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

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 determined for both methods and compared with the experimentally obtained

measurements.

INTRODUCTION

The ability to predict fatigue crack growth behavior of metal matrix composites 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 application of a closure pressure in the bridged zone proportional to the load carried 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 displacements, measurement of crack growth rates and identification of active fatigue

failure mechanisms.

Both types of models were used to predict the fatigue crack growth behavior 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, Companion 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 consideration 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 calculating the effective crack driving force, _Kef f. The effective stress intensity 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 factor, SIF, for an unbridged crack of length a is given by:
a

K(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:

u(x) 2(t - _c2Ja ) _ 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 pressure 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 function 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 displacement 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 distance 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 applicability 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

10-10 0

_ 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.
NatlonaI Aeronautics and Report Documentation Page

Space Administration

1. Report No. 2. Government Accession No. 3. Recipient's Catalog No.

NASA TM-103102

5. Report Date 4. 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 determined 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

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Unclassified - Unlimited

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