Residual thermal strains and stresses in nickel aluminide matrix composites

Scripta METALLURGICA et MATERIALIA

Vol.

25, pp. 2547-2552, 1991 Printed in the U.S.A.

Pergamon Press plc All rights reserved

RESIDUAL T H E R M A L STRAINS AND S T R E S S E S IN N I C K E L ALUMINIDE MATRIX C O M P O S I T E S A. Saigal Department of Mechanical Engineering Tufts University Medford, MA 02155 and D. S. Kupperman Materials and Components Technology Division Argonne National Laboratory Argonne, IL 60439 {Received August 12, 1991) {Revised September 9, 1991)

Introduction The mechanical performance of most engineering materials, including hightemperature composites, is influenced by process--induced residual thermA! strains and stresses that are locked in the constituents during postfabrication cooling. Saphikon and tungsten-fiber-reinforced nickel aluminide matrix composites, along with silicon carbide-fiber-reinforced titanium matrix composites, are currently being evaluated for structural applications in Jet engines and space applications because of their low weight and high specific strength and stiffness at high temperatures. NiAI matrix high-temperature composites are fabricated at a temperature of about 1260°C; because of mismatch between the coefficients of thermal expansion of reinforcing (Saphikon and W) fibers and the matrix, thermally induced residual strains and stresses can be significant. In many engineering composites, chemical bending between the reinforcements and the matrix is either weak or nonexistent (1,2). Thermal stresses play an important role in m a n y of the mechanical properties and subsequent behavior of the composites because they influence the load transfer characteristics of the fiber/matrlx interface. Therefore, it is important to know the residual strains and stresses that exist in the composites. For all composites with crystalline constituents, neutron diffraction (ND) is a powerful tool for measuring bulk elastic residual swains, from which residual stresses can be calculated in m u c h the same w a y as done with x-ray diffraction. N D can penetrate deeply into a material. In addition, the residual stresses and strains in the matrix and the fibers, parallel and perpendicular to the fibers, can be simultaneously determined by aligning the fibers 45 ° to the neutron b e a m with detectors 1-90° from the

