Mechanical Properties of Composites
Professor Joe Greene
CSU, CHICO
Copyright Joseph Greene 2001
1
Mechanical Properties
• Comparison with Other Materials
• Environmental Effects
• Test Considerations
Copyright Joseph Greene 2001
2
Objectives
• Recognize some of the basic differences in mechanical,
physical, and thermal properties of composite materials that
distinguish them from metals;
• Understand the various design techniques and advantages of
using composites to obtain high performance and highly
efficient structures;
• Describe the effects of t he specific use environment on the
behavior of composite materials for a range of operational
conditions;
• Discuss various test methods and approaches in evaluating and
characterizing the mechanical properties of composites for
design and analysis needs.
Copyright Joseph Greene 2001
3
Comparison with Other Materials
• Metals and metallic structures have been used for over 100 years in
engineering and are well understood materials with a large database of
design data and experience.
• Plastics have been used for the last 50 years and have extensive database
of properties and manufacturing information.
• Composites technology is much more recent (25 years) with a database
and analysis that are just emerging.
• Aerospace industry
– Relies heavily on aluminum and titanium alloys
• Automotive industry
– Relies heavily on steel and aluminum
• Al and titanium limitations
– Exposure to salt water and harsh environments causes corrosion
– Heavier than when compared to polymers, foam, and composites
– Low strain-to failure modes can cause permature failure
Copyright Joseph Greene 2001
4
Historical
• 1940s and 1950s, aerospace industry looked at high
performance composites as replacement for steel .
–
–
–
–
Early materials were glass fiber and polyester resin.
Limited to non-structural applications.
Resin and fibers developed and material systems matured.
During the 1960s new fiber systems were developed for
structural components
• High strength glass fibers (S-901),
• Aramid (Kevlar 49), carbon and graphite systems
– Composite advantages
• High strength to weight and stiffness to weight due to low density
• Manufacturing ease and environmental resistance
• Low cost and design versatility: fiber placement for strength and
stiffness selectivity.
Copyright Joseph Greene 2001
5
Mechanical Properties
• Traditional materials have homogeneous properties.
– The strength and modulus are the same no matter where the sample is
taken from. Ferrous (steel, iron) and non ferrous materials, (Al,Cu,Pb)
– If pieces were cut from different locations in a metal plate, the pieces
would have the same:
• Density, internal structure, tensile strength, modulus, elongation, impact, etc..
– If pieces were cut in one direction and then another one 90° from it,
the tensile strength, tensile modulus, impact and other properties
would be the same.
• Composite materials are made up of two or more distinct materials, one
for reinforcing and the other for holding the fibers together in a matrix.
• Composite materials have non-homogeneous properties and are called
inhomogeneous materials with anisotropic properties.
– Fibers are stronger in one direction than the other one due to aspect
ratio.
– The properties of the area around the resin is much lower than the
properties around the fiber.
Copyright Joseph Greene 2001
6
Mechanical Properties
• Common anisotropic materials
– Plywood, reinforced concrete due to steel rebar.
• Composites are often fabricated with stronger
properties in one direction versus the other one, or
have properties stronger in a particular region.
– Fibers are placed with woven roving or fabric with fibers in
the 0° /90° direction, or fibers in the 40° /60° direction.
– Filament winding and lay-up composite sheet can result in a
composite with uni-directional properties.
– Samples of the composite are often taken in the 0° direction
and reported as maximum values.
• The tensile strengths and modulus are divided by the density of the
composite to give the specific strength and specific modulus
• Figure 4-1 provides properties for unidirectional composites
• Figure 4-2 provides properties for quasi-isotropic composites
Copyright Joseph Greene 2001
7
Properties of Isotropic Materials
• Tensile modulus
– Low alloy steel 207GPa(30Mpsi)
– Aluminum
72GPa (10Mpsi)
• Tensile strength
– Low alloy steel 1500MPa(220Kpsi)
– Aluminum
500MPa(75Kpsi)
Density
Spec Mod
7.85 g/cc
2.8 g/cc
26spGPa
26spGPa
Density
Spec Str
7.85 g/cc
2.8 g/cc
191spMPa
178spGPa
• Thermoset resins and plastics are isotropic (properties are the
same in all 3 directions) due to homogeneous material.
