I NASA Technical Memorandum 100793
I . I I
I Mechanics of Composite Materials: Past, Present, and Future
christos c. chamis Lewis Research Center Cleveland, Ohio
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(EaSA-TB- l O O n 3 ) lECBABiICS CF CGCOPGSXTP m a - 13744 41 P CSCL 11D EILTEBZALS: PAST, FEESENT ALLC EGTUBE (NASS)
Uaclas ~ 3 1 2 4 o 3 2 ~ 3
Presented at the I
21st Annual Meeting of the Society for Engineering Science Blacksburg, Virginia, October 15-17, 1984
MECHANICS OF COMPOSITE MATERIALS: PAST, PRESENT, AND FUTURE
C h r i s t o s C. Chamis N a t i o n a l Ae ronau t i cs and Space A d m i n i s t r a t i o n
Lewis Research Center C leve land, Oh io 44135
ABS TRACT
Composite mechanics d i s c i p l i n e s a r e presented and desc r ibed a t t h e i r
v a r i o u s l e v e l s o f s o p h i s t i c a t i o n and a t t e n d a n t sca les o f a p p l i c a t i o n .
C o r r e l a t i o n w i t h exper imenta l da ta i s used as t h e pr ime d i s c r i m i n a t o r between
a l t e r n a t i v e methods and l e v e l of s o p h i s t i c a t i o n . Ma jor emphasis i s p laced
on: ( 1 ) where composi te mechanics has been; ( 2 ) what i t has accompl ished; ( 3 )
where i t i s headed, based on p resen t research a c t i v i t i e s ; and ( 4 ) a t t h e r i s k
o f be ing presumptuous, where i t shou ld be headed. The d i s c u s s i o n i s developed
u s i n g se lec ted , b u t t y p i c a l , examples o f each composi te mechanics d i s c i p l i n e
i d e n t i f y i n g degree o f success, w i t h r e s p e c t t o c o r r e l a t i o n w i t h exper imenta l
da ta , and problems remain ing . The d i s c u s s i o n i s cen te red about f i b e r / r e s i n
composi tes drawn m a i n l y from t h e a u t h o r ' s research a c t i v i t i e s l e x p e r i e n c e
spanning two decades a t Lewis.
STAR CATEGORY 24
Key words: Fiber-compos t e s ; R e s n -mat r ices ; I n t e r p l y h y b r i d s ; I n t r a p l y
h y b r i d s ; Micromechanics; Macromechanics; Combined-stress f a i l u r e ; Laminate
theo ry ; S i n g u l a r i t y mechanics; L i f e l d u r a b i l i t y ; F r a c t u r e toughness; Damage
t o l e r a n c e ; P rog ress i ve f r a c t u r e ; S t r u c t u r a l a n a l y s i s ; Envi ronmenta l e f f e c t s
INTRODUCTION/BACKGROUND
Composite mechanics has evolved to encompass a wide range of continuum
and discrete mechanics methods.
fiber/matrix composite behavior.
predicted at various inherent scales (corresponding to the fabrication
processes) in the composite from microstructure to structural response. Within
each inherent scale has evolved a specialty composites mechanics discipline
with several levels of sophistication.
These methods are used to study and predict
The composite behavior is studied and/or
The various levels of sophistication that have evolved in each composite
mechanics discipline were influenced by three important factors: (1)
capturing the intrinsic physics; ( 2 ) degree o f local detail desired; and (3)
technical interests of the investigator(s1. Collectively, these three factors
have led to numerous significant contributions at the various scales of
composite behavior.
The objective of this report is to describe/discuss composite mechanics
at its various levels of sophistication and attendant inherent scales of
application with respect to past, present, and future.
such a report is to stimulate thinking which will hopefully lead t o
"revolutionary" research.
(1) composite mechanics inherent scales; ( 2 ) composite mechanics disciplines;
( 3 ) composite mechanics discipline levels of sophistication; ( 4 ) factors
influencing composite mechanics discipline; scale, and level of
sophistication; ( 5 ) discriminators between alternate methods of level of
sophistication; ( 6 ) composite mechanics - where it has been; ( 7 ) composite
mechanics - what it has accomplished; ( 8 ) composite mechanics - where it is
headed; and ( 9 ) composite mechanics - where it should go (a personal view).
The intent of preparing
The description/discussion is organized as follows:
2
Examples are used to supplement and complement the discussion. These
examples are mainly taken from the author and his Lewis collegues' research
over the years.
mechanics during that period. The references sited are NASA reports which are
available in practically all technical libraries. Each of these references
includes relevant references for that subject.
However, they are representative of the evolution of composite
A
C
D
d
E
E
F
.F
G
I
i
K
M
m
N
NQ
R
s SN
SYMBOLS
laminate axial stiffness
global damping matrix; laminate stiffness matrix; stress wave speed
laminate bending stiffness
fiber diameter
elastic properties matrix as defined by subscripts; modulus, as defined
by subscripts
failure strain as defined by subscripts
global force; failure criterion function
hygrothermal property degradation factor
strain energy release rate
i denti ty matri x index
global stiffness matrix; coupling coefficient in failure criterion
global mass matrix; laminate moment as defined by subscripts
moi s ture
laminate in-plane force as defined by subscripts
number of layers in a laminate
ply orientation matrix; impacting sphere radius
strength as defined by subscripts
fatigue strength
3 -
T temperature
t thickness as defined by subscripts
U global displacement
x,y,z global (structural axes) coordinates
1,2 ,3 ply material axes coordinates
a thermal expansion coefficient as defined by subscripts
n 6 inter fiber spacing
& strain as defined by subscripts
EO global reference plane strain
x eigenvalue; resin selection criteria ratio as defined by
X global curvatures as defined by subscripts
V Poisson's ratio as defined by subscripts
P density as defined by subscripts
U stress as defined by subscripts
w circular frequency
Subscripts
C compress i on
C compos i te property
HTM hygrothermornechanical effect
moisture expansion coefficient as defined by subscripts
Q PlY property m moisture, hygrothermal effects
r resin property
S shear
S sphere
T tension, temperature
xyz respective coordinate directions, properties
subscripts
I 4
123 p l y m a t e r i a l axes r e s p e c t i v e p r o p e r t i e s
a T-tens ion or C-compression
I3 T- tens ion or C-compression
M a t r i c e s
[ 1 a r ray , m a t r i x
v e c t o r , column m a t r i x
[ 1-1 m a t r i x i n v e r s e
I: I T m a t r i x t ranspose
COMPOSITE MECHANICS: INHERENT SCALES AND DISCIPLINES
The v a r i o u s composite sca les correspond t o t h e way the composite i s
made. A schematic i l l u s t r a t i n g how a p o l y i m i d e composite b lade i s made i s
shown i n F ig . 1. The sca les may be v i s u a l i z e d as t h e dimension
(homogenizat ion d imension) w i t h i n which t h e heterogeneous l o c a l s t r u c t u r e i s
desc r ibed and i n t e g r a t e d . W i t h i n t h i s sca le , the i n d i v i d u a l c o n s t i t u e n t s a re
homogenized. R e f e r r i n g t o F i g . 1, t h e micromechanics sca le i s t h e f i b e r
spac ing w i t h i n t h e u n i d i r e c t i o n composite ( a f t e r i n s i t u p o l y m e r i z a t i o n ,
F i g . 1 ) . The macromechanics sca le i s t he p l y th i ckness s ince the p l y
m a t e r i a l - a x i s may be r o t a t e d to p r o v i d e t h e d e s i r e d p r o p e r t i e s about the
s t r u c t u r a l axes (b road goods and p l y c u t t i n g , F i g . 1 ) . The lam ina te t h e o r y
sca le i s t he l am ina te th i ckness which i s an i n t e g r a l m u l t i p l e o f p l y
t h i c k n e s s . W i t h i n t h i s sca le t h e heterogeneous laye red s t r u c t u r e (made o f
p l i e s and i n t e r p l y l a y e r s ) i s homogenized i n t o a composite laminate ( s t a c k i n g
o f p l i e s , f i g . 1 ) . The s t r u c t u r a l mechanics sca le i s severa l t i m e s t h e
laminate th i ckness ( f i n i s h e d b lade , F i g . 1 ) . There fore , these a re the f o u r
impor tan t sca les w i t h i n which t h e v a r i o u s composite mechanics d i s c i p l i n e s a re
fo rmu la ted .
