Metal matrix composites (MMC) are the subject of intensive study and are receiving serious consideration for critical structural applications in advanced aerospace systems. MMC structural analysis and design methodologies are studied. Predicting the mechanical and thermal behavior and the structural response of components fabricated from MMC requires the use of a variety of mathematical models. These models relate stresses to applied forces, stress intensities at the tips of cracks to nominal stresses, buckling resistance to applied force, or vibration response to excitation forces. The extensive research in computational mechanics methods for predicting the nonlinear behavior of MMC are described. This research has culminated in the development of the METCAN (METal Matrix Composite ANalyzer) computer code

Hopkins, Dale A.

Murthy, Pappu L. N.

English

NASA Technical Reports Server

N88-22395
METCAN - THE METAL MATRIX COMPOSITE ANALYZER
Dale A. Hopkins and Pappu L.N. Murthy"
Structural Mechanics Branch
NASA Lewis Research Center
ABSTRACT
Metal matrix composites (MMC) have recently been the subject:of intensive study
and are receiving serious consideration for critical structural applications in
advanced aerospace systems. The routine application of MMC in aerospace struc-
tures will evolve as concurrent developments progress in related areas of proc-
essing and fabrication, experimental mechanics, and computational structural
analysis and design methodologies. This presentation concerns recent research
efforts related to the latter aspect, namely, MMC analysis and design.
Predicting the mechanical and thermal behavior and the structural response of
components fabricated f=Qm _s_iCrequires the use of a variety of mathematical
models. These models, for example, relate stresses to applied forces, stress
intensities at the tips of cracks to nominal stresses, buckling resistance to
applied force, or vibration response to excitation forces. The models just
mentioned require initial tangent and strain-dependent stress-strain relation-
ships. Experimental data indicate that the stress-strain responses of unidi-
rectional MMC are (I) slightly nonlinear in the longitudinal direction,
(2) mildly nonlinear in the transverse direction, and (3) highly nonlinear in
intralaminar shear. In-service loads on MMC structures can generally be
expected to strain the metal matrix nonlinearly. The stress-strain relation-
ships for a laminate may then become load-path dependent, and hence it is
important to be able to track the composite behavior throughout its loadhis-
tory. Moreover, the mechanical performance and structural integrity of MMC
are ultimately governed by the behavior of the constituents at a local level.
In general this behavior is dynamic because of various nonlinearities asso-
ciated with, for example, (i) large local stress excursions, (2) temperature-
dependent material properties, (3) time-dependent effects, and (4) constituent
chemical reactions. It is important also then to be able to track behavior at
the local level.
This presentation describes the extensive research in computational mechanics
methods for predicting the nonlinear behavior of MMC. This research has culmi-
nated in the development of the METCAN (metal matrix Eomposite analyzer)
computer code.
*Cleveland State University, Civil Engineering Department, Cleveland, Ohio
44115 (work funded under NASA Grant NAG3-550; monitor, Christos C. Chamis) and
NASA Resident Research Associate.
2-141
https://ntrs.nasa.gov/search.jsp?R=19880013011 2020-03-20T06:32:19+00:00Z
OVERVIEWOF STRUCTURALNALYSIS
The process of structural analysis can be viewed simplistically as the solution
of pertinent governing equations to arrive at estimates of important response
variables that are usually of interest in comparison with some limiting values.
This is summarized below, where the matrix notation implies solution by a dis-
crete numerical technique such as the finite element method. Nonlinear problems
are commonly approached by using a piecewise linear approximation in which the