Density, g/cc
Tensile Strength, psi
Tensile Modulus, psi
Tensile Elongation, %
Impact Strength ftlb/in
CLTE
10-6 mm/mm/C
HDT
264 psi
Epoxy
1.11-1.40
Polyester
1.04 - 1.46
PET (Thermoplastic)
1.29-1.40
Polyurethane
1.03 - 1.15
4,000 – 13,000
350K
3%-6%
0.20 - 1.0
600 – 13,000
300K - 640K
2% - 6%%
0.2 - 0.4
7,000 – 10,500
400K - 600K
30% - 300%
0.25 - 0.70
175 - 10,000
10K - 100K
3% - 6%
25 to no break
45-65
55 - 100
65
100 - 200
115F-550F
140F -400F
70F -100F
70F - 150F
Copyright Joseph Greene 2001
8
Properties of Anisotropic Materials
• Composites are anisotropic due to directional nature of fiber
which is stronger in the axial (length) direction than in the
transverse (thickness) direction
Material
Density Ten Mod 0 (Gpa) Ten Mod 90 (MPa) Ten Str 0 (MPa) Ten Str 90
Glass
2.56g/cc
76
15.2
2000
400
Carbon Fiber 1.8 g/cc
300
60
2400
480
Aramid
1.4g/cc
125
25
3000
600
Epoxy/ Glass
1.8
39
4.8
1130
96.5
Epoxy/Carbon
1.54
127.5
9
1447.5
62
Epoxy/Kv49
1.38
76
5.5
1379
28.3
Material
Glass
Carbon Fiber
Aramid
Epoxy/ GF
Epoxy/CF
Epoxy/Kv49
Density Ten Mod 0 (Mpsi) Ten Mod 90 (MPsi) Ten Str 0 (KPsi) Ten Str 90 (Kpsi)
2.56g/cc
11.02
2.204
290
58
1.8 g/cc
43.5
8.7
348
69.6
1.4g/cc
18.125
3.625
435
87
1.8
5.655
0.696
163.85 13.9925
1.54
18.4875
1.305
209.8875
8.99
1.38
11.02
0.7975
199.955
4.1035
Copyright Joseph Greene 2001
9
Mechanical Properties of Composites
• Polymer composites are made up of a resin and a fiber
renforcement.
– Both contribute to the strength and stiffness of the
composite
• The higher the fiber % the higher the properties
• The more unidirectional the fiber, the higher the properties are in
that direction and the weaker they are in the transverse direction.
– Filament winding and prepreg tape have very high directional
properties
• Directional effects are minimized by having alternating fiber
angles
– Example, 0°/90° ply with +/-45° fiber ply.
• Fiber bonding to matrix is key to high strength properties.
Copyright Joseph Greene 2001
10
Composites Have a Fiber Plus Matrix
• Resin type
– Influences strength and thermal properties.
– Resin must flow through fiber mat, then into fiber bundle to wet fiber.
• Fiber type
– Roving form that is woven into a glass sheet and then formed to shape
(preform)
Copyright Joseph Greene 2001
11
Composites Have Directional Properties
• Fiber type
– Different fibers have different strength, modulus, and strain at failure
• Figure 4-3
• Generally, the stiffer the fiber, the smaller the strain at failure.
– Kevlar-Epoxy unidirectional properties- Table 4.3
• Fiber %
– The higher the fiber %, the higher the properties
• Fiber % for automotive is 35% by volume
• Fiber % for aerospace is 60% by volume
• Fiber orientation
–
–
–
–
The more unidirectional the fiber the stronger the properties are.
Properties of unidirectional glass-Epoxy Composites- Table 4.6
Properties of Unidirectional Materials- Table 4.7
Properties of Pan and Pitch Carbon Fibers- Table 4.9
Copyright Joseph Greene 2001
12
Composites Have Directional Properties
• Fiber Orientation
– Carbon fiber is Amoco high modulus pitch based fiber
– Unidirectional laminate with 60% fiber and epoxy resin tested along
the fibers (0°) and across the fibers (90°)
– Isotropic laminate has 0°, 30°, 60°, 90°, 120°, 150° stacking sequence
– Table 4.10: Effect of orientation on carbon fiber properties
• Unidirectional had double the strength and triple the modulus as a quasiisotropic material
• Unidirectional material had 10% of the strength and 3% of the modulus in the
transverse direction as the quasi-isotropic laminate
– Table 4.11: Mechanical Properties of Carbon-Fiber Composites with
Epoxy and PEEK
• Epoxy resin had 25% higher tensile strength and 60% higher tensile modulus
than the peek composite in the 0° direction
• Peek resin had 40% higher strength and 330% higher Fracture strain in the 45°
direction than epoxy.
