Abstract

An optimization procedure was developed to deduce the fiber bridging stresses from crack opening displacements measured in situ during crack growth. This procedure was used to determine the bridging stress distribution during fatigue crack growth in a unidirectionally reinforced metal matrix composite (SCS-6/TIMETAL®21S). The bridging stress is non-zero at the crack tip contrary to predictions from conventionally used shear lag models. The bridging stress at the crack tip is proportional to the applied far-field stress. The deduced bridging law is similar to the new shear lag models with non-zero bridging stresses at the crack tip. Any bridging model can be used to predict the crack growth behavior by choosing appropriate values of the frictional shear stress (τ). Consequently, the magnitude of the stresses in the fibers bridging the crack will depend on the fiber bridging model. Hence, the fiber tensile strength required to predict the onset of fiber failure will also depend on the fiber bridging model.

References

1.
Marshall
,
D. B.
,
Cox
,
B. N.
, and
Evans
,
A. G.
, “
The Mechanics of Matrix Cracking in Brittle-Matrix Fiber Composites
,”
Acta Materialia
 1359-6454, Vol.
33
, No.
11
,
1985
, pp.
2013
-
2021
.
2.
McCartney
,
L. N.
, “
Mechanics of Matrix Cracking in Brittle-Matrix Fiber-Reinforced Composites
,”
Proceedings of Royal Society of London
, Vol.
A409
,
1987
, pp.
329
-
350
.
3.
Hutchinson
,
J. W.
and
Jensen
,
H. M.
, “
Models of Fiber Debonding and Pullout in Brittle Composites with Friction
,”
Mechanics of Materials
, Vol.
9
,
1990
, pp.
139
-
163
.
4.
Xia
,
Z. C.
,
Hutchinson
,
J. W.
,
Evans
,
A. G.
, and
Budiansky
,
B.
, “
On Large Scale Sliding in Fiber-Reinforced Composites
,”
Journal of the Mechanics and Physics of Solids
 0022-5096, Vol.
42
, No.
7
,
1994
, pp.
1139
-
1158
.
5.
Majumdar
,
B. S.
,
Newaz
,
G. M.
, and
Rosenfield
,
A. R.
, “
Yielding Behavior of Ceramic Matrix Composites
,”
Advances in Fracture Research, Proceedings of the 7th International Conference on Fracture
,
Houston, Texas
, Vol.
4
,
1989
, pp.
2805
-
2814
.
6.
Danchaivijit
,
S.
and
Shetty
,
D. K.
, “
Matrix Cracking in Ceramic-Matrix Composites
,”
Journal of the American Ceramic Society
 0002-7820 https://doi.org/10.1111/j.1151-2916.1993.tb03972.x, Vol.
76
, No.
10
,
1993
, pp.
2497
-
2504
.
7.
Chiang
,
Y.-C.
,
Wang
,
A. S. D.
, and
Chou
,
T.-W.
, “
On Matrix Cracking in Fiber Reinforced Ceramics
,”
Journal of the Mechanics and Physics of Solids
 0022-5096, Vol.
41
, No.
7
,
1993
, pp.
1137
-
1154
.
8.
Meda
,
G.
and
Steif
,
P. S.
, “
A Detailed Analysis of Cracks Bridged by Fibers—II. Cracks of Intermediate Size
,”
Journal of the Mechanics and Physics of Solids
 0022-5096, Vol.
42
, No.
8
,
1994
, pp.
1323
-
1341
.
9.
McMeeking
,
R. M.
and
Evans
,
A. G.
, “
Matrix Fatigue Cracking in Fiber Composites
,”
Mechanics of Materials
, Vol.
9
, No.
3
,
1990
, pp.
217
-
227
.
10.
John
,
R.
,
Jira
,
J. R.
,
Larsen
,
J. M.
, and
Ashbaugh
,
N. E.
, “
Analysis of Bridged Fatigue Cracks in Unidirectional SCS-6/Ti-24A1-11Nb Composites
,”
Fatigue 93
,
Engineering Materials Advisory Services Ltd.
,
West Midlands, U. K.
, Vol.
II
,
1993
, pp.
1091
-
1096
.
11.
John
,
R.
,
Kaldon
,
S. G.
, and
Ashbaugh
,
N. E.
, “
Application of Fiber Bridging Models to Describe Fatigue Crack Growth in Unidirectional Titanium Matrix Composites
,”
Titanium Metal Matrix Composites II
, WL-TR-93-4105,
Air Force Research Laboratory, Wright-Patterson AFB
,
OH 45433
,
1993
, pp.