2547 0036-9748/91 $3.00 + .00 Copyright (c) 1991 Pergamon Press plc

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n e u t r o n b e a m direction, as s h o w n in Fig. I. ND h a s b e e n u s e d to m e a s u r e residual s t r e s s e s a n d strains in a n u m b e r of m e t a l m a t r i x a n d c e r a m i c m a t r i x composites (3-6). In addition, MaJumdar et al. u s e d the I n t e n s e Pulsed Neutron Source a n d the a s s o c i a t e d General Purpose Powder Diffractometer at Argonne National L a b o r a t o r y to m e a s u r e residual strains in a n u m b e r of engineering c o m p o s i t e m a t e r i a l s a n d to c o m p a r e the resulting values with t h o s e e s t i m a t e d b y finite e l e m e n t analysis (7). In the p r e s e n t study, finite e l e m e n t a n a l y s i s w a s u s e d to e s t i m a t e the residual t h e r m a l s t r a i n s and s t r e s s e s t h a t develop d u r i n g postfabrication cooling of S a p h l k o n a n d tungsten-fiber-reinforced NiAI h i g h - t e m p e r a t u r e c o m p o s i t e s . T h e n u m e r i c a l s t u d y w a s conducted over the t e m p e r a t u r e r a n g e of 2 0 - 1 2 6 0 o c . ND w a s u s e d to m e a s u r e the residual t h e r m a l strains in the NtAI m a t r i x a t r o o m t e m p e r a t u r e a n d to c o m p a r e the values with those estimated b y the n u m e r i c a l analysis. Finite E l e m e n t Model The finite element m e t h o d is i n c r e a s i n g l y b e i n g u s e d to m o d e l r e s i d u a l s t r e s s e s a n d strains, deformation, interaction of constitutive p h a s e s , a n d plastic behavior of metal m a t r i x composites. The finite e l e m e n t model a s s u m e s t h a t the composite c a n be a p p r o x i m a t e d b y an infinite s q u a r e a r r a y of cylindrical fibers e m b e d d e d in the matrix. B e c a u s e the idealized model is r e g u l a r a n d s y m m e t r i c , only one unit-cell containing o n e - q u a r t e r of the fiber is analyzed (8.9). T h e n u m e r i c a l a n a l y s e s were performed with the commercial finite e l e m e n t code ANSYS (10). An elastoplastic m a t r i x is a s s u m e d , a n d a bilinear s t r e s s - s t r a i n curve is u s e d to define its properties b e y o n d the yield point. Fibers were a s s u m e d to be linearly elastic a n d isotropic. The fiber a n d the matrix were discretized u s i n g eight-noded, linear, i s o p a r a m e t r i c , t h r e e - d i m e n s i o n a l solid e l e m e n t s a n d were analyzed u n d e r conditions of gener~liTed p l a n e strain. The composite s y s t e m s investigated c o n s i s t of 30 vol.% S a p h i k o n fibers a n d 35 vol.% W fibers in an NiAl matrix. The S a p h i k o n a n d W fibers were 150 ~ m and 200 ~m in diameter, respectively. The c o m p o s i t e s a m p l e s were in the form of p l a t e s with 6 plies a n d were h o t - p r e s s e d at I 0 9 3 ° C / 1 0 3 . 5 MPa for 3 0 rain a n d t h e n h o t - i s o s t a t i c p r e s s e d at 1 2 6 0 ° C / 1 3 8 MPa for 4 h. The sWain-free t e m p e r a t u r e is a s s u m e d to be 1260°C. The m a t e r i a l properties of the fibers a n d the m a t r i x u s e d in t h e analyses are t e m p e r a t u r e - d e p e n d e n t . The t h e r m a l e x p a n s i o n coefficient of S a p h i k o n is given b y a ( m / m °C) = 5.852 x 10 - 6 + 8.248 x 10 - 9 T - 3.488 x 10 - 1 2 T 2 The t h e r m a l e x p a n s i o n s of W a n d NiAI are given b y AL/L x 100 = - 8.69 x 10 - 3 + 3.83 x 10 - 4 T + 7.92 x 10 - 8 T 2 and AL/L x I 0 0 = - 9.1 x 10 - 4 + 1.281 x 10 - 3 (T-20) + 2.7 x 10 - 7 (T-20) 2 - 3.62 x 10 - 1 1 (T_20)3,