Copyright Joseph Greene 2001
13
Composites Have Directional Properties
• Fiber Type
– Table 4.12. Tensile Properties of different types of carbon fiber
• T200, T50, T650, T1000, P55, P100 types of carbon fiber
– Table 4.13. Unidirectional Composite Properties
• ATB and ATS are acetylene terminated epoxy resins
• XAS and Celion are PAN based carbon fibers
• Narmco and 117951 are BMI matrix resins, Bismaleimide
– Table 4.14. Unidirectional Fiber and Thermoplastic Composites
• PEEK, APC, and PEKK are different grades of aromatic ketones
– Table 4.15. Mechanical Properties of Hybrid Yarn
– Table 4.16. Unidirectional, comingled, and cowoven fabric
– Table 4.17. Mechanical Properties of Composites
Copyright Joseph Greene 2001
14
Mechanical Properties Pitch versus PAN
• Carbon Fiber Properties for 62% volume carbon fiber
– PITCH fiber has higher density
– PAN Fiber intermediate modulus has tensile strength and shear
strength but a lower tensile modulus and lower thermal conductivity
than PITCH intermediate modulus fiber.
– PITCH High modulus fiber has higher tensile modulus and higher
thermal conductivity but lower tensile strength and compressive
strength than PAN Intermediate fiber.
Property
PAN Int Mod PITCH Int Mod PITCH High Mod
Density, g/cc
1.6
1.7
1.8
Tensile Strength (MPa)
2585
896
1206
Tensile Modulus (GPa)
172
220
517
Compressive Strength (MPa)
1723
510
268
Shear Strength (Mpa)
124
55
27
Thermal Conductivity (W/m-K)
8.65
74
398
Copyright Joseph Greene 2001
15
Directional Properties Carbon Fiber
• Different types of carbon fiber composites
• Epoxy resin with 60% volume carbon fiber, PITCH or PAN
• Results
– High strength PAN fibers have lower modulus that high modulus PAN
– High strength PITCH fibers have lower modulus that high modulus
PITCH
Fiber
T300
Tensile (Brittle Resin)
PAN
Strength (MPa)
Modulus (GPa)
Tensile (Ductile Resin)
Strength (MPa)
Modulus (GPa)
Compresion
Strength (MPa)
Modulus (GPa)
T50
PAN
T650
PAN
1862
138
1311
241
T1000
P55
P100
PAN
PITCH
PITCH
2413
3447
723
1138
170
159
234
483
2790
138
1414
241
3070
170
3795
234
890
483
1206
1725
124
965
234
1650
151
1690
199
483
505
276
Copyright Joseph Greene 2001
16
Directional Properties Carbon Fiber PEKK Laminates
• Fiber Volume Fraction is 60% Aerospace Quality
– Continuous fiber has higher strength and modulus for tensile,
compression, and shear in the 0° than long fiber composite.
– Long Fiber PEKK composites has higher Tensile strength and
modulus and Poisson ratio in the 90° direction than continuous fiber.
Property
Tensile (MPa)
Strength, 0°
Modulus, 0°
Poisson ratio
Strength, 90°
Modulus, 90°
Compressive (MPa)
Strength, 0°
Modulus, 0°
Flexural (MPa)
Strength, 0°
Modulus, 0°
Shear (MPa)
Strength, 0°
Modulus, 0°
Short Beam strength
Long Fiber
(56mm)
Continuous
1610
123.5
0.35
91
10.3
1676
129.7
0.33
73.1
8
%Increase
Continuous
4.09937888
5.02024291
-5.7142857
-19.67033
-22.330097
1262
111
1393 10.3803487
121.4 9.36936937
1655
120
1931 16.6767372
127.6 6.33333333
146
5.5
110
142 -2.739726
5.8 5.45454545
117 6.36363636
Long Fiber
(56mm)
Continuous
Fraction Transverse (90°) versus In-plane (0°)
1
1
1
1
0.056521739 0.043616
0.08340081 0.061681
Copyright Joseph Greene 2001
17
Directional Properties Carbon Fiber
• Unidirectional (0°/ 90°) versus Quasi-isotropic laminate
(0°/30°/60°/90°/120°/150°)
• Fiber Volume Fraction is 60% Aerospace Quality
– Polymer is Epoxy and Carbon Fiber is PITCH High Modulus fiber
• Results
– Uni-directional laminate is 40 times stronger and 92 times stiffer in
the 0° direction versus the transverse 90° direction in tensile.