5 -
The various composite mechanics disciplines that have evolved to
describelstudy composite behavior may be grouped into those listed in Table 1 .
The respective scales and homogenization dimensions are summarized in
Table 2. The math model sophistication for each discipline, including region
modeled and key assumptions made, are summarized in Table 3. Continuum
mechanics includes theory of elasticity, plasticity as well as related
subjects, for example fatigue and defect growth.
Several of the composite mechanics disciplines have been integrated into
These codes generally simulate the composite behavior at its computer codes.
various scales. How the integration can be implemented in a code is
schematically shown in Fig. 2 .
The left part of Fig. 2 depicts the upward integration (synthesis) o f
constituent material behavior through the successively larger composite scales
and up to the structure.
(decomposition) of the structural behavior through the progressively smaller
composite scales and down to the constituent material space ( P
f (u, T, m)). This figure pictorially represents the major disciplines of
composite mechanics and parallels the fabrication process in Fig. 1. The
combined stress failure criteria, singularity mechanics, and life/durability
disciplines (Table 2) generally need the composite behavior (stresses,
strains, displacements) predicted by this type o f integrated computer code at
The right part depicts the downward traced
=
I the various scales. The results presented and discussed later were obtained
using such a code [ l l .
COMPOSITE MECHANICS: WHERE HAS IT BEEN? WHAT HAS IT ACCOMPLISHED?
A summary of where composite mechanics has been and what has been
accomplished by using it i s presented in Table 4. The summary, expected
presented in qualitative terms. It includes: (1 ) research conducted on
Y , i s
that
6
d i s c i p l i n e ; (2 ) success ach ieved - t o t h e e x t e n t t h a t t h e r e s e a r c h has
suceeded i n p r o v i d i n g t h e fo rma l i sms to unders tand and /o r q u a n t i f y t h e
composi te b e h a v i o r w i t h wh ich the d i s c i p l i n e i s d e a l i n g ; and ( 3 ) a p p l i c a t i o n -
how e x t e n s i v e l y t h e composi tes community i s u s i n g t h a t d i s c i p l i n e .
I t i s worth n o t i n g t h a t those d i s c i p l i n e s wh ich have r e c e i v e d r a t h e r
min ima l amount o f r e s e a r c h a r e used most e x t e n s i v e l y . The reasons a r e : ( 1 )
t h e t h e o r e t i c a l fundamenta ls a r e e a s i l y unders tood - fo l low c l a s s i c a l
mechanics; ( 2 ) t h e a p p l i c a t i o n i s r e l a t i v e l y s t r a i g h t f o r w a r d ; and (3) t h e
p r e d i c t e d r e s u l t s c o r r e l a t e w i t h measured d a t a .
The r e s u l t s to be p resen ted subsequen t l y were s e l e c t e d t o demonst ra te , t o
some e x t e n t , t h e q u a l i t a t i v e e v a l u a t i o n summarized i n Tab le 4 .
Composite Micromechanics
A schematic on which composi te micromechanics can be based i s shown i n
F i g . 3. The concepts d e p i c t e d i n t h i s f i g u r e i n c o n j u n c t i o n w i t h mechanics
p r i n c i p l e s and assuming i n t e g r a t e d average b e h a v i o r l eads t o t h e t y p e o f
micromechanics equa t ions summarized i n F i g . 4 [21. A complete s e t o f p l y
hygrothermomechanical behav io r r e l a t i o n s h i p s i s summarized i n F i g . 5.
Comparisons o f no rma l i zed r e s u l t s p r e d i c t e d by u s i n g t h e equa t ions i n F i g . 4
w i t h measured d a t a a r e shown i n F i g . 6 f o r s e v e r a l i n t r a p l y h y b r i d
composi tes. A s can be seen, t h e comparisons a r e g e n e r a l l y i n good agreement.
A n o t i c e a b l e e x c e p t i o n i s t h e shear modulus ( S M ) . T h i s modulus i s d i f f i c u l t
t o measure a c c u r a t e l y ; t h i s may account f o r apparen t d i s c r e p a n i e s .
Micromechanics equa t ions for p l y u n i a x i a l s t r e n g t h s a r e summarized i n
F i g . 7 [31. Comparisons w i t h measured d a t a a r e shown i n F i g . 8 f o r t h e same
i n t r a p l y h y b r i d s as i n F i g . 6 . The comparisons a r e a l s o i n g e n e r a l l y good
agreement. The d a t a i n F i g s . 6 and 8 a r e from R e f . 4.
P r e d i c t e d r e s u l t s i n c l u d i n g hyg ro the rma l e f f e c t s a r e shown i n F i g . 9 151.
Again, t h e agreement i s v e r y good c o n s i d e r i n g t h e c o m p l e x i t y of t h e composi te
behav io r s i m u l a t e d by t h e r e l a t i v e l y s imp le e q u a t i o n s . C o l l e c t i v e l y , t h e
comparisons shown i n F
p r e d i c t un i d i r e c t i o n a l
I accuracy". Acceptab le
agreement between p r e d
gs . 5, 6 , 8, and 9 demonst ra te t h a t micromechanics
compos i te b e h a v i o r w i t h i n "accep tab le e n g i n e e r i n g
e n g i n e e r i n g accuracy i s used h e r e i n t o mean t h a t t h e
c t e d r e s u l t s and measured d a t a i s cons ide red t o be as
good as can be expec ted based on e n g i n e e r i n g judgement and on c o n s i d e r a t i o n s
o f t h e c o m p l e x i t i e s and u n c e r t a i n t i e s i n v o l v e d .
Composite Macromechanics
The composi te macromechanics d i s c i p l i n e has genera ted t h e equa t ions t o
p r e d i c t o f f - a x i s ( u n i d i r e c t i o n a l composi tes loaded a t an ang le t o t h e f i b e r
d i r e c t i o n ) p r o p e r t i e s when t h e p r o p e r t i e s abou t t h e m a t e r i a l axes a r e known.
