tensile strength of continuous fiber-reinforced lamina
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Tensile Strength of Continuous Fiber-Reinforced Lamina. M.E. 7501 – Lecture 6 Dr. B.J. 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 - PowerPoint PPT PresentationTRANSCRIPT
Tensile Strength of Continuous Fiber-Reinforced Lamina
M.E. 7501 – Lecture 6Dr. B.J. 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= Longitudinal compressive strength= Transverse tensile strength= Transverse compressive strength = Shear strength
(See Fig. 4.1)
)(LS
)(LS
)(TS
)(TS
LTS
1
1
1
1
)(Ls
)(Le
)(Ls
)(Le
Longitudinal Uniaxial Loading
Stress-strain curves for uniaxial and shear loading showing lamina strengths and ultimate strains.
Tension
Compression
Transverse Uniaxial Loading
2
2
2
2
)(TS
)(Te)(
TS
)(Te
Stress-strain curves for uniaxial and shear loading showing lamina strengths and ultimate strains.
Tension
Compression
Shear Loading
Stress-strain curves for uniaxial and shear loading showing lamina strengths and ultimate strains.
12
LTs
LTe
12
12
Assuming linear elastic behavior up to failure:)(
1)( LL eES
)(1
)( LL eES)(
2)( TT eES
)(2
)( TT eES
LTLT eGS 12
(4.1)
where are the corresponding ultimate strains.
,)(Le ,)(
Le ,)(Te ,e )(
T
LTe
Transverse tensile strength ST(+) is low because of stress concentration in matrix at fiber/matrix interfaces.
22
Fibers are, in effect, “holes” in matrix under transverse or shear loading.
Typical values of lamina strengths for several composites
Material SL(+) ksi(MPa)
SL(-) ksi(Mpa)
ST(+) ksi(Mpa)
ST(-) ksi(Mpa)
SLT ksi(Mpa)
Boron/5505 boron/epoxy
vf = 0.5 (*)230 (1586) 360 (2482) 9.1 (62.7) 35.0 (241) 12.0 (82.7)
AS/3501 graphite/epoxy
vf = 0.6 (*)210 (1448) 170 (1172) 7.0 (48.3) 36.0 (248) 9.0 (62.1)
T300/5208 graphite/epoxy
vf = 0.6 (*)210 (1448) 210 (1448) 6.5 (44.8) 36.0 (248) 9.0 (62.1)
Kevlar 49/epoxy aramid/epoxy
vf = 0.6 (*)200 (1379) 40 (276) 4.0 (27.6) 9.4 (64.8) 8.7 (60.0)
Scotchply 1002 E-glass/epoxy
vf = 0.45 (*)160 (1103) 90 (621) 4.0 (27.6) 20.0 (138) 12.0 (82.7)
E-glass/470-36 E-glass/vinylester
vf = 0.30 (*)85 (584) 116 (803) 6.2 (43) 27.1 (187) 9.3 (64.0)
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.
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.)
Tensile Failure of Lamina Under Longitudinal StressRepresentative stress-strain curves for typical fiber, matrix and composite materials
(matrix failure strain greater than fiber failure strain)
(a) Fiber Failure ModeFiber
Composite
Composite Matrix
Strain
Stress)(
1
fS
)(LS
)(1
mfS
)(1
mS
)(LS
)(1
fe )(
1
me
)( critf vv
)( critf vv
Typical of polymer matrix
composites
Tensile Failure of Lamina Under Longitudinal StressRepresentative stress-strain curves for typical fiber, matrix and composite materials
(fiber failure strain greater than matrix failure strain)
(a) Matrix Failure ModeFiber
Composite
Matrix
Strain
Stress)(
1
fS
)(LS
)(1
fmS
)(1
mS
)(1
fe)(
1
me
Typical of ceramic matrix
composites
Longitudinal Tensile Strengtha) Fiber failure mode (ef1
(+)<em1(+)); polymer matrices
Rule of mixtures for longitudinal stress:
when mmffc vv 111
)(11
ff S)(
1)(
11 fmmfm eES
)(1
Lc S
mfmffL veEvSS )(1
)(1
)( mmfff vSvS )(
1)(
1
(only valid if vf is large enough)
(3.22)
(4.22)
Critical fiber volume fraction, vfcrit
when )(1
)( mL SS
)(1
)(1
)(1
)(1
mff
mfmf SS
SSv
crit
Once fibers fail, when vf <vfcrit
mmL vSS )(1
)(
(4.23)
(4.24)
Longitudinal Tensile Strength
This defines
)(1
)(1
)(1
)(1
)(1
min
mmff
mfmf SSS
SSv (4.25)
Longitudinal Tensile Strength
In most of the cases, vfcrit is very small,
so fmfffL vSvSS 1)(1
)(1
)( (4.22)
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 )(1
fS
)(1
mfS
)(1
mS
fcritvminfv
Equation (4.24)
1.00
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 )(1
fS
)(mfS
1
)(1
mS
minfv
Equation (4.26)
Longitudinal Tensile Strength
fmffmL vSvSS 1)(1
)(1
)((4.26)
Fibers can withstand ef1(+)>em1
(+) and remaining area of fibers is such that
ffL vSS )(1
)( (4.27)
which applies for practical vf
(see Fig. 4.13 – previous two slides)
(b) Matrix Failure Mode; ceramic matrices