– The quasi isotropic laminate is stronger and stiffer in tension in the 0°
direction than the 90° direction. The opposite is true for compression
Unidirectional Laminate
Quasi-isotropic Laminate
Testing Angle
0°
90°
0°/90° Ratio 0°
90° 0°/90° Ratio
Tensile Strength (MPa)
793
20
39.65
379
241
1.57
Tensile Modulus (GPa)
303
3.3
91.82
104
97
1.07
Tensile Ultimate Strain, %
0.25
0.5
0.50
0.27
0.23
1.17
Compressive Strength (MPa)
400
158
2.53
172
200
0.86
Compressive Modulus (GPa)
255
6.7
38.06
76
88
0.86
Compressive Ultimate Strain, % ------0.55
0.86
0.64
Copyright Joseph Greene 2001
18
Directional Properties Carbon Fiber
• Unidirectional (0°) versus Quasi-isotropic laminate (45°)
• Results
– Uni-directional laminate is stronger and stiffer in the 0° direction
versus the transverse 45° direction in tensile for Epoxy and PEEK
– The quasi isotropic laminate is has higher fracture strain% in the 45°
direction than the 0° direction for epoxy and for PEEK.
Fiber
Tensile Strength Tensile
Fracture
Polymer Matrix Orientation (MPa)
Modulus(GPa) Strain %
Epoxy
0°
932
83
1.1
Epoxy
45°
126
1.3
PEEK
0°
740
51
1.1
PEEK
45°
194
14
4.3
Copyright Joseph Greene 2001
19
Directional Properties Thermoplastic Composites
• Unidirectional Composite Properties with thermoplastic matrix
• Results
– PEEK APC2 and AS-4 Carbon fiber had the highest tensile strength
– Kevlar 49 had high strength but the lower tensile modulus than carbon
Resin
PEEK (APC2)
APC aromatic
ketone
PEKK
PPS Ryton
Torlon-C
Polyamidlimide
ULTEM 1000
polyetherimide
AVIMID
Polyimide
UDEL
Polysulfone
J-2 Poly
arylamide
Fiber
AS-4
Carbon
Fiber
Tensile Strength
(MPa)
Tensile
Compresive
Modulus (GPa) Strength (M Pa)
2242
138
1069
138
AS-4
AS-4
AS-4
1656
138
1138
1390
655
C-6000
1390
140
1390
AS-4
138
IM-6
AS
1345
131
1035
Kevlar
1310
76
276
Copyright Joseph Greene 2001
20
Directional Properties Carbon Fiber Composites
• Unidirectional Composite Properties from Hybrid Yarn
• Results
– PEEK with AS-4 Carbon fiber had higher flex modulus and about the same flexural
strength as PEEK with S2 glass and PEEK with Astroquartz
– Elongation was less than 1% for all composites and especially low for
S2 glass
Matrix
PEEK
PEKEKK
PEEK
Reinforcement
Type
AS4 3K Carbon AS4 3K Carbon Fiber S2 Glass
Vol %
62
62
Laminate
Properties
Flexural Strength
(MPa)
2380
2380
Flexural Modulus
(GPa)
138
134
Tensile Strength
(MPa) 90°
82
84
Tensile Modulus
(GPa) 90°
9.93
10.1
Elongation %
0.91
0.89
Copyright Joseph Greene 2001
PEEK
Astoquartz
63
64
2030
2205
58
46
50
78
20.3
0.25
18.6
0.42
21
Directional Properties Carbon Fiber Composites
• Unidirectional Composite Properties from Comingled Fabric
– Comingled fabric is where the fiber and polymer are interspersed at
filament level
• Results
– Comingled composites have comparable properties as prepreg tape
with PEEK and AS4 carbon fiber for equal vol% fiber
Properties of
Laminates
Nuber of Plies
Specific Gravity
Vol%
Void %
Flex Strength M
Pa
Flex Mod, G Pa
Transverse
Tensile strength
(M Pa)
Moisture %
Unidirectional
Prepreg Tape
PEEK AS4
10
1.56
60
1.9
Comingle Fabric Comingled Fabric Cowoven Fabric
16
8
12
1.55
1.53
1.53
56.1
57.7
61.8
2.1
3.2
4.4
1687
108
1514
98
1222
106
1150
65
91
0.15
64
0.22
25
0.17
2
Copyright Joseph Greene 2001
22
Properties of Carbon, glass, kevlar Fiber Composites
• Epoxy resin and polyester resin
• Results
– UD Carbon fiber has the highest strength and modulus in the 0°
direction than glass fiber or kevlar composites.
– Woven fabrics give more isotropic properties
– The higher the fiber percentages the higher the strength and modulus.