These equa t ions a r e summarized i n F i g . 10 i n m a t r i x form 161. The schematic
i n t h i s f i g u r e de f i nes t h e two c o o r d i n a t e axes and t h e r o t a t i o n . R e s u l t s
p r e d i c t e d by these e q u a t i o n s a r e compared w i t h measured d a t a i n F igs . 1 1 and
12 171. A s can be seen, t h e agreement i s v e r y good. What i s more s i g n i f i c a n t
I about these comparisons i s t h a t p r o p e r t i e s about t h e m a t e r i a l axes were
p r e d i c t e d u s i n g t h e micromechanics e q u a t i o n s d e s c r i b e d p r e v i o u s l y .
Combined S t r e s s F a i l u r e C r i t e r i a
An expanded form o f a combined s t r e s s f a i l u r e c r i t e r i o n e q u a t i o n
i n c l u d i n g hygro thermal and c o n s t a n t a m p l i t u d e c y c l i c l o a d e f f e c t s i s shown i n
F i g . 1 3 [ 6 1 . R e s u l t s p r e d i c t e d from t h i s e q u a t i o n a r e compared w i t h measured
I da ta i n F i g . 14 C71. The d a t a i s a t room tempera tu re , d r y monotonic l o a d
c o n d i t i o n s . The agreement i s e x c e l l e n t .
Laminate Theory
A form of laminate theory equations are summarized in Fig. 15 111.
Results predicted by using these equations are compared with measured data in
Table 5 [81 for moduli and Poisson's ratios.
10 percent except for two of the in plane shear moduli. It is well known that
measuring composite shear properties is a rather delicate task. Uncertainties
in measured data are just as much in question for these types of tests as are
some of the assumptions made in deriving laminate theory equations.
The agreement is better than
Laminate strength (stress at fracture) predicted by linear laminate
theory (equations Fig. 15) in combination with combined stress failure
criteria (equations similar to that in Fig. 13) are compared with measured
data in Fig. 16 C81. The data in this figure is for three different laminates
subjected to 'ive different load conditions and tested at hot-wet
environmental conditions. The spread in the predicted results is for two
cases: ( 1 ) f rst ply failure - lower bound and ( 2 ) last ply failure - upper
bound. It is very important to observe that the predicted lower bound (first
ply failure) i s below the lowest measured data for the majority of the cases.
Needless to say, the agreement is well within acceptable engineering accuracy.
Laminate fracture s t r e s s predictions for a composite thin tube subjected
to combined tension and torsion (Fig. 17) are compared in Table 6 191. The
agreement is excellent and what is even more important, the predicted upper
bound is below the measured data. It is accepted
community that linear laminate theory for first-.p
conservative fracture stresses for the laminate.
results shown in Table 6.
within the composites
y-failure tends to pred
This is consistent with
ct
the
9 -
Singularity Mechanics
Singularity mechanics in composites has received and continues to receive
substantial research attention. Singularity mechanics is required in order to
determine stress concentrations in the vicinity of: (1) defects (cracks,
holes, delaminations, ply drops); ( 2 ) free-edge interlaminar planes; (3)
joints; ( 4 ) load applications; and (5) support conditions. The level o f
sophistication for composite singularity mechanics varies from the simple
net-section-area stress, to anisotropic elasticity, to three-dimensional
finite difference or finite element analysis.
The equations for predicting the hoop stress concentration in the
periphery of a circular hole in an anisotropic infinite plate due to in-plane
loads are shown in Fig. 18 [61 . These equations are significant since
measured data show that the stress concentration in crack-like defects is
similar to a circular hole with equivalent diameter (Fig. 19, 161). It may be
concluded, therefore, that laminate defect stress concentrations are readily
estimated within acceptable engineering accuracy, using closed form equations
for equivalent diameter circular holes in infinite anisotropic plates.
Stress singularity fields near free edges, near interlaminar
delaminations, and near transply cracks are frequently evaluated using
appropriate three-dimensioal finite element analyses. Representative results
obtained from these analyses are shown in Fig. 20 1101 for free-edge and in
Fig. 21 1 1 1 1 for interlaminar delamination. The corresponding local failure
modes induced by these stress fields, cumulative damage, and subsequent
progressive fracture will be discussed later.
Life/Durabi 1 i ty
Life/durability is generally used to describe how long a composite
structure with inadvertent defects will survive in its monotonic or cyclic
10
load service environment. Fracture toughness and damage tolerance are
equivalently used to imply lifeldurability.
seek to answer one or more of the following important questions: (1) what is
the number of load cycles which will induce structural fracture in a composite
without and/or with assumed defects? ( 2 ) what is the critical size that an
assumed defect will grow to for imminent structural fracture under applied
service loading conditions? and (3) what is the defect size that a loaded
composite structure can safely withstand? The first two questions are
associated with the life/durability under cyclic loads; while the third
question is associated with a suddenly induced damage and it is traditionally
considered a composite material characterstic. The answers to all three
questions are clearly structural, since they require simultaneous
consideration of composite material, laminate configuration structure, and
loading conditions.
Both of these equivalent terms
The results summarized in Fig. 22 [121 are an answer to the first
question.
simplified composite mechanics model in conjunction with empirical data C121.
This procedure can be used to quantify laminate configuration and/or loading
environment effects on laminate lifeldurability. The answer to the second
question requires evaluation of local damage occurrence, cumulative damage,
and progressive fracture. This evaluation is, by necessity, performed by
developing and using sophisticated and integrated computer codes such as
CODSTRAN (EmPosite Durability S u c t u r a l flalysis, [131>. Results obtained
using CODSTRAN are compared with measured data in Fig. 23 [131. A s can be
observed, the agreement is well within acceptable engineering accuracy. The
These were obtained using a procedure which consists of a
1 1
l o c a l f a i l u r e modes c o n t r i b u t i n g t o damage growth a r e summarized i n Table 7
C141. C l e a r l y CODSTRAN can be used t o c o m p u t a t i o n a l l y s i m u l a t e t h e l o c a l
damage occurrence, c u m u l a t i v e damage, and p r o g r e s s i v e f r a c t u r e .
The answer t o t h e t h i r d q u e s t i o n i s o b t a i n e d by e v a l u a t i n g what i s
d e f i n e d h e r e i n as "Composite S t r u c t u r e F r a c t u r e Toughness." Composite
s t r u c t u r e f r a c t u r e toughness i s p r e d i c t e d by u s i n g composi te mechanics i n
c o n j u n c t i o n w i t h f r a c t u r e mechanics concepts and w i t h f i n i t e element
a n a l y s i s . The genera l procedure i s summarized i n F i g . 24 C111.
R e p r e s e n t a t i v e r e s u l t s o b t a i n e d a r e shown i n F i g . 25 1111 where ranges o f
measured d a t a a r e a l s o i n c l u d e d . The impor tance o f composi te mechanics i n
answer ing t h e t h i r d q u e s t i o n i s f a r r e a c h i n g . I t makes i t p o s s i b l e t o
q u a n t i f y composi te damage t o l e r a n c e i n terms o f two e a s i l y i d e n t i f i a b l e
f r a c t u r e toughness parameters: s t r a i n energy r e l e a s e r a t e and d e f e c t s i z e
( c r a c k l e n g t h ) .