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NiAI M A T R I X COMPOSITES

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respectively. Figure 2 s h o w s the m o d u l u s of elasticity of the fibers a n d the m a t r i x u s e d in the analyses. Yield s t r e n g t h of the NiAI m a t r i x is s h o w n in Fig. 3 (11). For a 3--D s t a t e of stress, the yon Mises s t r e s s (effective stress) is c o m m o n l y u s e d a s the criterion for ductile materials. Results a n d Discussion At room t e m p e r a t u r e , the m a x i m u m t h e r m a l l y induced effective s t r e s s in the NiAI matrix in the 30 vol.% S a p h i k o n / N i A l a n d 35 vol.% t u n g s t e n / N i A l c o m p o s i t e s are on the order of 2000 a n d 2500 MPa, respectively. T h e s e v a l u e s far exceed the yield s t r e n g t h of NIAI, and t h u s the m a t r i x u n d e r g o e s significant plastic deformation. Figure 3 illustrates the m a x i m u m thermally i n d u c e d residual s t r e s s e s (based on linear elastic analyses) in the NiAI m a t r i x as the 30 vol.% Saphlkon/NiA1 a n d 35 vol.% W/NiAI c o m p o s i t e s are cooled from the s t r a i n - f r e e t e m p e r a t u r e of 1260°C to r o o m t e m p e r a t u r e . The estimated r e s i d u a l s t r a i n s (plastic a n d elastic axial matrix, elastic t r a n s v e r s e matrix, and elastic axial fiber) for 30 vol.% Saphikon/NiAl a n d 35 vol.% tungsten/NiAl composites are shown in Figs. 4 a n d 5, respectively. These e s t i m a t e s are b a s e d on elastoplastic finite e l e m e n t a n a l y s e s . Axial s t r a i n s in the m a t r i x are f o u n d to be tensile, whereas transverse s t r a i n in the m a t r i x a n d axial strain in the fibers are compressive. In the ND experiments, t h e n e u t r o n b e a m p a s s e d t h r o u g h the t h i c k n e s s of t h e composites. Figures 4 a n d 5 also c o m p a r e the average m e a s u r e d residual s t r a i n s in the NiAI matrix (symbols), parallel a n d p e r p e n d i c u l a r to the fiber direction, w i t h t h o s e e s t i m a t e d b y finite element analyses. T h e m e a s u r e d axial a n d t r a n s v e r s e s t r a i n s in the m a t r i x are in excellent a g r e e m e n t w i t h the c o m p u t e d values. For the 30 vol.% S a p h i k o n / N I A l composites, the m e a s u r e d axial a n d t r a n s v e r s e s t r a i n s in the m a t r i x are +0.14% a n d -0.04%, respectively. For the 35 vol.% W/NiAI composites, t h e m e a s u r e d axial and t r a n s v e r s e s t r a i n s in the m a t r i x are +0.13% a n d -0.05%, respectively. The s t r a i n s in the m a t r i x a n d the fibers are similar for b o t h t h e c o m p o s i t e s except for the plastic axial s t r a i n in the matrix, w h i c h is larger in t h e 35 vol.% W/NiAI composite t h a n in the 3 0 vol.% S a p h i k o n / N i A l composite. Figures 6 a n d 7 s h o w the various s t r a i n s in the S a p h i k o n / N i A l a n d W/NiAI composites a s a function of the volume fraction of the reinforcing fibers. For b o t h composites, the elastic s t r a i n s in the m a t r i x are i n d e p e n d e n t of the v o l u m e fraction of the reinforcing fibers. In addition, a s the volume fraction of the reinforcing fibers increases, the plastic axial m a t r i x s t r a i n increases a n d the elastic axial fiber s t r a i n decreases. As s h o w n in Fig. 8, t h e residual axial s t r e s s e s in the two c o m p o s i t e s are similar. The residual s t r e s s e s are c a l c u l a t e d u s i n g the Hooke's law a n d elastic strains. In addition, as the volume fraction of t h e reinforcing fibers increases, the axial s t r e s s e s in the fibers decrease, w h e r e a s , t h o s e in the m a t r i x are relatively u n c h a n g e d . T h i s s u g g e s t s t h a t the residual m a t r i x s t r e s s e s a n d s t r a i n s are controlled more b y t h e I o w - m a t r l x yield stress t h a n b y the f i b e r / m a t r i x e x p a n s i o n m i s m a t c h .

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Conclusions 3-D elastoplastic finite element analyses were used to estimate the thermally induced residual strains and stresses in Saphikon/NiAl and tungsten/NiAl composites. Large residual strains and stresses develop in these composites during cool-down from the processing temperature to room temperature. The thermally induced effective stress in the matrix exceeds the yield stress, and the matrix undergoes significant plastic deformation. The fiber is under compressive residual strains and stresses. Average axial and transverse strains in the matrix are tensile and compressive, respectively, and are similar for both Saphikon and W-fiber-reinforced NiAI composites. This suggests that the residual matrix stresses and strains are controlled more by the low-matrix yield stress than by the fiber/matrix expansion mismatch. Neutron diffraction was used to measure residual thermal strains in the matrix of these hightemperature composites. The measured data are in excellent agreement with finiteelement predictions and validate the results of the numerical analyses. Acknowledgments This work was supported by NASA and GE Aircraft Engines, and by the U,S. Department of Energy unde r Contract W-31-109-Eng-38. The work benefited from the use of the Intense Pulsed Neutron Source at Argonne. The authors t hank P. IC Wright for supplying the samples and 1~ L. Hitterman for assistance in data acquisition. References 1. 2. 3.