270
-
290
.
12.
John
,
R.
,
Stibich
,
P. R.
,
Johnson
,
D. A.
, and
Ashbaugh
,
N. E.
, “
Bridging Fiber Stress Distribution During Fatigue Crack Growth in [0]4 SCS-6/TIMETAL®21S
,”
Scripta Materialia
 1359-6462, Vol.
33
,
1995
, pp.
75
-
80
.
13.
Buchanan
,
D. J.
,
John
,
R.
, and
Johnson
,
D. A.
, “
Determination of Crack Bridging Stresses From Crack Opening Displacement Profiles
,”
International Journal of Fracture
, Vol.
87
, No.
2
,
1997
, pp.
101
-
117
.
14.
John
,
R.
,
Jira
,
J. R.
, and
Larsen
,
J. M.
, “
Effect of Stress and Geometry on Fatigue Crack Growth Perpendicular to Fibers in Ti-6A1-4V Reinforced With SiC Fibers
,”
Composite Materials: Fatigue and Fracture, Seventh Volume
, ASTM STP 1330,
R. B.
Bucinell
, Ed.,
American Society for Testing and Materials
,
West Conshohocken, PA
,
1998
, pp.
122
-
144
.
15.
Hutson
,
A.
,
John
,
R.
, and
Jira
,
J. R.
, “
The Effect of Temperature on Fiber/Matrix Interface Sliding in SCS 6/TIMETAL®21S
,”
Scripta Materialia
 1359-6462, Vol.
40
, No.
5
,
1999
, pp.
529
-
535
.
16.
Larsen
,
J. M.
,
Jira
,
J. R.
,
John
,
R.
, and
Ashbaugh
,
N. E.
, “
Crack-Bridging Effects in Notch Fatigue of SCS-6/TIMETAL@21S Composites Laminates
,”
Life Prediction Methodology of Titanium Matrix Composites
, ASTM STP 1253,
W. S.
Johnson
,
J. M.
Larsen
, and
B. N.
Cox
, Eds.,
American Society for Testing and Materials
,
West Conshohocken PA
,
1996
, pp.
114
-
136
.
17.
Ghosn
,
L. J.
,
Telesman
,
J.
, and
Kantzos
,
P.
, “
Specimen Geometry Effects on Fiber Bridging in Composites
,”
Fatigue 93
,
Engineering Materials Advisory Services Ltd.
,
West Midlands, U. K.
, Vol.
II
,
1993
, pp.
1231
-
1238
.
18.
Davidson
,
D. L.
, “
The Micromechanics of Fatigue Crack Growth at 25°C in Ti-6Al-4V Reinforced with SCS-6 Fibers
,”
Metallurgical Transactions
 0026-086X, Vol.
23A
,
1992
, pp.
865
-
879
.
19.
Cox
,
B. N.
and
Marshall
,
D. B.
, “
The Determination of Crack Bridging Forces
,”
International Journal of Fracture
, Vol.
49
,
1991
, pp.
159
-
176
.
20.
Zheng
,
D.
and
Ghonem
,
H.
, “
High Temperature/High Frequency Fatigue Crack Growth in Titanium Metal Matrix Composites
,”
Life Prediction Methodology of Titanium Matrix Composites
, ASTM STP 1253,
W. S.
Johnson
,
J. M.
Larsen
, and
B. N.
Cox
, Eds.,
American Society for Testing and Materials
,
West Conshohocken, PA
,
1996
, pp.
137
-
163
.
21.
Connell
,
S. J.
and
Zok
,
F. W.
, “
Measurement of the Cyclic Bridging Law in a Titanium Matrix Composite and It's Application to Simulating Crack Growth
,”
Acta Materialia
 1359-6454, Vol.
45
,
1997
, pp.
5203
-
5211
.
22.
Cardona
,
D. C.
,
Barney
,
C.
, and
Bowen
,
P.
, “
Micromodelling of Effective Stress Intensities for Bridged Cracks in Fibre Reinforced Titanium Metal Matrix Composites
,”
Composites
 0010-4361, Vol.
24
,
1993
, pp.
122
-
128
.
23.
Bakuckas
,
J. G.
and
Johnson
,
W. S.
, “
A Methodology to Predict Damage Initiation, Damage Growth, and Residual Strength in Titanium Matrix Composites
,”
Life Prediction Methodology of Titanium Matrix Composites
, ASTM STP 1253,
W. S.
Johnson
,
J. M.
Larsen
, and
B. N.
Cox
, Eds.,
American Society for Testing and Materials
,
West Conshohocken, PA
,
1996
, pp.