Fiber Vol %
UTS (0°) M Pa
UTS (90°) M Pa
UCS (0°) M Pa
UCS (0°) M Pa
USS (0°) M Pa
Ten Mod or E,
(0°) GPa
E (90°) GPa
Shear Mod or
G, GPa
ILSS (M Pa)
Poisson's ratio
Density (g/cc)
UD
UD Eglass Carbon Epoxy
epoxy
53
57
1190
2040
73
90
1001
1000
159
148
67
49
0/90
UD
Woven
Kevlar49 Eglass-epoxy epoxy
60
33
1379
360
30
360
276
240
138
205
60
98
+/-45
woven
Eglassepoxy
33
185
185
122
122
137
0/90
Woven
Carbonepoxy
50
625
625
500
500
130
+/-45
woven
Carbonepoxy
50
240
240
200
200
0/90
Woven
CSM
Kevlar- Eglass
epoxy
polyester
50
19
517
108
517
108
172
148
172
148
110
85
39
15
134
11
76
5
17
17
10
10
70
70
18
18
31
31
8
8
4
90
5
94
0.263
1.57
2
83
0.34
1.38
5
60
0.24
1.92
8
48
0.7
1.92
5
57
27
57
2
70
2.75
1.92
Copyright Joseph Greene 2001
1.53
1.53
1.33
0.32
1.45
23
Rule of Mixtures
• Mechanical properties of a composite material made from two
materials can be estimated based upon the volume fraction of
each material times the material property of each.
– Modulus, strength, CLTE, shrinkage, density, and others
– formula: Ec = Ef*Vf + EmVm = Ef*Vf + Em(1-Vf), where E is
Tensile modulus, f is fiber, m is matrix, and c is composite
– Example,
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
given
Ef
Em
ten str glas
ten str epox
75
5
1200
50
Gpa
Gpa
MPa
MPa
formula: Ec = Ef*Vf + EmVm = Ef*Vf + Em(1-Vf)
Copyright Joseph Greene 2001
Rule of Mixtures for
tion
vol frac fib
Composite: Epoxy and Glass
modulus, Gpastrength, Mpa
5
50
12
165
19
280
26
395
33
510
40
625
47
740
54
855
61
970
68
1085
75
1200
1
0.8
24
Rule of Mixtures
dens glass
dens epoxy
• Example, Density
2.56 g/cc
1.2 g/cc
– Epoxy and Glass,
– formula: c = f*Vf + mVm = f*f + m(1-Vf), where  is
density, f is fiber, m is matrix, and c is composite
vilume fraction
fibers
Rule of Mixtures for Density
1
0.8
0.6
0.4
0.2
0
Series1
0
0.5
1
Weight fraction fibers
Copyright Joseph Greene 2001
25
Rule of Mixtures
• Example, Epoxy and Glass
– Formula: Ec = Ef*Vf + EmVm = Ef*Vf + Em(1-Vf), where E is
Tensile modulus, f is fiber, m is matrix, and c is composite
– Formula: TSc = TSf*Vf + TSmVm = TSf*Vf + TSm(1-Vf), where TS
is Tensile strength, f is fiber, m is matrix, and c is composite
Tensile Strength of Polyester
Composite
Tensile Modulus of Polyester
Composite
80
1200
60
Strength (MPa)
Tensile Modulus, GPa
1400
40
20
0
0
0.5
1
Volume Fraction fiber
1000
800
600
400
200
0
0
Copyright Joseph Greene 2001
0.5
Volume Fraction fiber
1
26
Rule of Mixtures
• Comparison with published data
• Example,
– Polyester with 33% glass fibers 0/90 Ply
– Experimental
• Tensile strength = 360 MPa
• Tensile modulus = 17 GPa
– Rule Mixture (Theoretical)
• Tensile strength = 395 MPa
• Tensile modulus = 26 GPa
– % Experimental with Theoretical
• Tensile strength = - 8.86%
• Tensile modulus = - 34.6%
Copyright Joseph Greene 2001
27
Rule of Mixtures
• Comparison with published data
• Example,
– Epoxy with 60% carbon fibers 0/90 Ply
– Experimental
• Tensile strength = 2040 MPa
• Tensile modulus = 134 GPa
– Rule Mixture (Theoretical)
• Tensile strength = 2283 MPa
• Tensile modulus = 197 GPa
– % Experimental with Theoretical
• Tensile strength = - 10.6%
• Tensile modulus = - 31.4%
Copyright Joseph Greene 2001
28
Composites Properties with Exposure
• Exposure type
Copyright Joseph Greene 2001
29
Polyimides
• Bismaleimide (BMI) resins
– Advantages
• Low processing temperature versus polyimides (Cured at
350F)
• Standard epoxy processing equipment can be used since
same T.