solution becomes an incremental or iterative process. Unique aspects associ-
ated with the analysis of a composite structure derive from the additional
models required (I) to arrive at a description of the structure characteristics
and (2) to determine the localized response, which becomes important for these
systems. The additional models are collectively referred to as composite
mechanics.
SYSTEM
EQUATIONS
OF
MOTION
[M] [u'l+ [C](ul+ [K][ul= [F(t)l
[ul--[UA_
CONSTITUTIVE
EQUATION
Ie} = [D][B]Iul
NATURAL
FREQUENCY
EIGENPROBLEM
<[K] - oo2[M])[u}= (ol
o__< ooA
CD-88-32579
2-142
INTEGRATEDAPPROACHTOMETALMATRIXCOMPOSITEANALYSIS
The integrated approach implemented in the METCANcomputer code is illustrated
in the figure. The cyclic arrangement defines the computational effort for
each load increment. Material nonlinearity is treated at the constituent
(fiber, matrix, interphase) level, where the current material model describes
a time-temperature-stress dependence of a constituent's mechanical and thermal
properties at any instant in its "material history space." Characteristic
properties of the composite, at the various levels of simulation, are approxi-
mated from the instantaneous constituent properties by composite mechanics.
This process, termed "synthesis" here, results in a point description of
"equivalent pseudo-homogeneous" properties for the composite. These proper-
ties could be used, for example, to specify elemental properties for a subse-
quent global structural analysis by the finite element method. In the reverse
or "decomposition" process, global response variables are "decomposed" into
localized response, again at the various levels of simulation. The METCAN
code, at this point, does not incorporate the global structural analysis capa-
bility, and hence "a priori" load histories are specified as part of the input
to the code.
FINITE ELEMENT
t
"SYNTHESIS"
/
..,,,m-
COMPONENT
_ _ FINITE ELEMENT
GLOBALSTRUCTURAL
ANALYSIS
LAMINATE LAMINATE
t-'--,,,o,, , LAMINATE"DECOMPOSITION"THEORY
/:/i:_iiii_:¢PLY NONLINEARIMATERI LMODEL /:i PLYI-/
COMPOSITE COMPOSITE
MICROMECHANICS MICROMECHANICS
THEORY THEORY
CONSTITUENTS
CD-88-32580
2-143
COMPOSITE LOCAL BEHAVIOR AND RESPONSE
A unique feature of the METCAN computer code is its treatment of the interphase
as a separate constituent. This is an important consideration for metal matrix
composites in high-temperature applications where the fiber and the matrix may
chemically react, forming an interphase. At the most local level constituent
behavior and response variables are tracked in the three intralaminar sub-
regions illustrated in the figure.
SUBREGIONSOF
INTRALAMINAR .,, _...
NONUNIFORMITY.-_
3
MATRIX
_..,_ _._- INTERPHASE
i--- I
CD-88-32581
2-144
MODULAR STRUCTURE OF METCAN
In developing the METCAN computer code priority has been placed on maintaining
a modular software structure and providing a user-friendly interface. The code
features include (I) a dynamic storage allocation scheme for efficient use of
computer resources, (2) a resident data bank of constituent material proper-
ties, (3) user-selective control of primary (printed) output, (4) generation of
a secondary output file for subsequent graphics postprocessing, and (5) both
interactive and batch modes of operation.
DYNAMIC
STORAGE
ALLOCATION
I I ,L I I
DATABANK MATERIAL I
MODEL
.UT [COMPOS,TEMICROMECHANICS
GRAPHICS
FILE
LAMINATE
ANALYSIS
CD-88-32582
2-145
METCAN CURRENT AND FUTURE CAPABILITIES
The current capabilities of the METCAN computer code provide for most of the
essential aspects of metal matrix composite analysis and design. The code also
serves as a framework within which future capabilities will be developed. The
current and planned future capabilities are summarized below.
• SIMULATED BEHAVIORAND RESPONSE
MECHANICALPROPERTIES
THERMAL PROPERTIES
STRESSESAND STRAINS
MICROSTRESSES
FRACTURESTRESSES
FINITE ELEMENTCOMPATIBILITY
,, LOAD AND EFFECT
MONOTONICLOAD HISTORIES
CYCLIC LOAD HISTORIES
* INTERPHASE PROPERTIESAND GROWTH
