The weight function method was used to determine the effective stress intensity factor and the crack opening profile for a fatigue tested composite which exhibited fiber bridging. The bridging mechanism was modeled using two approaches; the crack closure approach and the shear lag approach. The numerically determined stress intensity factor values from both methods were compared and correlated with the experimentally obtained crack growth rates for SiC/Ti-15-3 (0)(sub 8) oriented composites. The near crack tip opening profile was also determined for both methods and compared with the experimentally obtained measurements

Ghosn, Louis J.

Kantzos, Peter

Telesman, Jack

English

NASA Technical Reports Server

NASA Technical Memorandum 103102
Fatigue Crack Growth in
Unidirectional Metal
Matrix Composite
Louis J. Ghosn
Sverdrup Technology, Inc.
Lewis Research Center Group
Brook Park, Ohio
Jack Telesman and Peter Kantzos
National Aeronautics and Space Administration
Lewis Research Center
Cleveland, Ohio
Prepared for the
International Fatigue Series (FATIGUE 90)
Honolulu, Hawaii, July 15-20, 1990
(_dA"A-T_-_0310,/) FATIGUe: CPaCK GROWTH TN
UNIgI_eCTIt;NAL MeTAl MATRIX CqMPOSITt:
(_AgA) 'i ij CSCl_ 20K
N90-2_117
https://ntrs.nasa.gov/search.jsp?R=19900012801 2020-03-19T23:04:51+00:00Z