I t i s w o r t h n o t i n g t h a t t h e use o f composi te mechanics i n c o n j u n c t i o n
w i t h f i n i t e e lement a n a l y s i s i n o r d e r t o c o m p u t a t i o n a l l y s i m u l a t e composi te
l i f e l d u r a b i l i t y ( f r a c t u r e - toughness/damage-tolerance) i s a r e c e n t and
e v o l v i n g development. The t r a d i t i o n a l p r a c t i c e t o e v a l u a t e these i s t h e use
o f a p p r o p r i a t e exper imen ts .
S t r u c t u r a l A n a l y s i s
The gove rn ing equa t ions f o r composi te s t r u c t u r a l a n a l y s i s a r e summarized
i n F i g . 26 i n m a t r i x f o rm. These equa t ions a r e embedded i n genera l purpose
s t r u c t u r a l a n a l y s i s codes. Composite mechanics a r e used t o genera te a l l t he
m a t e r i a l p r o p e r t i e s r e q u i r e d i n these e q u a t i o n s . Represen ta t i ve r e s u l t s
o b t a i n e d fo r t h e n a t u r a l f r e q u e n c i e s o f a h y b r i d composi te f a n b l a d e ( F i g . 26)
a r e summarized and compared w i t h measured d a t a i n Table 8 1151 and i n F i g . 27
C151 fo r r e s u l t s o b t a i n e d f o r impact response. The agreement i s v e r y good.
12
The fan b lade was s e l e c t e d t o i l l u s t r a t e t h e e f f e c t i v e n e s s o f composite
mechanics i n d e s c r i b i n g composi te behav io r a t a l l sca le l e v e l s and i n c l u d i n g
i n t e r p l y and i n t r a p l y h y b r i d s as w e l l as a m e t a l l i c l e a d i n g edge dev i ce . The
composite mechanics used, i n t h i s case, i s i n t e g r a t e d i n t o a computer code
COBSTRAN ( B m p o s i t e g lade m u c t u r a l AJalysis, 1161). A un ique f e a t u r e i n
t h i s code i s i t s r e s i d e n t c o n s t i t u e n t m a t e r i a l s databank where the p r o p e r t i e s
o f a l a r g e number o f f i b e r s and m a t r i c e s a re a v a i l a b l e .
composite micromechanics and lam ina te t h e o r y make i t p o s s i b l e t o s i m u l a t e a l l
t ypes o f composites and even combina t ions w i t h me ta l s . I t i s t he good
agreement w i t h measured d a t a (Tab le 8 and F i g . 27) t h a t has l e d t o t h e
ex tens i ve use o f composi te s t r u c t u r a l a n a l y s i s no ted i n Table 4.
Th is databank,
The p r e d i c t i o n o f l i f e l d u r a b i l i t y o f composite s t r u c t u r e s g e n e r a l l y
r e q u i r e s e x t e n s i v e use o f composi te s t r u c t u r a l a n a l y s i s . The s t r u c t u r a l
a n a l y s i s i s used to p r e d i c t t h e g l o b a l s t r u c t u r a l response (d isp lacements ,
f requencies, b u c k l i n g , e t c . ) w h i l e s i n g u l a r i t y mechanics and methods desc r ibed
i n t h e l a s t s e c t i o n a r e used t o p r e d i c t l o c a l behav io r i n c l u d i n g dominant
f a i l u r e modes.
COMPOSITE MECHANICS: WHERE I S I T HEADED? WHERE SHOULD I T GO?
Where composi te mechanics i s headed (based on r e c e n t research emphasis)
and where i t shou ld go ( a u t h o r ' s persona l v i e w ) a re summarized i n Table 9 f o r
the seven d i f f e r e n t d i s c i p l i n e s . A s can be seen i n Table 9, the t rends f o r
where i t s go ing are : ( 1 ) t r a d i t i o n a l , c l a s s i c a l , or conven t iona l ; ( 2 )
m o s t l y ne l i g i b l e a n t i c i p a t e d research e f f o r t ; and ( 3 ) major emphasis on user
f a m i l i a r i t y w i t h a v a i l a b l e genera l purpose f i n i t e element codes. S i n g u l a r i t y
mechanics, and l i f e l d u r a b i l i t y however, w i l l con t i nue t o r e c e i v e cons ide rab le
c l a s s i c a l and/or semiconvent ional a t t e n t i o n .
13 -
On the other hand, the author sees need for balanced research in all the
disciplines. This research should focus on developing methods and criteria
for: ( 1 ) fracture initiation and propagation at all scale levels; ( 2 )
combined mode fracture and mode tracking; (3) in situ ply strengths and
failure mode branching; ( 4 ) three-dimensional behavior with detailed account
of local heterogeneities and nonlinearities; ( 5 ) environmental
(moisture/temperature) effects; (6) composite mechanics, specialty finite
elements and substructuring techniques for all scale levels; and ( 7 )
dedicated, self-adaptive, expert-system-driven algorithms for enhanced
computational efficiency while retaining acceptable engineering accuracy in
the predicted results. The development of these methods will more than likely
require innovative, creative, and even revolutionary thinking in order to
introduce the new variables that define/describe the local physics. Two
illustrative examples in this direction are: the effect of interlaminar
delamination on natural frequencies (Fig. 28) and a rectangular array with an
off-center fiber for formulating micromechanics (Fig. 29).
CONCLUSIONS
A personal, but representative, assessment of composite mechanics has
been presented. The assessment is presented by grouping composite mechanics
into seven disciplines: (1) micromechanics; ( 2 ) macromechanics; (3) combined
stress failure; ( 4 ) laminate theory; ( 5 ) singularity mechanics; ( 6 )
lifejdurability; and ( 7 ) structural analysis. The scale levels associated
with each discipline and the various levels of sophistication of composite
math models in each discipline are described. What has been accomplished in
each discipline, emphasis on current research, and future trends are
summarized. The future trends are mainly conventional. Greater progress will
be achieved by pursuing unconventional and innovative methods which are
14
dedicated, adaptive, and expert-system-driven. Composite mechanics spans many
disciplines with each playing a very significant role in its future growth and
success. Successful contributions, which are timely and cost-effective, will
require the col lective/coord
di sc i pl i nes .
C11 Murthy, P.L.N. and Cham
nated research efforts of experts from these
REFERENCES
s , C.C., "ICAN: Integrated Composites Analyzer,"
NASA Report TM-83700, National Aeronautics and Space Administration,
Washington, DC, 1984.
C21 Chamis, C.C., "Simplified Composite Micromechanics Equations for Hygral,
Thermal and Mechanical Properties," SAMPE Quarterly, Vol. 15, Apr. 1984,
pp. 14-23. (NASA Report TM-83320, National Aeronautics and Space
Administration, Washington, DC, 1983.)
C31 Chamis, C.C., "Simplified Composite Micromechanics Equations for Strength,
Fracture Toughness, and Environmental Effects," NASA Report TM-83696,
National Aeronautics and Space Administration, Washington, DC, 1984.
[41 Chamis, C.C., Lark, R.F., and Sinclair, J.H., "Mechanical Property
Characterization o f Intraply Hybrid Composites," NASA Report TM-79306,
National Aeronautics and Space Administration, Washington, DC,. 1979.
C51 Chamis, C.C. and Sinclair, J.H., "DurabilitylLife of Fiber Composites in
Hygrothermomechanical Environments," in Composite Materials: Testinq and
Design, ASTM, Philadelphia, PA, 1982, pp. 498-512. (NASA Report TM-82749,
National Aeronautics and Space Administration, Washington, DC, 1981.)