* STEADY-STATECREEP
* THERMAL RATCHETTING
* CREEP RUPTURE
* DAMAGE
* THERMAL SHOCK
" IMPACT LOADING
CD-88-32583
2-146
UNIDIRECTIONALGRAPHITE/COPPERMMCPROPERTYPREDICTIONS
A fairly comprehensive summaryof the mechanical and thermal properties for a
unidirectional graphite/copper metal matrix composite at several fiber volume
fractions is given in the table. The properties were determined (I) by using
the METCAN computer code and (2) from a detailed three-dimensional finite ele-
ment analysis in which both the fiber and the matrix were modeled discretely.
The METCAN-predicted properties, based on the simplified composite mechanics
equations, show excellent agreement overall with the finite-element-simulated
properties.
PROPERTY
E_I, Msi
E_2, Msi
Em, Msi
Gn2, Msi
Gm, Msi
Gn3,.Ms!
_r12, II1.1111.
_z3, in./in.
_'n3, in.lin.
_nl, ppm
aM, ppm
czm, ppm
K.1, Btu in.l°F hr in.2
K_, Btu in.l°F hr in.2
Kin, Stu in.l°F hr In.2
FIBER VOLUME FRACTION, PERCENT
22.3 46.6
METCAN FINITE
ELEMENT
37.3 36.7
10.2 ---
10.2 11.0
4.5 4.8
4.2 4.5
4.5 ---
0.26 0.30
0.30 0.26
0.30 ---
3.0 3.7
9.6 10.9
9.6 ---
20.6 ---
20.4 ---
20.4 ---
METCAN FINITE
ELEMENT
58.4 58.0
6.5 ---
6.5 6.9
3.2 3.4
2.8 2.7
3.2 ---
0.25 0.29
0.30 0.22
0.30 ---
0.83 1.40
9.4 11.1
9.4 ---
22.0 ---
21.7 ---
21.7 ---
62.2
METCAN FINITE
ELEMEN1
72.0 71.8
4.6 ---
4.6 5.0
2.5 2.6
2.1 1.8
2.S ---
0.24 0.28
0.30 0.19
0.24 ---
0.09 0.42
9.2 10.9
9.2 ---
22.8 ---
22.6 ---
22.6 ---
CD-88-32584
2-147
UNDIRECTIONALBORSIC/TITANIUMMCPREDICTEDMODULI
An example of the METCANcomputer code's capability for predicting composite
material properties is illustrated in the figure. The results shownare the
longitudinal and transverse moduli for a unidirectional borsic/titanium metal
matrix composite. The results demonstrate an excellent agreement between
METCANpredictions, detailed three-dimensional finite element simulations, and
experimentally measuredvalues.
MODULUS,
Msi
40--
-- r/f/
30-- __--
20-- --
_---
1o- __--
o -
LONGITUDINAL
MEASURED
THREE.DIMENSIONALFINITE ELEMENTSIMULATION
METCAN
CD-88-32585
2-ia8
UNIDIRECTIONALGRAPHITE/COPPER MMC TRANSVERSE STRENGTH BOUNDS
A result of a study of fiber/matrix interface effects (bond quality) on compos-
ite transverse strength that used the METCAN computer code is shown in the
figure. The yield and fracture stress are presented for a unidirectional
graphite/copper metal matrix composite with two different copper matrix treat-
ments (annealed and hardened). Shown are the predicted stress levels without
an interface (no bond) and with an interface (perfect bond). The two condi-
tions can be viewed as extremes, or bounds, on the bond quality achieved in
actual fabrication. Indeed, experimental data for transverse strength exhibit
significant scatter and, although not shown in the figure, generally fall
within the bounds predicted by METCAN.
TRANSVERSE
STRESS,
ksi
25 I
20_
15:_
4N
Iu
5--
0
re_m_J U/ITLIf_IIT ild'rrD_Ar_
llll,lvu i ii! i bill M_G
WITH INTERFACE
ANNEALED
YIELD
I-I%%%%%%%%
%%%
%%%
%%%
%N%
ANNEALED
FRACTURE
%%%%
%\\%
'_.\\%
%\\%
\\\\
\\\%
_.\\\
till
//// %%\_
fl/_ %\%%
_'ii./
Ill/ %N_\
fill %\N'%
/IIi _\\',
i //,/,/ \\\%II1,, ",.\ \',
HARDENED
YIELD
\\\',
__x.x_,
_\NN
HARDENED
FRACTURE
CD-88-32586
2-149
UNDIRECTIONALTUNGSTEN/COPPERMMCSTRESS-STRAINRESPONSE
An example of the type of information obtained from the METCAN computer code
is given in the figure, which shows the nonlinear stress-strain response due
to monotonic loading at room temperature for unidirectional tungsten/copper
metal matrix composites with two different fiber volume fractions. Evident
from the figure is the excellent agreement between the METCAN-predicted and
experimentally measured responses.
LONGITUDINAL
STRESS,
ksi
2OO
150
100
50
FIBERVOLUME
FRACTION,
PERCENT
-- 0 EXPERIMENTALDATA _,.............0 46.5
11.9
,
.5 1.0
LONGITUDINAL STRAIN, PERCENT
CD-88-32587
2-150
UNDIRECTIONAL GRAPHITE/COPPER MMC STRESS-STRAIN RESPONSE
Another example of METCAN computer code predictive capability is shown here.
The results shown in the figure are the nonlinear stress-strain response to