FATIGUE CRACK GROWTH IN UNIDIRECTIONAL METAL MATRIX COMPOSITE
Louis J. Ghosn
Sverdrup Technology, Inc.
Lewis Research Center Group
Brook Park, Ohio 44142
and
lack Telesman and Peter Kantzos
National Aeronautics and Space Administration
Lewis Research Center
Cleveland, Ohio 44135
¢M
!
SL_tARY
The weight function method was used to determine the effective stress
intensity factor (bKef f) and the crack opening profile for a fatigue tested
composite which exhibited fiber bridging. The bridging mechanism was modeled
using two approaches; the crack closure approach and the shear lag approach.
The numerically determined bKef f values from both methods were compared and
correlated with the experimentally obtained crack growth rates for SiC/Ti-15-3
[0]8 oriented composites. The near crack tip opening profile was also deter-
mined for both methods and compared with the experimentally obtained
measurements.
INTRODUCTION
The ability to predict fatigue crack growth behavior of metal matrix com-
posites is of particular interest due to the presence of many cracklike
defects which tend to be present in these materials. Experimental studies on
a number of these composites (refs. I to 3) have shown that cracks tend to
propagate in the metallic matrix leaving behind unbroken fibers which bridge
the two cracked surfaces.
A number of researchers (refs. 3 to 6) have attempted to model crack
bridging. The crack bridging model that has received the most attention for
composite materials is the so-called shear lag model (refs. 3 to 5). This
model is based on the relative sliding between the fiber and the matrix in the
region where the interface shear stresses exceed the frictional shear forces.
This model was developed for brittle matrix fiber composites which have purely
frictional bonding between the fibers and matrix. This model was also applied
to metal matrix composite systems (ref, 3). Another type of bridging model
which may be applicable for these types of composites is based on the applica-
tion of a closure pressure in the bridged zone proportional to the load car-
ried by the bridging fibers (henceforth this model will be termed crack closure
model). This methodology had been applied previously to model the effect of
unbroken ligaments in a fast fracture test of steels (ref. 6).
In order to decide whether these types of models can represent the actual
fatigue behavior, an experimental FCGtest program was conducted. Testing was
performed using a specially designed loading stage mounted inside an SEM.
This apparatus permits an accurate measurement of the crack opening displace-
ments, measurement of crack growth rates and identification of active fatigue
failure mechanisms.
Both types of models were used to predict the fatigue crack growth behav-
ior and the near tip crack displacements. Analytical predictions were compared
to the test data.
EXPERIMENTAL
Fatigue crack growth tests were conducted on two single edge notch (SEN)
metal matrix composite specimens. The test material was a SiC (SCS-6) fiber
reinforced composite with a Ti-15V-3Cr-3AI-3Sn (Ti-15-3) matrix. The testing
was performed on unidirectionally oriented specimens with the fiber direction
being parallel to the loading axis and perpendicular to the starter notch, Com-
panion testing was performed on compact tension (CT) specimens machined out of
laminated, unreinforced matrix material which was processed in a similar manner
as the composite.
RESULTS
The fatigue crack growth behavior of the SEN composite specimens consisted
mostly of stable crack growth perpendicular to the loading axis. Crack growth
was confined to the matrix ligaments only, leaving behind in its wake unbroken
fibers bridging the two cracked surfaces (ref. 2). A plot of the crack length
versus number of cycles (fig. 1) revealed a continuous decrease in the fatigue
crack growth rate with increasing crack length. After growth around four row
of fibers (approximately 1 mm of growth) the crack growth arrested.
As a first attempt, the fatigue crack growth rate of the composite was
plotted as a function of the stress intensity factor range (6Kaoo) and is
shown in figure 2. The stress intensity range was calculated b_-considering
only the applied load and the crack length and without taking into considera-
tion the fiber bridging of the cracked surfaces. The data show crack growth
rate decreasing with an increasing _Kao p. Also shown in the figure is the
fatigue crack growth data of the unreinTorced matrix material. The crack
growth rates for the composite are at least a factor of 10 3 lower than those
of the unreinforced composite for the same AKap p.
ANALYSIS
Both of the models evaluated use fracture mechanics as the basis for cal-
culating the effective crack driving force, _Kef f. The effective stress inten-
sity factors and the crack opening displacements were determined using the