D.C . Phillips, J. of Materials Science, 9, 1847 (1974). IC M. Prewo and J. B. Brennan, J. of Materials Science, 15, 463 (1980). P. Predecki, ~ Abuhasan, and C. S. Barrett, Advances in X-Ray Analysis, 3 1 . 2 3 1 (1988). 4. A.J . Alien, M. Bourke, M. T. Hutchings, A. D. Krawitz, and C. G. Windsor, Residual Stresses in Science and Tech., E. Macherauch and V. I-Iauk, Eds., DGM Informations-gesellschaft Verlag, Oberursel, 1, 151 (1987). 5. D.S. Kupperman, S. Majumdar, S. R. MacEwen, R. L. Hitterman, J. P. Singh, R. A. Roberts, and J. L. Routbort, Review of Progress in Quantitative Nondestructive Evaluation, D.O. Thompson and D.E. Chimenti, Eds., Plenum, 7B, 961 (1988), 6. A.D. Krawitz, D. G. Reichel, and R. L. Hitterman, J. of Materials Science and Engineering, Al19, 127 (1989)., 7. S. MaJumdar, J. P. Singh, D. S. Kupperman, and A. D. Krawitz, J. of Engineering Materials and Technology, 113, 51 (1991). 8. J . R . Brockenbrough, S. Suresh and H. A. Wienecke. Acta Metall., 39, 735 (1991). 9. R.P. Nimmer, R. J. Bankert, E. S. RuseU, and G. A. Smith, Proc. 13th Annual Conf. on Composite Materials and Structures, Cocoa Beach, FL, (1989). 10. ANSYS Users Manuals, Vol. I and II, SASI, (1990). 11. R. D. Noebe, et al., 3rd HITEMP Review, NASA Conf. Pub., 20-1 (1990).

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450

i

,

i

D

~eL4 0 0 n Beam 90"-L

~,250 u m 300

8aphikon ----Tungsten ......

~ 260 o

Pxtldl¢l m F fro~ ~De.R I

--NIAI

~200 o ~ 100

Oiffmctq

2~o

100

4~o

600

'

Fig. 1,

2600

•~

Fig. 2.

Schematic representation of experimental setup.

i

,

i

i

i

,

i

i

'

2000

1400

, 30

I vol.%

s Sephlkon/NIAI

0.0 ~"...

~' ~. •

ofloetlve

max. "~

35 v o l . %

m a t r i x stress, W/NiAI

~ 0.4

N

~ 1600

o.°

c ~n0.2

~1000 W efteotlve matrix s t r e s s , " - . 30 vol.% 8sphlKoNNIA! "'-...

max.

500

1200

(°C)

Modulus of elasticity as a function of temperature.

0.8

,

~o~o

800

Temperature

'

-I

200

Fig. 3.

vltld strength, NIAI i

400

i

,

0 "'"" I

600 000 1000 Temperature (eC)

~ ""~

1200

400

Yield strength and effective residual stresses in NiAI matrix as a function of temperature

-0.2

ins.ix, .,.stir-. t ~ "~"W' 200

.,..,i . . . . ,;i 400

600

800

Temperature

Fig. 4.

10100

12100

(°C)

Residual strains in 30 vol.% Saphikon/NiAl composite as a function of temperature.

400

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NiAI MATRIX COMPOSITES

0.5

i

i

i

0.8

i

35 vol.% Tungxtan/NiAI 0.5

i

i

0.6

+-,

~ 0.4

Vol. 25, No. ii

=O.l

o

matrix,

-0.2

,~o

,~o

5+o

.o.4

5~o ,o'oo ,,'oo ,,oo

210

0,6

Fig. 6.

Residual strains in 35 vol.% tungsten/NiAl composite as a function of temperature.

~

0.8

2OO

0.4 malrlx,

allllll:,

-0.4

ellrlx~

~ o , 210

Fig. 7.

matrix,

olaall¢,

ixlal

matrix,

olaatlo,

trarllvOrll

axial

2l, 310 316 410 4f, Fiber volume friction (%)

510

55

matrix

llllnO,

_

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-600

1 4C -800 -1000

axial

2Is 310 315 410 418 Fiber volume fraction (%)

$sphlkon/NIAI - - -- TungatenlNIAI

j -400

axial

{O

-0.2

IXIS.~_,..,.._..-.----

4OO galen/NIAI

E

0

i

Residual strains in Saphikon/ NiAl composite as a function of volume fraction of reinforcing Saphikon fibers.

0 eL X~..200

_: 0.2

i

Sxphlkon/NIAI

axial

Temperature (°C)

Fig. 5.

i

matrix, plastic,

. . . . - • o r ,O l l l t l a ~

.o.2 OllSlla,

i

0.4

~0.2 V) •

i

I

50

5S

Residual strains in t u n g s t e n / NiAI composite as a function of volume fraction of reinforcing t u n g s t e n fibers.

-120C

S

rag. 8.

210

215 310 '318 410 ,415 Fiber volume fraction (%)

510

Residual axial stresses in Saphikon/NIAl and t u n g s t e n / NiAI composites as a function of volume fraction of reinforcing fibers.

S5