[ 6 1 Chamis, C.C. and Smith, G.T., "Resin Selection Criteria for Tough
Composite Structures," AIAA Journal, Vol. 23, June 1985, pp. 902-911.
(NASA Report TM-83449, National Aeronautics and Space Administration,
Washington, DC, 1983.)
15 *
[ 7 1 Chamis, C.C. and S i n c l a i r , J.H., "Mechanical Behav io r and F r a c t u r e
C h a r a c t e r i s t i c s of O f f - A x i s F i b e r Composites: 11-Theory and Comparisons,"
NASA Repor t TP-1082, N a t i o n a l Ae ronau t i cs and Space A d m i n i s t r a t i o n ,
Washington, DC, 1978.
[ 8 1 Chamis, C.C., L a r k R.F., and S i n c l a i r , J.H., "An I n t e g r a t e d Theory for
P r e d i c t i n g t h e Hygrothermomechanical Response o f Advanced Composite
S t r u c t u r a l Components," NASA Repor t TM-73812, N a t i o n a l Ae ronau t i cs and
Space A d m i n i s t r a t i o n , Washington, DC, 1977.
[ 9 1 Chamis, C.C. and S u l l i v a n , T . M . , "Combined-Load S t r e s s - S t r a i n
R e l a t i o n s h i p s for Advanced F i b e r Composites," NASA Repor t TM-X-71825,
N a t i o n a l Ae ronau t i cs and Space A d m i n i s t r a t i o n , Washington, DC, 1976.
[ l o ] Mur thy , P.L.N. and Chamis, C.C., "A S tudy o f I n t e r p l y Layer E f f e c t s on
t h e Free Edge S t r e s s F i e l d of A n g l e p l i e d Laminates," Computers and
S t r u c t u r e s , Vol. 20, No. 1-3, 1985, pp. 431-441. (NASA Repor t TM-86924,
N a t i o n a l A e r o n a u t i c s and Space A d m i n i s t r a t i o n , Washington, DC, 1984.)
1111 Mur thy , P.L.N. and Chamis, C.C. , " I n t e r l a m i n a r F r a c t u r e Toughness:
Three-Dimensional F in i t e -E lemen t Mode l i ng f o r End-Notch and Mixed Mode
F lexu re , " NASA Repor t TM-87138, N a t i o n a l Ae ronau t i cs and Space
A d m i n i s t r a t i o n , Washington, DC, 1985.
[121 Chamis, C.C. and G i n t y , C . A . , "Composite D u r a b i l i t y and Damage
To lerance: S i m p l i f i e d P r e d i c t i v e Methods," NASA Repor t TM-100179,
N a t i o n a l Ae ronau t i cs and Space A d m i n i s t r a t i o n , Washington, DC, 1987.
[131 Chamis, C.C. and Smith, G . T . , "CODSTRAN: Composite D u r a b i l i t y S t r u c t u r a l
A n a l y s i s , " NASA Repor t TM-79070, N a t i o n a l Ae ronau t i cs and Space
I A d m i n i s t r a t i o n , Washington, DC, 1978. I
1 6
1141 I r v i n e , T.B. and Gin ty , C.A., "Progress ive F r a c t u r e o f F i b e r Composites,"
Journal o f Composite M a t e r i a l s , Vol. 20, Mar. 1986, pp. 166-184. (NASA
Report TM-83701, Nat iona l Aeronaut ics and Space A d m i n i s t r a t i o n ,
Washington, DC, 1983.)
C151 Chamis, C.C. and S i n c l a i r , J.H., "Ana lys is o f High V e l o c i t y Impact on
H y b r i d Composite Fan Blades," NASA Report TM-79133, i n S t r u c t u r e s ,
S t r u c t u r a l Dynamics, and M a t e r i a l s , A I A A , New York, 1979, pp. 249-257.
(Nat iona l Aeronaut ics and Space A d m i n i s t r a t i o n , Washington, DC, 1979.)
[161 Chamis, C.C. and Lynch, J.E., "High-Tip-Speed F i b e r Composite Fan Blades:
V i b r a t i o n and S t r e n g t h Ana lys is , : NASA Report TM-X-71589, N a t i o n a l
Aeronaut ics and Space A d m i n i s t r a t i o n , Washington, DC, 1974.
TABLE 1 . - COMPOSITE MECHANICS DESCIPLINES
Micromechanics - I n t r a p l y h e t e r o g e n e i t y
Macromechanics - P l y homogenizat ion
Combined s t r e s s f a i l u r e c r i t e r i a - F i v e s t r e n g t h s
Laminate t h e o r y - Layered a n i s o t r o p i c medium
S i n g u l a r i t y mechanics - S t r e s s c o n c e n t r a t i o n s
L i f e / d u r a b i l i t y - Cumulat ive damage and p ropaga t ion
S t r u c t u r a l mechanics - Composite or l am ina te homogenizat ion
TABLE 2. - COMPOSITE MECHANICS SCALE LEVELS
D i s c i p l i n e s
Micromechanics
Macromechanics
Combined s t r e s s f a i l u r e c r i t e r i a
Laminate t h e o r y
S i n g u l a r i t y mechanics
L i f e l d u r a b i l i t y
S t r u c t u r a l mechanics
Scale
F i b e r d iamete r
Ply t h i c k n e s s
Ply t h i c k n e s s
Laminate t h i c k n e s s i n t e r p l y l a y e r t h i c k n e s s
I n f i n i t e s i mal
Ply t h i c k n e s s
Laminate t h i c k n e s s f i n i t e element s i z e
Homogenizat ion r a t i o , f i b e r d iameters ( F . D . )
1.2 F .D . ( F V R = 0.6)
15 F.D. (excep t boronlepoxy)
1 5 F.D. (excep t boronlepoxy)
M u l t i p l e s o f p l y t h i c k n e s s 15 F.D. and g r e a t e r
< < F i b e r d iameter
15 F .D . ( excep t boron/epoxy)
Many t imes t h e l a m i n a t e t h i c k n e s s
TABLE 3. - COMPOSITE MECHANICS MATH MODEL S O P H I S T I C A T I O N ~~ ~
D i s c i p l i n e
~
Micromechanics
Macromechani cs
Combined s t r e s s f a i 1 u r e
Laminate t h e o r y
S i n g u l a r i t y mechanics
L i f e l d u r a b i 1 i t y
S t r u c t u r a l mec han i c s
Region modeled
S i n g l e f i b e r a r r a y
Cont inuum
Cont inuum
L i n e th rough t h i c k n e s s
Cont inuum
Con t i nuum
Continuum
Key assumpt ion(s)
No i n t e r f a c e o r t h o t r o p i c cons t i tuen t s
Homogeneous o r t h o t r o p i c
Homogeneous o r t h o t r o p
Ani s o t r o p i c no i n t e r p
A n i s o t r o p i c
C
1 aye rs y l a y e r
O r t h o t r o p i c
A n i s o t r o p i c