weight function method. The weight function used is based on the Bueckner
(ref. 7) formulation for the stress intensity factor calculation of a single
edge notch in a finite geometry specimen (fig, 3). The stress intensity fac-
tor, SIF, for an unbridged crack of length a is given by:
aK(a) =4_-2-Io p(×)H(a,×_%/__×dx (i)
where H(a,x) = (1 + ml(a - x)/a + m2(a - x)2/a 2) and where mI and m2 are
given by:
mI = 0.6147 + 17.1844 (a/w) 2 + 8.7822 (a/w) 6
m2 = 0.2502 + 3.2889 (a/w) 2 + 70.0444 (a/w) 6
The unbridged displacement profile is given by:
2Jau(x) 2(t - _c ) _ p(x)H(_,x +) dx'= r.c_ _ %/'_ - x'
X
d_ (2)
where Ec and _c are the composite elastic modulus and Poisson's ratio,
respectively.
For a partially bridged crack the distribution of the pressure function
p(x) is divided into two parts:
unbridged region p(x)= a _, for 0 < x <a0 {3a)
bridged region p(x}= o_ - c(x), for a 0 < x <a (3b)
where a 0 and a are the unbridged crack length and the total crack length,
respectively. The pressure distribution c(x) is an approximate closure pres-
sure due to bridging. Equations (1) and (2) can be modified for a partially
bridged crack by substituting the appropriate pressures given in equation (3).
Up to this point both models are identical. The primary difference
between the two models is the manner by which they account for the closure
pressure c(x). For the shear lag model, references 3 and 4, c(x) is a func-
tion of the fiber/matrix interfacial friction shear stress and is proportional
to the square root of the displacement and given by:
U(X) "c vf 2 Ef EC]
c(x) = 2[ R(1 - vf)Em j
1/2
(4)
where
"t
Ef
Em
vf
R
fiber/matrix interfacial friction stress
fiber modulus
matrix modulus
fiber volume fraction
fiber radius
By substituting equation (4) into equation (3b), the solution of the displace-
ment field, equation (2), becomes an integral equation which has to be solved
3
numerically using an iterative schemewith a small damping factor to guarantee
convergence. After reaching a converged displacement profile, the composite
SIF for the shear lag model is calculated using equation (1). Finally, the
effective crack driving force is related to the composite SIF by:
K Em
Keff - Ec (5)
For the crack closure model, c(x) is equal to the stress carried by the
fibers in the bridged region averaged over the total bridged area and is given
by:
w 6WaO[ 0.5x(w - ao) - (x - ao) ]
c(x) = + (6)
w - a 0 (w - ao)3
Equation (6) represents the normal and bending stresses in the bridged fiber
region and is valid only for a partially bridged crack. The closure load in
equation (6) is independent of the displacement, hence the SIF for the closure
model can be solved directly without an iterative procedure. The effective
crack driving force, Kef f, for the closure model is calculated by substituting
the results of equation (6) into equations (3) and (1).
The values of the parameter used for the composite system tested are given
in table 1. The value of the interface shear stress _ depicted in the table
is a calculated value from experimental indentation tests (ref 3).
DISCUSSION
The calculated results of the _Kef f values for both bridging models are given
in figure 4 as a function of the crack length. Also shown is the AKaDD for
the unbridged case. As shown in the figure, the AKef f values for bo_h
models decrease with an increase in the crack length. The decrease in the
_Kef f values corresponds to the observed behavior where the crack growth
rates decreased and finally crack growth stopped with an increase in the crack
length. The _Kef f for the shear model is slightly lower than AKef f for
the closure model.
The experimentally obtained composite FCG data was replotted in terms of
the effective SIF, _Kef f, calculated using both crack bridging models. As
shown in figure 2, the predicted crack growth rate data for both models are in
agreement with the data trends exhibited by the unreinforced matrix material.
An additional check of the accuracy of the bridging models are the numerically
determined displacements near the crack tip. Both the predicted and observed
displacements were plotted in figure 5 for a given crack length as a function
of the distance behind the crack tip. The predicted crack tip displacement
fields by the two methods are almost identical and are difficult to distinguish
from each other. Excellent correlation is observed between the measured and
numerically determined displacement range in the crack tip area. As the dis-
tance from the crack tip increases some disagreement is observed for both
models.
SUMMARYOFRESULTS
Two fracture mechanics based fiber bridging models were successfully used
in an attempt to describe experimentally observed fatigue crack growth behavior
in a SiC/Ti-15-3 composite. The crack closure model and the shear lag model,
in agreement with the experimentally observed behavior, predicted a decrease