• Postcure of 475 F is required to complete
polymerization.
• BMI are fully formed polyimides when reacted to form
composite
• Thus, no volatiles are removed and no consolidation
problems
• Tack and drape are quite good because of the liquid
component of the reactants
Copyright Joseph Greene 2001
30
Test Considerations
• Metal systems
– isotropic, linear, and elastic such that only a few tests are required to
obtain basic tensile stiffness properties that describe the mechanical
performance in most situations
– Only two values are needed: Tensile modulus (stiffness) and poisson’s
ratio (longitudinal strain divided by axial strain)
– Both are determined from the same tensile test
• Shear modulus (G) is related to shear strain () by Shear Stress :
 = G() or Shear Stress = Shear Modulus times strain
Copyright Joseph Greene 2001
31
Mechanical Test Considerations
• Principle factors are in three main areas
– manner in which the load is applied
– condition of material specimen at time of test
– surrounding conditions (environment) during testing
• Tests classification- load application
– kind of stress induced. Single load or Multiple loads
– rate at which stress is developed: static versus dynamic
– number of cycles of load application: single versus fatigue
• Primary types of loading
tension
shear
compression
torsion
flexure
Copyright Joseph Greene 2001
32
Stiffness
• Stiffness is a measure of the materials ability to resist
deformation under load as measured in stress.
– Stiffness is measures as the slope of the stress-strain curve
– Hookean solid: (like a spring) linear slope
•
•
•
•
steel
aluminum
iron
copper
F  kx
– All solids (Hookean and viscoelastic)
•
•
•
•
  E
metals
plastics
composites
ceramics
Copyright Joseph Greene 2001
33
Strain
• Permanent set is a change in form of a specimen
once the stress ends.
• Axial strain is the strain that occurs in the same
direction as the applied stress.
• Lateral strain is the strain that occurs perpendicular
to the direction of the applied stress.
• Poisson’s ratio is ratio of lateral strain to axial strain.
Poisson’s ratio = lateral strain
axial strain
Lateral
Strain
Axial
Strain
– Example
• Calculate the Poisson’s ratio of a material with lateral strain
of 0.002 and an axial strain of 0.006
• Poisson’s ratio = 0.002/0.006 = 0.333
Note: For most materials, Poisson’s ratio is between 0.25 and 0.5
Copyright Joseph Greene 2001
34
Test Considerations
• Degree of anisotropy
– Degree of anisotropy depends on how symmetrical the material is.
• Metals are isotropic materials that have an infinite number of symmetry planes
(properties are the same in different directions or planes) and end up as noted above with
two material properties (E and )
• Opposite extreme are materials with no symmetry planes and would require 21 material
properties and require extensive testing inorder to design a structure with the best finite
element computer programs (NASTRAN)
• Most composites used today are developed in two-dimensional form and consequently
have one plane of symmetry.
– Called transversely isotropic for unidirectional materials
– Stress-strain relationships requires 5 material properties
» Modulus in 2 directions, E11 and E22
» Shear Modulus in 2 directions, E12, E21
» Poisson’s ratio, 
Copyright Joseph Greene 2001
35
Test Considerations
• Transversely isotropic stress-strain relationships
–
–
–
–
E11
G21
G31
Stress = modulus times strain
Tensile stress = tensile modulus times tensile strain
Shear stress = shear modulus times shear strain
Shear modulus = tensile modulus divided by 2(1+poisson’s ratio)
G12 G13
E11 G12 G13
E11 G12 G12
E22 G23
0 E22 G23
0 E22 G23
G32 E33
0
0
E33
0
0
E
22
E11
G12
0
E22
0
0
All combinations Simplify with Symmetry Simplify with ignoring thickness. Make 2D
• E11 is the modulus obtained from simple tensile tests on a unidirectional
composite in the direction of the fiber orientation.
• Poisson’s ratio ,12 is obtained by measuring the lateral contraction strain and
the axial elongational strain
• E22 is the tensile in the transverse direction to E11 and is found by cutting a test
coupon so that it can be pulled in the transverse direction. 21 is also found
which is muss less than 12. The third direction Poisson’s ratio, 23 , is usually
ignored by assuming 2-D
• G12, the shear modulus, is measured using a simple hoop-wound tubes or +/- 10°
to +-15° tensile coupons. Shear strains are measured then the modulus is
calculated.
Copyright Joseph Greene 2001
36
Test Considerations
• Estimating properties with micromechanics
– Some basic properties can be estimated using what is called structure-property
relationships or micromechanics.
