Tensile Strength of Continuous Fiber-Reinforced Lamina

1. Tensile Strength of Continuous Fiber-Reinforced Lamina M.E. 7501 – 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. Stress-strain curves for uniaxial and shear loading showing lamina strengths and ultimate strains. Longitudinal Uniaxial Loading Tension Compression

4. 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. Shear Loading

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. Typical values of lamina strengths for several composites

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. (From Weeton, J.W., Peters, D.M., and Thomas, K.L., eds. 1987. Engineers’GuidetoCompositeMaterials. 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 (3.22) • Fiber failure mode (ef1(+)<em1(+)); polymer matrices Rule of mixtures for longitudinal stress: when (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) 0 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. 4.13 – previous two slides)