Math model
Mechanics o f m a t e r i a l s cont inuum mechanics f i n i t e element
Mechanics o f m a t e r i a l s
Cont inuum mechanics f i v e i n p l a n e s t r e n g t h
f i n i t e element
Cont inuum mechanics f i n i t e element f i n i t e d i f f e r e n c e
" F r a c t u r e " mechanics
S t r u c t u r a l mechanics
Mechanics o f m a t e r i a l s
f i n i t e element
I 18
TABLE 4. - COMPOSITE MECHANICS
[Where has i t been? What has i t accomp l i shed? l
D i s c i p l i n e
Compos i t e
Compos i t e
Combined s t r e s s
Laminate t h e o r y
S i ngu l a r i t y mechanics
L i f e l d u r a b i 1 i t y
S t r u c t u r a l
m i cromechani cs
macromechanics
f a i 1 u r e
mechanics
Research conducted
Cons ide rab le
N e g l i g i b l e
Min imal
Cons ide rab le
S u b s t a n t i a l
S u b s t a n t i a l
Min imal
Success (understood/ q u a n t i f i e d )
~
P a r t i a1
Excep t iona l
N o t i c e a b l e
Acceptable
Promi s i ng
Promi s i ng
H i g h l y accep tab le
A p p l i c a t i o n
L i m i t e d
Ex tens i ve
Ex tens i ve
E x t e n s i v e
L i m i t e d
L i m i t e d
Ex tens i ve
TABLE 5 . - COMPARISON OF MEASURED AND PREDICTED ELASTIC PROPERTIES OF ANGLEPLIED LAMINATES
[AS/3531-5 w i t h 1.8 p e r c e n t m o i s t u r e and room tempera tu re . ]
Laminate
[0 /*452/0/+45Is
Measured
P r e d i c t e d
Percen t d i f f e r e n c e
1 0 2 / ~ 4 5 / 0 2 / 9 0 / 0 3 5
Measured
P r e d i c t e d
Percen t d i f f e r e n c e
[ ( 0 / * 4 5 / 9 0 ) 2 I s
Measured
P r e d i c t e d
Percen t d i f f e r e n c e
L o n g i t u d i n a l modulus, M S I
6.3
6.3
0
13.0
13.0
0
6.68
7.20
+7.8
Transverse modulus,
MS I
3.08
3.2
+3.9
4.2
4.5
+7.1
6.62
7.20
+8.7
Shear Modulus,
MS I
3.21
3.80
+18.4
1 . 5
1.6
+6.7
2.34
2.70
15.4
Ma jo r Poi sson ' s
R a t i o
0.803
.781
-2.70
0.325
.318
-2.2
0.350
f333
-4.8
19
TABLE 6 . - COMPARISON OF FRACTURE STRESSES
[The specimen was loaded t o f r a c t u r e i n combined a x i a l compression and t o r s i o n a l
l o a d i n g c o n d i t i o n . ]
S t r e s s type S t r e s s va lue , KSI
A x i a l
To rs i onal
Measured P r e d i c t e d
Lower bound Upper bound
20.2 17 .9 19.4
2 3 . 1 2 0 . 6 2 2 . 3
Notch type - 90
P l y o r i e n t a t i o n ; [&IS; e i n degrees
aLT = L o n g i t u d i n a l t e n s i o n . TT = Transverse t e n s i o n . S = I n t r a p l y shear.
Numbers denote f a i l u r e modes as f o l l o w s : ( 1 ) i n i t i a l f r a c t u r e due t o i n t r a p l y shear i n the
no tch t i p zone (2 ) minimal i n t r a p l y shear ing d u r i n g f r a c t u r e ( 3 ) some i n t r a p l y shear o c c u r r i n g near c o n s t r a i n t s
( g r i p s ) (4 ) de lamina t ions occur i n no tch t i p zone p r i o r t o any i n t r a p l y damage
I = I n t e r p l y de lamina t ion .
Unnotched -- s o l i d
Notched -- through s l i t
Notched -- through ho le
20
0 3 5
LT LT LT -- s3 s 3
s1 51 s1 LT LT LT
s1 s1 s1 LT LT LT
Mode Measured
1 62
2 190
3 288
4 42 5
5 6 6 7
TABLE 9. - COMPOSITE MECHANICS
[Where is it headed? Where should it go?]
Predicted Predicted/ measured
6 4 1.03
186 .98
3 0 3 1.05
4 5 4 1.01
6 5 3 .98
___
Di scipl i ne
Compos i te mi cromechani cs
Compos i te macromechanics
Combined stress fai 1 ure
Laminate theory
Singularity mechanics
Life/durabi 1 i ty
Structural mechanics
Effort/approach
Negligible
Negl i gi b 1 e
Negl igi ble
Nonl i near
(traditional)
(classical)
(classical )
(conventional)
Extensive homogeneous anisotropy (classical)
Progressive fracture (semi conventional)
Fami 1 iari ty with available GPFEC (user mode) limited FE development
Should go (personal view)
Fracture initiation and propagation
Combined mode fracture and mode tracking
In situ ply strengths and failure mode branching
Increase computational efficiency and three- dimensional behavior
Local heterogeneity and nonl ineari ty
Hygral, thermal, mechani- cal, and temporal aspects properly and tractably integrated
Development of composite mechanics specialty finite elements and substructuring methods
21
TAKEUP DRUM MONOMER SOLUTION
BROAD GOODS
I N SITU POLYMERIZATION
PL IES D I E
FIGURE 1. - PMR POLYIMIDE PROCESS.
FROM GLOBAL
ANALYSIS
COMPONENT TO GLOBAL STRUCTURAL STRUCTURAL
ANALYS I S /--- f ,I--- \
\ / 0 \
\ I' /'
/ I LAM1 NATE / \ I
I I \ \ \ \
\ \
LAMINATE \ / !-/z-!p I t THEORY
THEORY
LAMINATE \ / !-/z-!p I t THEORY
PLY
COMPOS I TE MICROMEC"""'rC THEORY - k -
IICS
/
I I
\ /
~ O P - D O W N CONSTITUENTS , ' TRACED
MATERIALS PROPERTIES P ( , T, M)
/ OR \
UPWARD INTEGRATED
"SYNTHESIS" I -------- "DECOMPOSITION" OR 'I.
BLADE
FIGURE 2. - ICAN: INTEGRATED COMPOSITES ANALYZER.
22
ONE END ARRAY
7 1
MATRIX ,! FILAMENT
REPEATED ELEMENT
FIGURE 3. - SCHEMATIC OF PLY, INTERNAL GEOMETRIC RELATIONSHIPS.
LONGITUDINAL NODULUS :
TRANSVERSE NODULUS:
SHEAR NODULUS:
SHEAR NODULUS :
POISSON'S RATIO:
POISSON'S RATIO:
31
L~~~~~ ( f ) L PLY ( a ,
FIGURE 4. - COMPOSITE NICROMECHANICS. MECHANICAL PROPERTIES.
23
EXPANDED FORM:
t
/
1
FIGURE 5. - PLY HYGROTHERMOMECHANICAL RELATIONSHIPS. LINEAR BEHAVIOR.
24
1
$ 1 I AS/E//KEV/E 3
0 sri 2 -
0 SM ,r LM ,r TM
PR 0 PR @ TM 8 LM
AS/E//S-G/E
I HMS/E//S-G/E
I n TM
HMS/E//KEV/E
I 1 I 0 10 20 30
SECONDARY COMPOSITE VOLUME. PERCENT
FIGURE 6. - ELASTIC PROPERTY TRANSLATION EFFICIENCY SUMMARY OF INTRAPLY HYBRIDS.
