1. Tensile Strength of Continuous Fiber-Reinforced Lamina
M.E – Lecture 6
Dr. B.J. Sullivan

2. 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)

3. Longitudinal Uniaxial Loading
Stress-strain curves for uniaxial and shear loading showing lamina strengths and ultimate strains.
Longitudinal Uniaxial Loading
Tension
Compression

4. Transverse Uniaxial Loading
Stress-strain curves for uniaxial and shear loading showing lamina strengths and ultimate strains.
Transverse Uniaxial Loading
Tension
Compression

5. Stress-strain curves for uniaxial and shear loading showing lamina strengths and ultimate strains.

6. Assuming linear elastic behavior up to failure:
(4.1)
where are the corresponding ultimate strains.

7. Transverse tensile strength ST(+) is low because of stress concentration in matrix at fiber/matrix interfaces.
Fibers are, in effect, “holes” in matrix under transverse or shear loading.

8. Material SL(+) ksi(MPa) SL(-) ksi(Mpa) ST(+) ksi(Mpa) ST(-) ksi(Mpa)
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 (*)
6.5 (44.8)
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 E-glass/epoxy vf = 0.45 (*)
160 (1103)
90 (621)
20.0 (138)
E-glass/ E-glass/vinylester vf = 0.30 (*)
85 (584)
116 (803)
6.2 (43)
27.1 (187)
9.3 (64.0)

9. 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.

10. Statistical distribution of tensile strength for boron filaments
Statistical distribution of tensile strength for boron filaments. (From Weeton, J.W., Peters,
D.M., and Thomas, K.L., eds Engineers’ Guide to Composite Materials.
ASM International, Materials Park, OH. Reprinted by permission of ASM International.)

11. 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)
Stress
(a) Fiber Failure Mode
Fiber
Typical of polymer matrix composites
Composite
Matrix
Composite
Strain

12. 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)
Stress
Fiber
(a) Matrix Failure Mode
Typical of ceramic matrix composites
Composite
Matrix
Strain

13. Longitudinal Tensile Strength
Fiber failure mode (ef1(+)<em1(+)); polymer matrices
Rule of mixtures for longitudinal stress:
when
(3.22)
(4.22)
(only valid if vf is large enough)

14. Longitudinal Tensile Strength
Critical fiber volume fraction, vfcrit
when
(4.23)
Once fibers fail, when vf <vfcrit
(4.24)

15. Longitudinal Tensile Strength
This defines
(4.25)
In most of the cases, vfcrit is very small, so
(4.22)

16. Variation of composite longitudinal tensile strength with fiber volume fraction for composites having matrix failure strain greater than fiber failure strain
Strength
Equation (4.22)
Equation (4.24)
1.0
Fiber Volume Fraction

17. Variation of composite longitudinal tensile strength with fiber volume fraction for composites having fiber failure strain greater than matrix failure strain
Strength
Equation (4.27)
Equation (4.26)
Fiber Volume Fraction

18. Longitudinal Tensile Strength
(b) Matrix Failure Mode; ceramic matrices
(4.26)
Fibers can withstand ef1(+)>em1(+) and remaining area of fibers is such that
(4.27)
which applies for practical vf
(see Fig – previous two slides)