in the crack growth rates and eventual crack arrest with an increase in the
crack length. Both models also predicted the near crack tip displacements.
The advantage of the closure model is that no numerical iteration is required
to obtain the solution. The success of these models points to the applicabil-
ity of fracture mechanics to describe the fatigue behavior of certain
composites.
REFERENCES
1. Gabb, T.P.; Gayda, J.; and Mackay, R.A.: Isothermal and Nonisothermal
Fatigue Behavior of a Metal Matrix Composite. 1. Compos. Mater., June
1990. To be published.
2. Kantzos, P.; Telesman, l.; and Ghosn, L.J.: Fatigue Crack Growth In A
Unidirectional SCS-6/Ti-15-3 Composite. Presented at the ASTM Third
Symposium on Composite Materials: Fatigue And Fracture, Lake Buena Vista,
FL, Nov. 1989. To be published in ASTM STP.
3. Sensmeier, M.D.; and Wright, P.K.: The Effect of Fiber Bridging on Fatigue
Crack Growth in Titanium Matrix Composites. Fundamental Relationships
Between Microstructures and Mechanical Properties of Metal Matrix
Composites. P.K. Liaw and M.N. Gungor, eds., Minerals, Metals, and
Materials Society, Warrendale, PA, 1990, pp. 441-457.
4. Marshall, D.B., Cox, B.N. and Evans, A.G., "The Mechanics of Matrix
Cracking in Brittle-Matrix Fiber Composites," Acta Metall., vol. 33,
Nov. 1985, pp. 2013-2021.
5. Evans, A.G. and McMeeking, R.M., "On The Toughening Of Ceramics By Strong
Reinforcements," Acta Metall., vol. 34, Dec. 1986, pp. 2435-2441.
6. Hoagland, R.G., Rosenfield, A.R., and Hahn, G.T., "Mechanisms of Fast
Fracture and Arrest in Steels," Metall. Trans., vol. 3, Jan. 1972,
pp. 123-136.
7. Bueckner, H.F., "Weight Functions for Notched Bar," Z. Angew. Math. Mech.,
vol. 51, 1971, pp. 97-109.
5
TABLEI. - SiC/Ti-15-3 METAL MATRIX PARAMETERS ASSUMED
o,_max = 220 MPa
a0 = 1 mm
Ef = 427 GPa
R = 72.5 pm
O_mi n = 22 MPa
w = 5.12 mm
Em = 89 GPa
vf = 0,36
R ratio = 0.1
b = 2.03 mm
Ec = 184 GPa
x = 276 MPa
2.0 B
1,8
E
E
___'1.6
1.4
0
1.2
1.0
/ / o o _,,_
'S,6' 2 o $,oE.
" I I I I
100 200 300 400x103
CYCLES
Figure 1. - Crack length versus number of cycles.
10-6
u
uJ 10-7
_ 10-6
-_ 10-6
0
10-100
_ TRTD
_oo_ _'_ _o
o • []
I t I ,I_Itl I : I
2 4 6 10 20 30 40
STRESS INTENSIFY RANGE, AK app' AK eh', MPa ._
Figure 2. - Fatigue c_ack growth (FCG) data.
W
I_
-- o- =J-o--c(x_
Figure 3. - Partially bridged single edge notch specimen.
30 I AK_--_
Z a
w o..
-- 10
O3
u.l
¢r
_ I I I I -
0
1.0 1.2 1.4 1.6 1.8
CRACK LENGTH a, mm
Figure 4. - Stress Intensity factor versus crack length.
]
2.0
16
12
uJ
_8
LU
0
5 4
0.
co
Q
UNBRIDGED
A SHEAR LAG
-- O CLOSURE MODEL
[] D D
- []/ [] .°2° °
,_c_l _ °l = I I
.2 .4 .6 .8
DISTANCE FROM CRACK TIP, mm
Figure 5. - Crack opening displacements as a function of the distance
to the crack _p.
Report Documentation PageNatlonaI Aeronautics and
Space Administration
1. Report No. 2. Government Accession No. 3. Recipient's Catalog No.
NASA TM-103102
5. Report Date4. Title and Subtitle
Fatigue Crack Growth in Unidirectional Metal Matrix Composite
7. Author(s)
Louis J. Ghosn, Jack Telesman, and Peter Kantzos
9. Performing Organization Name and Address
National Aeronautics and Space Administration
Lewis Research Center
Cleveland, Ohio 44135-3191
_._12.Sponsoring Agency Name and Address
National Aeronautics and Space Administration
Washington, D.C. 20546-0001
6. Performing Organization Code
8. Performing Organization Report No.
E-5426
10. Work Unit No.
510-01-01
11. Contract or Grant No.
13. Type of Report and Period Covered
Technical Memorandum
14. Sponsoring Agency Code
15. Supplementary Notes
Prepared for the International Fatigue Series (FATIGUE 90), Honolulu, Hawaii, July 15-20, 1990. Louis J. Ghosn,
Sverdrup Technology, Inc., Lewis Research Center Group, 2001 Aerospace Parkway, Brook Park, Ohio 44142.
Jack Telesman and Peter Kantzos, NASA Lewis Research Center.
16. Abstract
The weight function method was used to determine the effective stress intensity factor (&,Kerr) and the crack
opening profile for a fatigue tested composite which exhibited fiber bridging. The bridging mechanism was
modeled using two approaches; the crack closure approach and the shear lag approach. The numerically deter-
mined AK_j_- values from both methods were compared and correlated with the experimentally obtained crack
growth rates for SiC/Ti-15-3 [0]s oriented composites. The near crack tip opening profile was also determined
for both methods and compared with the experimentally obtained measurements.
17. Key Words (Suggested by Author(s))
Metal matrix composite; Fatigue crack growth; Fiber
bridging; Effective stress intensity; Crack tip displacement
18. Distribution Statement
Unclassified - Unlimited
Subject Category 39
19. Security Classif. (of this report) 20, Security Classif. (of this page) 21. No. of pages
Unclassified Unclassified 8
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