–342.
22.
McClung
R. C.
, and
Davidson
D. L.
,
1991
, “
High Resolution Numerical and Experimental Studies of Fatigue Cracks
,”
Engn. Fracture Mech.
, Vol.
39
, pp.
113
130
.
23.
McClung
R. C.
, and
Sehitoglu
H.
,
1989
, “
On the Finite Element Analysis of Fatigue Crack Closure-1. Basic Modeling Issues
,”
Engn. Fracture Mech.
, Vol.
33
, pp.
237
252
.
24.
McClung
R. C.
, and
Sehitoglu
H.
,
1989
, “
On the Finite Element Analysis of Fatigue Crack Closure-2. Numerical Results
,”
Engn. Fracture Mech.
, Vol.
33
, pp.
253
272
.
25.
McEvily
A. J.
, and
Boettner
R. C.
,
1963
, “
On Fatigue Crack Propagation In F.C.C Metals
,”
Acta Metallurgica
, Vol.
11
, pp.
725
742
.
26.
Miller, K. J., 1991, “Metal Fatigue-past, current, and future,” Proc. Instn. Mech. Engrs., p. 205.
27.
Morris, W. L., 1977, “A Comparison of Microcrack Closure Load Development for Stage I and Stage II Cracking Events for Al 7075-T651,” Metallurgical Transactions A, p. 8.
28.
Morris
W. L.
,
1988
, “
The Non continuum Crack Tip Deformation Behavior of Surface Microcracks
,”
Metallurgical Transactions A
, Vol.
11
, pp.
1117
1123
.
29.
Morris, W. L., and James, M. R., 1983, “Statistical Aspects of Fatigue Failure Due to Alloy Microstructure,” ASTM STP 811, pp. 179–206.
30.
Neumann
P.
,
1969
, “
Coarse Slip Model of Fatigue
,”
Acta Met.
, Vol.
17
, p.
1219
1219
.
31.
Neumann
P.
,
1974
, “
New Experiments Concerning the Slip Process at Propagating Fatigue Cracks-I
,”
Acta Metallurgical
, Vol.
22
, pp.
1155
1165
.
32.
Neumann
P.
,
1974
, “
The Geometry of Slip Processes at a propagating Fatigue Crack-II
,”
Acta Metallurgica
, Vol.
22
, pp.
1167
1178
.
33.
Newman, P., and Beevers, C. J., 1986, “Growth of Short Fatigue Cracks in High Strength Ni-Base Superalloys,” Small Fatigue Cracks, eds., R. O. Ritchie and J. Lankford, pp. 97–116.
34.
Pearson
S.
,
1975
, “
Initiation of Fatigue Cracks in Commercial Aluminum Alloys and the Subsequent Propagation of Very Short Cracks
,”
Engn. Frac. Mech
, Vol.
7
, pp.
235
247
.
35.
Pelloux
R. M. N.
,
1969
, “
Mechanisms of Formation of Ductile Fatigue Striations
,”
Trans. ASME
, Vol.
62
, pp.
281
285
.
36.
Rice, J. R., 1967, “Mechanics of Crack Tip Deformation and Extension by Fatigue,” Fatigue Crack Propagation, ASTM STP 415, pp. 247–309.
37.
Rice
J. R.
,
Hawk
D. E.
, and
Asaro
R. J.
,
1990
, “
Crack Tip Fields in Ductile Crystals
,”
International Journal of Fracture
, Vol.
42
, pp.
301
321
.
38.
Ritchie, R. O., W. Yu, D. K. Holm, and A. F. Blom, 1988, “Development of Fatigue Crack Closure with The Extension of Long and Short Cracks in Aluminum Alloy 2124: A Comparison of Experimental and Numerical Results,” Mechanics of Fatigue Crack Closure, ASTM STP 982, J. C. Newman, Jr. and W. Elber, eds., American Society for Testing and Materials, Philadelphia, pp. 300–316.
39.
Schijve, J., 1967, “Significance of Fatigue Cracks in Micro-Range and Macro-Range,” Fatigue Crack Propagation ASTM STP 415, p. 415.
40.
Schwalbe
K. H.
,
1973
, “
Approximate Calculation of Fatigue Crack Growth
,”
Inter. J. of Fract.
, Vol.
9
, pp.
381
395
.
41.
Sehitoglu
H.
, and
Sun
W.
,
1991
, “
Modeling of Plane Strain Fatigue Crack Closure
,”
ASME JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY
, Vol.
113
, pp.
31
40
.
42.
Sehitoglu
H.
,
Gall
K.
, and
Garcia
A. M.
,
1996
, “
Recent Advances in Fatigue Crack Growth Modeling
,”
IJF
, 1996, Vol.
80
, pp.
165
192
.
43.
Taira, S., Tanaka, K., and Hoshina, M., 1979, “Grain Size Effect of Crack Nucleation and Growth in Long Life Fatigue of Low Carbon Steels,” ASTM STP 675, pp. 135–173.
44.
Tanaka
K.
,
Hoshide
T.
, and
Sakai
N.
,
1984
, “
Mechanics of Fatigue Crack Propagation by Crack tip Plastic Blunting
,”
Engineering Fracture Mechanics
, Vol.
19
, pp.
805
825
.
45.
Tanaka, K., 1985, “Short Crack Fracture Mechanics in Fatigue Conditions,” Current Research on Fatigue Cracks, T. Tanaka et al., eds., The society of Materials Science, Japan, Materials Research Series, pp. 79–100.
46.
Tanaka, K., 1989, “Mechanics and Micromechanics of Fatigue Crack Propagation,” Fracture Mechanics: Perspectives and Directions (Twentieth Symposium), ASTM STP 1020. R. P. Wei and R. P. Gangloff, eds., American Society for Testing and Materials, Philadelphia, pp. 151–183.
47.
Taylor, D. PhD thesis, 1988, “Fatigue Crack Propagation in Nickel-Aluminum Bronze Castings,” University of Cambridge, p. 123.
48.
Tokaji, K., Ogawa, T., Osako, S., Harada, Y., 1987, “The Growth Behavior of Small Fatigue Cracks; The effect of Microstructure and Crack Closure,” Fatigue 87, Vol. I, pp. 313–322.
49.
Tomkins
B.
,
1968
, “
Fatigue Crack Propagation-An Analysis
,”
Philosophical Magazine, Eight Series
, Vol.
18, 155
, pp.
1041
1066
.
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