ME 7501 Lecture 6 Dr BJ Sullivan Strength of a Continuous Fiber Reinforced Lamina For the orthotropic lamina under simple uniaxial or shear stress there are 5 strengths Longitudinal tensile strength ID: 328008
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Slide1
Tensile Strength of Continuous Fiber-Reinforced Lamina
M.E. 7501 – Lecture 6
Dr. B.J. SullivanSlide2
Strength of a Continuous Fiber Reinforced Lamina
For the orthotropic lamina under simple uniaxial or shear stress, there are 5 strengths:
= Longitudinal tensile strength
= Longitudinal compressive strength = Transverse tensile strength = Transverse compressive strength = Shear strength (See Fig. 4.1)Slide3
Longitudinal Uniaxial Loading
Stress-strain curves for uniaxial and shear loading showing lamina strengths and ultimate strains.
Tension
CompressionSlide4
Transverse Uniaxial Loading
Stress-strain curves for uniaxial and shear loading showing lamina strengths and ultimate strains.
Tension
CompressionSlide5
Shear Loading
Stress-strain curves for uniaxial and shear loading showing lamina strengths and ultimate strains.Slide6
Assuming linear elastic behavior up to failure:
(4.1)
where are the corresponding ultimate strains. Slide7
Transverse tensile strength
S
T
(+) is low because of stress concentration in matrix at fiber/matrix interfaces.
Fibers are, in effect, “holes” in matrix under transverse or shear loading.Slide8
Typical values of lamina strengths for several composites
Material
S
L
(+)
ksi(MPa)
S
L
(-)
ksi(Mpa)
S
T
(+)
ksi(Mpa)
S
T
(-)
ksi(Mpa)
S
LT
ksi(Mpa)
Boron/5505 boron/epoxy v
f
= 0.5 (*)
230 (1586)
360 (2482)
9.1 (62.7)
35.0 (241)
12.0 (82.7)
AS/3501 graphite/epoxy v
f
= 0.6 (*)
210 (1448)
170 (1172)
7.0 (48.3)
36.0 (248)
9.0 (62.1)
T300/5208 graphite/epoxy v
f
= 0.6 (*)
210 (1448)
210 (1448)
6.5 (44.8)
36.0 (248)
9.0 (62.1)
Kevlar 49/epoxy aramid/epoxy v
f
= 0.6 (*)
200 (1379)
40 (276)
4.0 (27.6)
9.4 (64.8)
8.7 (60.0)
Scotchply 1002 E-glass/epoxy v
f
= 0.45 (*)
160 (1103)
90 (621)
4.0 (27.6)
20.0 (138)
12.0 (82.7)
E-glass/470-36 E-glass/vinylester v
f
= 0.30 (*)
85 (584)
116 (803)
6.2 (43)
27.1 (187)
9.3 (64.0)Slide9
Micromechanics Models for Strength
Strength more sensitive to material and geometric nonhomogeneity than stiffness, so statistical variability of strength is usually greater than that of stiffness.
Different failure modes for tension and compression require different micro -mechanical models.Slide10
Statistical distribution of tensile strength for boron filaments. (From Weeton, J.W., Peters,
D.M., and Thomas, K.L., eds. 1987.
Engineers’
Guide
to Composite
Materials. ASM International, Materials Park, OH. Reprinted by permission of ASM International.)Slide11
Tensile Failure of Lamina Under Longitudinal Stress
Representative stress-strain curves for typical fiber, matrix and composite materials (matrix failure strain greater than fiber failure strain)
(a) Fiber Failure Mode
Fiber
Composite
Composite
Matrix
Strain
Stress
Typical of polymer matrix compositesSlide12
Tensile Failure of Lamina Under Longitudinal Stress
Representative stress-strain curves for typical fiber, matrix and composite materials (fiber failure strain greater than matrix failure strain)
(a) Matrix Failure Mode
Fiber
Composite
Matrix
Strain
Stress
Typical of ceramic matrix compositesSlide13
Longitudinal Tensile Strength
Fiber failure mode (
e
f1(+)<em1(+)); polymer matricesRule of mixtures for longitudinal stress:
when
(only valid if
v
f
is large enough)
(3.22)
(4.22)Slide14
Critical fiber volume fraction,
v
fcrit
when
Once fibers fail, when
v
f <v
fcrit
(4.23)
(4.24)
Longitudinal Tensile StrengthSlide15
This defines
(4.25)
Longitudinal Tensile Strength
In most of the cases,
v
fcrit
is very small,
so
(4.22)Slide16
Variation of composite longitudinal tensile strength with fiber volume fraction for composites having matrix failure strain greater than fiber failure strain
Equation (4.22)
Fiber Volume Fraction
Strength
Equation (4.24)
1.0
0Slide17
Variation of composite longitudinal tensile strength with fiber volume fraction for composites having fiber failure strain greater than matrix failure strain
Equation (4.27)
Fiber Volume Fraction
Strength
Equation (4.26)Slide18
Longitudinal Tensile Strength
(4.26)
Fibers can withstand
e
f1
(+)
>em1(+) and remaining area of fibers is such that
(4.27)
which applies for practical
v
f
(see Fig. 4.13 – previous two slides)
(b) Matrix Failure Mode;
ceramic matrices