monotonic loading for a unidirectional graphite/copper metal matrix composite
at elevated as well as room temperature, and for transverse as well as longi-
tudinal loading direction.
LONGITUDINAL
STRESS,
ksi ,°°F //I ,Es,
/ / .f" TEMPERATURE,/ /,," ........ __
-- ,o-- -"-" 1500
.5
LONGITUDINALSTRAIN, PERCENT
I
1.0
CD-88-32588
TRANSVERSE
STRESS,
ksi
60--
30
TEST
TEMPERATURE,
---- 7o
1.0 2.0
TRANSVERSESTRAIN, PERCENT
CD-88-32589
2-151
METAL MATRIX COMPOSITE FABRICATION PROCESS
The METCAN computer code has recently been used to investigate the development
of residual stresses in a typical fabrication process, as illustrated in the
figure. The effect of fabrication residual stresses on subsequent in-service
performance of aerospace propulsion structures has also been investigated by
using METCAN in conjunction with other global structural analysis computer
codes.
METAL-MATRIX COMPOSITE FABRICATION PROCESS
MIX
MATRIX ._.p
,.owo,.
+
TEFLON _%
+
STODDARDSOLUTION
HEAT ROLL POWDER
CLOTH
lAY UP ANDHOTPRESS
COMPOSITE
CD-I18-32590
MMC PROCESSING CONDITIONS
TEMPERATURE,°F;
PRESSURE,psi
1830; 1830;
0 1000
45 05
1830;
1000
85
TIME, mln
175 180
CD-_B-32591
2-152
TUNGSTEN/SUPERALLOY MMC TURBINE BLADE
The figure shows a turbine airfoil fabricated from an angle-plied [+45°/-45°]s
tungsten/superalloy composite and subjected to hypothetical aircraft engine
flight mission conditions.
TURBINEAIRFOIL FINITE ELEMENTMODEL
2OO0
1500
TEM-
PERA-
TURE, 1000
OF
5OO
PRES-
SURE,
psi
m
I¢ I
2 40 60 80
150 --
IO0
5O
10 O00--
1 ENGINE
SPEED,
_ rpm
2 40 60 80
SO00
0 0 0
TIME, mln
2 4O
I I
6O 8O
CD-88-32592
2-153
TUNGSTEN/SUPERALLOYMMCTURBINEAIRFOIL ANALYSIS
The results from a quasi-static incremental analysis of the airfoil model show
a variety of behavior and response quantities corresponding to the outermost(exterior surface) ply at the midchord root location on the airfoil (identified
by arrow in previous figure). These results were obtained by interfacing the
METCANcomputer code with the familiar NASTRAN finite element structural analy-
sis computer code.
MODULUS
F FIBER
M MATRIX
O INTERPHASE
L PLY
BO--
LONGI.
TUDINAL, 30
Msi
F
f
0
__f
I I
_I o0 ,o
TRANS-
VERSE, 3O
Msi
TIME, mln
-- F ,
____J__I I
2 4O 60 8O
co-iM_32593
THERMALEXPANSIONCOEFFICIENT
10--
LONGI.
TUDINAL,
_.ln. In.l°F
F FIBER
M MATRIX
O INTERPHASE
L PLY
10--
-- _ TRANS-
VERSE,
-- _ _,in. ln./°F
F
I I
"_I_2 _O BO ,0
TIME, mtn
,__/,-----
F
NATURALFREQUENCYANDLONGITUDINALSTRESS
I
6O 8O
F FLEER
M MATRIX
O INTERPHASE
L PLY
FREQUENCY,
HZ
MODE
5-- 3
---- _ STRESS,
ksi
I_ _ I t -++oo2 4 60 80
TIME, min
loo
O
I J
_1 o0 o0
C0414-_
2-154
UNIDIRECTIONALBORON/ALUMINUMMMCCY LICSTRESS-STRAINRESPONSE
An example of planned future capability for the METCAN computer code, which is
currently under development, is shown in the figure and represents the pre-
dicted nonlinear stress-strain response to cyclic loading for a unidirectional
boron/aluminum metal matrix composite, for both longitudinal and transverse
loading directions. Further investigation of the nature of unloading at the
constituent level is needed before this feature can become a permanent capabil-
ity of the METCAN computer code.
LONGITUDINAL TRANSVERSE
300 --
2OO
i
100i
STRESS, 0
ksi
-100
-200
-300 I I
-1.0 -.5 0 .5
16--
8--
u
--0 --
I -16
1.0 -.15 -.10 -.05
STRAIN, PERCENT
0
I I I
.05 .10 .15
CD-88-32596
2-155
SUMMARY
" METCANPERFORMSMOST ESSENTIALASPECTSOF MECHANICS,ANALYSIS,
AND DESIGNOF METAL-MATRIX COMPOSITES
• METCANIS MODULAR, OPEN ENDED, AND USER FRIENDLY
• STANDARDMETAL-MATRIXCOMPOSITESAS WELL AS INTERPLY HYBRID METAL-
MATRIX COMPOSITESCAN BE ANALYZED
• RESPONSEDUE TO DIFFERENTTYPES OF THERMAL AND MECHANICALLOAD
HISTORIESACCOUNTINGFOR THERMOMECHANICALDEGRADATIONCAN BE
OBTAINEDROUTINELY
• KEY FEATURESOF METCAN INCLUDE
-- LINEAR AND NONLINEARANALYSIS
-- ROOM- AND HIGH-TEMPERATUREPROPERTIES
-- STRESSAND STRAIN INFLUENCECOEFFICIENTS
-- RESIDENT DATA BANK
C_32597
2-156


METCAN: The metal matrix composite analyzer

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