25
1. LONGITUDINAL TENSION:
2, LONGITUDINAL COMPRESSION :
FIBER COMPRESSION:
DELAMINATION/SHEAR:
MICROBUCKLING:
3. TRANSVERSE TENSION:
4. TRANSVERSE COMPRESSION:
5. INTRALAMI NAR SHEAR :
6. FOR VOIDS:
sj 11T " kf 'fl
Gm % l l C "
L T LONGITUDINAL TENSION TT TRANSVERSE TENSION IS I NTRALAMINAR SHEAR LF LONGITUDINAL FLEXURE TF TRANSVERSE FLEXURE L I LONGITUDINAL IMPACT T I TRANSVERSE IMPACT
2.0 I
I -my
I -
c 11 - [ 4k,N - k f h ] 1 12 I s, sm
VOID -'
FIGURE 7. - COMPOSITE MICROMECHANICS. UNIAXIAL STRENGTHS - IN-PLANE.
L AS/E//S - G/
I 0 10 20 30
SECONDARY COMPOSITE VOLUME, PERCENT
FIGURE 8. - STRENGTH TRANSLATION EFFICIENCY SUMMARY OF INTRAPLY HYBRIDS.
0 B/E 0 f lOD-II/E A HMS/E V AS/E
SOLID POINTS USED TO DETERMINE
0'. 90'. IS; 70, 250, 350 OF. DRY O', 90'. IS; 70, 250, 3 5 0 OF. DRY 0'. 90'. IS; 70, 250. 350 OF. DRY 90'. k45'; 73, 218 OF. D 8 1. 1% M
REFERENCE PROPERTIES
0 10 20 30 40 PREDICTED STRENGTH, KSI
FIGURE 9. - HYGROTHERMAL EFFECTS ON STRENGTH PREDICTED ACCURATELY.
26
COMP HGTM REL.
PLY HGTM REL.
STRAIN COMPAT .
STRESS EQUIL.
x. s
COMPARING COEFFICIENTS I N FIRST AND LAST EQUATIONS:
LOAD ANGLE. e7,
,r LOAD
0 MEASURED (CENTER GAGE) PREDICTED -
0 30 60 90
40x106 FIBER DIRECTION'
u) L 30 X X V
20
0
c 0 MEASURED (CENTER GAGE)
PREDICTED - G) I
m " m 30 60 90
LOAD ANGLE, e. DEG
FIGURE 11. - MODULUS CORPARISONS.
LOAD ANGLE, e -,
\
U
0 MEASURED (CENTER GAGE) PREDICTED - V
-1 I I 0 30 60 90
LOAD ANGLE, e, DEG
FIGURE 12. - COUPLING COEFFICIENT COM- PAR I SONS.
27
x. s
2
D
1
a, = TENSION OR COMPRESSION
FIGURE 13. - PLY COMBINED STRESS FAILURE CRITERION WITH HYGROTHERMOMECHANICAL EFFECTS.
LOAD 1 0 0 ~ 1 0 ~ ANGLE. e-,>
I ,r LOAD F I BER DIRECTION
v) Y
* 60 X X V
v,
0 30 60 90 LOAD ANGLE. DEG
FIGURE 14. - FRACTURE STRESS (STRENGTH) COMPARISONS.
28
FIGURE 15. - LAMINATE THEORY EQUATIONS FOR HYGROTHERNONECHANICAL (HGTM) LAMINATE.
29
150
125
100
75
5 0
2 5
0 1 2
MEASURED DATA (FROM AFFDL-TR-76-142, V. 1.1) 0 PREDICTED DATA (REF. 8) I
2 3 , , ’
1 C0/*452/0*451~
2
3
r PREDICTED
2 3 1 2 3 U L I I I I I I
TRANSVERSE SHEAR LONGITUDINAL LONGITUDINAL TRANSVERSE TENS I ON COMPRESSION TENS I ON COMPRESS I ON
FIGURE 16. - FRACTURE STRESS OF WET COMPOSITES IS ACCURATELY PREDICTED BY LERC INTEGRATED THEORY FOR HYDROTHERMOMECHANICAL RESPONSE.
I 30
AXIAL LOAD 4
*45'. 4-NIL BORON/ERLA- 4617. 0 .5 FVR
COORDI NAl AXIS -.
A - ROSETTE STRAIN GAGES-. ..
,- PRESSURE > , 2 I N .
10
\
I N .
\
FIGURE 17. - SCHEMATIC OF COMPOSITE TUBE SPECI- HEN SHOW I NG LOADS AND I NSTRUHENTATION.
31
2 2 ‘COO I & R, [ (R, + RDI) sin 501 cos e - I Qcxx Ecxx .. .l
rl \ y \ I
NORMAL STRESS
+ 1 (1 t R,) cos 2 8 + Ro - 11 sin 250 1 - - - c
SHEAR STRESS
FIGURE 18. - STRESS CONCENTRATIONS DEPEND SIGNIFICANTLY ON COMPOSITE MODULI.
FULL-PENETRATION HOLE
0 PRELOAD AT ROOM TEMPERATURE
0 ROOM TEMPERATURE PRELOAD AT 300 OF
40 R V 300 OF
a I- u
20
10 118 3/8 518 0 DEFECT SIZE, I N .
FIGURE 19. - DEFECTED LAMINATE STATIC FRACTURE DATA.
*OOo8 I
,006
,003
8
'N
X X
b 0 N
W
t .0004
-
-
.0004 -
8 X
x o c -.0004 - t - ,0004
- .0008 1
8 X X
X X
e D
8 X X
X e 0"
.6 mgl
.3 c LCLASSICAL 1
LAM I NATE \ THEORY \
\ I I
I I
0 \ .032
,024
,016
.008
0
- .008 0 .2 .4 . 6 .8 1 .o
\ -32 \ 'L CLASSICAL \
INTERPLY LAYER \ CENTER OF PLY I
I
- ---- c I .08
0 I
- .003
- ,006
8 X X
P > >
D
0 .2 4 . 6 .8 1 .o FREE-EDGE DISTANCE. X I IN.
FIGURE 20. - 3-D PLY AND INTERPLY STRESS FIELDS AS THE FREE EDGE IS APPROACHED (+20°PLY. Ck201 AS/E LAM I NATE 1 .
33
15
9 LCRACK T I P
I
v)
* 3 v) v)
2 -3 5
CYCLIC LOADING CONDITION
Ucxx = 30 K S I
T = 250 OF
T = -300 OF
-9 t
CYCLES TO CRACK I N I T I A T I O N
c*45/0/90 1 [ 9O2/fl 01s [+30/03 Is
36 500 4 220 -100 M I L L I O N
76 600 234 000 987 000 180 275 000 -100 M I L L I O N
0 -05 -10 .I5 -20 .25 DISTANCE FROM CRACK-TIP. I N .