– Assumptions
•
•
•
•
•
Composite ply is macroscopically homogeneous and linearly elastic
Fibers are linearly elastic and homogeneous
Matrix is linearly elastic and homogeneous
Both fiber and matrix are free of voids
Interface is completely bonded, and there is no transitional region between the matrix
and reinforcement
• Mechanical properties of individual constituents re the same whether they are made by
themselves or made up within the composite
– The values of E11 (longitudal modulus), 12 (principal Poisson’s ratio), and 11
(principal expansion coefficient), can be expressed in terms of the matrix/fiber
properties themselves and the volume fraction of the respective ingredients.
– These expressions are derived from the Rule of Mixtures theory as:
Tensile modulus: E11 = Vf Ef + Vm Em
Poisson’s ratio : 12 = Vf  f + Vm  m
Expansion coefficient  11 = Vf  f + Vm  m
Density: 11 = Vf f + Vm m
Copyright Joseph Greene 2001
where, f is the fiber, m is the matrix,
V is the volume fraction of fiber (Vf)
or matrix (Vm) and same subscripts
work for the others properties as well.
37
Fatigue Properties
• Fatigue
– High performance composites were developed for aerospace applications because Al
has poor fatigue performance.
• Aircraft applications can have 106 to 108 load cycle range.
– Al and some steels falter in this range
– Al has 10% fatigue endurance limit versus static values
» Aluminum will only be able to support 10% of the static load before the
fatigue test.
– Composites have 60% the static (one cycle) ultimate strength
• Fiber reinforced composites are more stable and forgiving in fatigue applications and do
well in fatigue tests since a loss of a few failed fibers is not noticeable to the overall
strength of the fiber composite
– Figure 4-4. Axial compressive fatigue of graphite/epoxy laminate
– Composites tend to stabilize early in fatigue loading through the following
mechanisms, each of which absorbs energy or redirects the energy to other parts of
the composite
» Matrix micro-cracking which absorbs energy by breaking matrix bonds
» Blunting of cracks at the fiber surface which reduces further crack growth
» Delamination between layers which may relieve internal cure stresses
» Stress redistribution and load sharing in composite structure
» Energy dissipation resulting through matrix viscoelastic effects (internal
damping)
Copyright Joseph Greene 2001
38
Vibration and Damping Properties
• Vibrations are often a natural consequence of stiffness
– For composites, the fiber stiffness is balanced with the matrix resin
plasticity
– Composites provide excellent properties for aircraft and missile
control surfaces where fast, rigid response is needed.
– Composites are less noisy and provide lower vibration transmission
than metals.
• Damping in composites is due to microcracking, internal tip blunting, matrix
viscoelastic effects and plasticity.
• Damping capability of composites can be almost twice that of some steels, and
ten times better than aluminum and titanium alloys.
• Figure 4-5. Specific damping capacity versus stress
Copyright Joseph Greene 2001
39
Design Approach Comparison
• Metal structures provide a well-established database from 100
years of structural use that include exposure to a wide range of
environmental and operational conditions.
• Material choice for metallic structures
– Define operational loads and environments
– Select several candidate metal materials to meet service environment
– Conduct trade studies using the basic design properties.
• For metals the following mechanical properties are needed:
– Tensile modulus (E), Poisson’s ratio, and thermal expansion (CLTE)
– Compare the material allowables and select the appropriate metal
candidates to satisfy structural, cost, and manufacturing considerations
Copyright Joseph Greene 2001
40
Design Approach Comparison
• Composites widen the options for designers who can now
tailor the composite to meet structural requirements through a
variety of combinations of fibers and matrices and percentages
of each.
– Selection of specific fiber (or several) to meet stiffness and strength requirements
– Orientation of the fiber into the load direction to take the majority of the loads
– Selection of resin-to-fiber volume ratio for optimizing fiber delivery
• Structural analysis with finite elements is needed to asses
structural integrity
– Along with the required material properties,
• Two stiffness values in two directions (E and ) and two thermal expansion
coefficients.
• More values might be needed if the composite is very anisotropic.
• Fewer are required if more isotropic.
Copyright Joseph Greene 2001
41
Environmental Effects
• Composites are affected by thermal, moisture, fatigue, creep, and aging
(service life)
– For metals
• Environment attacks homogeneous material and not at interfaces, layers, and porous
regions
– For composites
• Environment attacks inhomogeneous material at interfaces, layers, and porous regions
• Temperature
– Often the most severe environmental effect
• Affects the entire service life of the composite
– Initially part is cured in molding operation and then post cured
– Max use temperature is usually the highest temperature the composite is exposed to
during molding or post cure
» If molded at 250F and not post cured, then the highest use temperature is 250F
» If molded at 250F and then post cured at 350F, then the use temp is 350F
» If molded at 600F (PEEK or Polyimids) then the use temp is 600F.