497
-
519
.
24.
Cox
,
B. N.
, “
Life Prediction for Bridged Fatigue Cracks
,”
Life Prediction Methodology of Titanium Matric Composites
, ASTM STP 1253,
W. S.
Johnson
,
J. M.
Larsen
, and
B. N.
Cox
, Eds.,
American Society for Testing and Materials
,
West Conshohocken, PA
,
1996
, pp.
552
-
572
.
25.
Warrier
,
S. G.
and
Majumdar
,
B. S.
, “
Effects of Interface on the Fatigue Crack Growth Response of Titanium Matrix Composites: Modeling and Impact on Interface Design
,”
Materials Science & Engineering A
, Vol.
237
,
1997
, pp.
256
-
267
.
26.
Hermann
,
D. J.
and
Hillberry
,
B. M.
, “
A New Approach to the Analysis of Unidirectional Titanium Matrix Composites With Bridged and Unbridged Cracks
,”
Engineering Fracture Mechanics
 0013-7944, Vol.
56
, No.
5
,
1997
, pp.
711
-
726
.
27.
Rödel
,
J.
,
Kelly
,
J. F.
, and
Lawn
,
B. R.
, “
In Situ Measurements of Bridged Crack Interfaces in the Scanning Electron Microscope
,”
Journal of the American Ceramic Society
 0002-7820 https://doi.org/10.1111/j.1151-2916.1990.tb06454.x, Vol.
73
,
1990
, pp.
3313
-
3318
.
28.
Fett
,
T.
,
Munz
,
D.
,
Seidel
,
J.
,
Stech
,
M.
, and
Rödel
,
J.
, “
Correlation between Long and Short Crack R-Curves in Alumina Using the Crack Opening Displacemen tand Fracture Mechanical Weight Function Approach
,”
Journal of the American Ceramic Society
 0002-7820 https://doi.org/10.1111/j.1151-2916.1996.tb08571.x, Vol.
79
,
1996
, pp.
1189
-
1196
.
29.
Guo
,
Z. K.
,
Kobayashi
,
A. S.
, and
Hawkins
,
N. M.
, “
Further Studies on Fracture Process Zone for Mode I Concrete Fracture
,”
Engineering Fracture Mechanics
 0013-7944, Vol.
46
,
1993
, pp.
1041
-
1049
.
30.
Hay
,
J. C.
and
White
,
K. W.
, “
Grain Boundary Phases and Wake Zone Characterization in Monolithic Alumina
,”
Journal of the American Ceramic Society
 0002-7820, Vol.
78
,
1995
, pp.
1849
-
1854
.
31.
Hartman
,
G. A.
and
Nicholas
,
T.
, “
An Enhanced Laser Interferometer for Precise Displacement Measurements
,”
Experimental Techniques
, Vol.
2
, No.
2
,
1987
, pp.
24
-
26
.
32.
Sharpe
,
W. N.
,
Jira
,
J. R.
, and
Larsen
,
J. M.
, “
Real-Time Measurements of Small-Crack Opening Behavior Using an Interferometric Strain/Displacement Gage
,”
Small-Crack Test Methods
, ASTM STP 1149,
J.
Larsen
and
J.
Allison
, Eds.,
American Society for Testing and Materials
,
Philadelphia, PA
,
1992
, pp.
92
-
115
.
33.
IMSL
,
Problem-Solving Software Systems, User's Manual
, Math/Library Version 2.0, Houston, TX, USA,
1996
.
34.
Kantzos
,
P.
,
Eldridge
,
J.
,
Koss
,
D. A.
, and
Ghosn
,
L. J.
, “
The Effect of Fatigue Loading on the Interfacial Shear Properties of SCS-6/Ti-Based MMCs
,”
Intermetallic Composites II
,
D. B.
Miracle
,
D. L.
Anton
, and
J. A.
Graves
, Eds.,
MRS Proceedings
,
Pittsburgh, PA
, Vol.
273
,
1992
, pp.
135
-
142
.
35.
Buchanan
,
D. J.
,
Ashbaugh
,
N. E.
, and
Rosenberger
,
A. H.
, “
Damage and Deformation Prediction of [0] Titanium Matrix Composites Under Fatigue-Dwell Loading
,” To be submitted for publication,
1999
.
36.
Tada
,
H.
,
Paris
,
P. C.
, and
Irwin
,
G. R.
,
The Stress Analysis of Cracks Handbook
,
Paris Productions
,
St. Louis, MO
,
1985
.
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