FIGURE 21. - STRESS F I E L D I N INTERPLY LAYER
-15
NEAR CRACK T I P .
t I t t STEADY STATE CYCLIC CYCLIC CYCLIC
STRESS (L) STRESS (L) TEMPERATURE ( T ) MOISTURE (M) CYCLIC LOADING CONDITIONS
F IGURE 22. - COMPUTATINAL S IMULATION OF HYGROTHERMOMECHANICAL FATIGUE I N F I B E R COMPOSITES.
34
(a ) NO LOAD. (b) LOAD EQUAL APPROXIMATELY ONE-HALF FRACTURE LOAD.
C-SCAN RECORD
G
0 SELECT CRITICAL "G" AND CRITICAL "a"
C-SCAN RECORD CODSTRAN
INTERCHANGE
__ _ _ _ _ _
I
12 000
10 000
8 000 m d
d 6 000 4 0 2
4 000
2 000
0
2 a = 0.625
NOTE: CRACK OPENING DIS- PLACEMENT BETWEEN A AND B
I ,001 .002 .003 ,004 .005
CRACK OPENING DISPLACEMENT, I N .
FIGURE 23. - CODSTRAN PREDICTED RESULTS COMPARED WITH EXP DATA.
0 DETERMINE REQUISITE PROPERITIES AT DESIRED CONDITIONS USING COMPOSITE MICROMECHANICS
0 RUN 3-D F I N I T E ANALYSIS ON ENF ("F) FOR AN ARBITRARY LOAD
0 SCALE LOAD TO RATCH INTERLAMINAR SHEAR STRESS AT ELEMENT NEXT TO CRACK-TIP
0 WITH SCALED LOAD EXTEND CRACK AND PLOT STRAIN ENERGY RELEASE (GI VERSUS CRACK LENGTH (a )
EXTENDED CRACK LENGTH. a
0 METHOD HAS VERSATILITY/GENERALITY
FIGURE 24 . - GENERAL PROCEDURE FOR PREDICTING COMPOSITE INTERLAMINAR FRACTURE TOUGHNESS USING THE END-NOTCH-FLEXURE (ENF) OR MIXED- MODE-FLEXURE (NNF) METHOD.
35
5
4
3
2
1
0
-1 . a 1
17.0
r MIDSPAN DEFLECTION ( W )
, .
MODE / - GLOBAL MIXED ( I & 11) ----- LOCAL MIXED ( I & 11) --- LOCAL I
A 0' -----/@
i /i i
MODE / / - GLOBAL MIXED ( I & 11) ----- LOCAL MIXED ( I & 11) --- LOCAL I
A 0' -----/@ -- LOCAL 1 1
I I 1.2 1.3 1 1.1
EXTENDING CRACK-TIP DISTANCE. I N .
FIGURE 25. - MIXED-MODE-FLEXURE ENERGY RELEASE RATE AND COMPONENTS (ASIE).
36
LOCAL TRANSVERSE q- BORON TORSIONAL STRENGTHENING P L I E S 7 / / I STIFFENING PLIES
/ I / 1 ' ; , .
GRAPHITE/ KEVLAR CENTR I FUGAL AND FLE URAL LOAD P L I
LEADING EDGE
S- GLASS FLEX ROOT PLIES
FIGURE 26, - STRUCTURAL BEHAVIOR/RESPONSE GOVERNING EQUATIONS.
0 2 TIME. MSEC
4
FIGURE 27. - Z-COMPONENT OF L.E. T I P DIS- PLACEMENT. HYBRID COMPOSITE FAN BLADE, 2-LB BIRD IMPACT.
37
38
10
8
N I
z 6 a a W
a W cc L L
3 4 a t 9
i
\ < BENDING
3
2 1
1 2 3 4 0 a. IN.
FIGURE 28. - EFFECT OF CRACK LENGTH ON LOW- EST NATURAL FREQUENCIES.
rsx I
rs-
S, df
SQUARE ARRAY (2)
RECTANGULAR ARRAY (6)
PLY (1)
FIGURE 29. - COMPOSITE NICROMECHANICS - SCALE LEVELS.
39
1. Report No. 2. Government Accession No. 3. Recipient's Catalog No.
Mechanics o f Composite M a t e r i a l s : Pas t , P resen t , and Fu tu re
NASA TM-100793 4. Title and Subtitle 5 . Report Date
10. Work Unit No.
7. Author@)
C h r i s t o s C. Chamis
I 505-63-1 1
8. Performing Organization Report No.
E-3936
9. Performing Organization Name and Address
N a t i o n a l A e r o n a u t i c s and Space A d m i n i s t r a t i o n Lewi s Research Center C leve land , O h i o 44135-3191
' iber-composi t e s ; Resin-matr ices; I n t e r p l y h y b r i d s : n t r a p l y h y b r i d s ; M i cromechani cs; Combi ned-stress a i l u r e : Laminate t h e o r v , S i n q u l a r i t v mechanics;
11. Contract or Grant No.
~
U n c l a s s i f i e d - U n l i m i t e d S u b j e c t Category 24
13. Type of Report and Period Covered
9. Security Classif. (of this report)
Uncl a s s i f i ed
~~ 1 Techn ica l Memorandum 2. Sponsoring Agency Name and Address
20. Security Classif. (of this page) 21. No of pages 22. Price'
Uncl ass i f i ed 40 A03 ,
N a t i o n a l A e r o n a u t i c s and Space A d m i n i s t r a t i o n Washington, D.C. 20546-0001
14. Sponsoring Agency Code
~
~~
5. Supplementary Notes
Presented a t t h e 2 1 s t Annual Mee t ing o f t h e S o c i e t y for E n g i n e e r i n g Science, B lacksburg , V i r g i n i a , October 15-17, 1984. I n v i t e d paper .
6. Abstract
Composite mechanics d i s c i p l i n e s a r e p resen ted and d e s c r i b e d a t t h e i r v a r i o u s l e v e l s o f s o p h i s t i c a t i o n and a t t e n d a n t sca les o f a p p l i c a t i o n . C o r r e l a t i o n w i t h exper imen ta l d a t a i s used as t h e p r ime d i s c r i m i n a t o r between a l t e r n a t i v e methods and l e v e l o f s o p h i s t i c a t i o n . Ma jo r emphasis i s p l a c e d on: ( 1 ) where composi te mechanics has been; ( 2 ) what i t has accompl ished; ( 3 ) where i t i s headed, based on p r e s e n t r e s e a r c h a c t i v i t i e s ; and ( 4 ) a t t h e r i s k o f b e i n g presumptuous, where i t shou ld be headed. The d i s c u s s i o n i s developed u s i n g s e l e c t e d , b u t t y p i c a l examples o f each compos i te mechanics d i s c i p l i n e i d e n t i f y i n g degree o f success, w i t h r e s p e c t t o c o r r e l a t i o n w i t h exper imen ta l d a t a , and problems rema in ing . The d i s c u s s i o n i s c e n t e r e d about f i b e r i r e s i n composi tes drawn m a i n l y from t h e a u t h o r ' s r e s e a r c h a c t i v i t i e s / e x p e r i e n c e spanning two decades a t Lewis .
7. Key Words (Suggested by Author@)) I 18. Distribution Statement
i f e / d u r a b i l i t y ; F r a c t u k e toughness:-Damage t o l e r a n c e ; ' r o g r e s s i v e f r a c t u r e ; S t r u c t u r a l a n a l y s i s ; n v i ronmental e f f e c t s