– Cure process generates some undesirable effects, e.g., creation of residual cure
stresses that can lead to porosity, microcracking, and delamination.
» To reduce these effects, reduce the cure temperature, reduce ramp temperature
during heating and cool-down processing cycles.
– Especially, important with compression fatigue loading in addition to inherent
thermal stresses
Copyright Joseph Greene 2001
42
Environmental Effects
• Temperature (continued)
– Thermal cycling
• Solar radiation, daily temperature variations due to transportation, weather
conditions due to seasons and geography
– Normal operational limits for static or isothermal exposure
• Rocket motor cases- -65°F to 165°F range for operational and storage conditions
• Automotive body panels (doors, hoods, etc.)- -40F to 140F
• Automotive engine parts (valve covers, hood inners)- -40F to 300F
– Extended limits for
• Cryogenic tanks or operations in high temperature (engine blades), moderate
temperature (aircraft parts) and low temperature (space structures)
• Very often these exposures are for short duration (few seconds to a few hundred
hours). If longer the exterior is usually protected with insulating material.
– Aeroheating for nose cone (reentry) and rocket motor applications
• Requires careful analysis of thermal stresses and review of allowable elevated
temperature mechanical properties
– The mechanical properties are tested at service temperatures for
• Modulus, strength, impact, etc.
– Figure 4-6- Effect of thermal post cure on fracture toughness of
Copyright Joseph Greene 2001
43
Environmental Effects
• Moisture
– Composites absorb moisture through the matrix, the fiber, the fiber-matrix interface,
and porous regions or area where microcracking or delamination have occurred
– Table 4-1 illustrates the degree to which polymer absorbs moisture
• Sample is submerged in water at a particular temperature and the amount of water
absorbed is measured for several days and weeks until saturation.
– Moisture degrades the mechanical properties of polymer materials.
• Rule of thumb is to have a maximum of 3% moisture for a polymer material
• Materials that absorb more then that should NOT be selected for applications that are
exposed to a wet environment (contact with water for long periods of time), but can be
used in applications with short exposure to moisture.
– Fibers do not absorb water (except for aramid Kevlar 49 fiber)
– Resins absorb moisture for the composite and results in
• Lower strengths, modulus, and microcracking
• Properties of composite materials are tested in the wet condition if product will be used
in a wet environment, e.g., submersible crafts
– Moisture barriers can be used, e.g., coatings, paints, vapor deposited metallic layers,
aluminum foil layers, grease seals, plastic film.
Copyright Joseph Greene 2001
44
Environmental Effects
• Fatigue
– Composites perform well under fatigue loadings when compared to
metals, maintaining 60% of their ultimate tensile strength.
– Tension fatigue and stress rupture under tension loading have not had
a substantial effect on composite strength degradation.
– Primary fatigue difficulty has been in compression fatigue.
• Fibers are normally designed to carry tension loads
• Compression loading puts more dependence on the resin to transfer shear and
compression loads to adjacent fibers and from layer to layer than does tensile
loading.
• Primary concern for aircraft industry has always been with compression fatigue
under hot-wet conditions (90-100% relative humidity and 180°F temperatures)
• Figure 4-4
Copyright Joseph Greene 2001
45
Environmental Effects
• Creep/Delamination Behavior
– Fiber behaves in a rigid manner
– Resin is prone to creep or relax under load, especially at higher
temperatures or long durations
– For metals, creep isn’t important unless at temperatures above 400F
– For polymer matrix composites, creep can be an issue at temperatures
above 100F (for thermoplastics) and 200F (urethanes) and 300F
(epoxies)
– Creep is a result of the viscoelastic nature of polymers, but can be
offset by
•
•
•
•
•
Fiber orientation in the direction of high loads to reduce creep loading
Increased fiber content
Select stiffer fibers
Reduction of level of stress in the design
Utilization of initial loading cycles to relieve residual stresses
Copyright Joseph Greene 2001
46
Environmental Effects
• Aging/Service life considerations
– Typical composite structures are designed to survive 10 to
25 years
– Following steps help in design
•
•
•
•
Define service environment in terms of exposure time
Review database of materials for a match
Conduct accelerated aging test
Verify aging tests with real time aging on samples stored near
operational conditions
• Figure 4-7- Pressure vessel with series of burst tests after exposure
to environmental conditions
Copyright Joseph Greene 2001
47