Tensile Strength of Continuous FiberReinforced Lamina M E

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 = Longitudinal compressive strength = Transverse tensile strength = Transverse compressive strength = Shear strength (See Fig. 4. 1)

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

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

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

Assuming linear elastic behavior up to failure: (4. 1) where are the corresponding ultimate strains.

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.

Typical values of lamina strengths for several composites Material Boron/5505 boron/epoxy vf = 0. 5 (*) SL(+) ksi(MPa) SL(-) ksi(Mpa) ST(+) ksi(Mpa) ST(-) ksi(Mpa) SLT ksi(Mpa) 230 (1586) 360 (2482) 9. 1 (62. 7) 35. 0 (241) 12. 0 (82. 7) AS/3501 graphite/epoxy = 0. 6 (*) vf 210 (1448) 170 (1172) 7. 0 (48. 3) 36. 0 (248) 9. 0 (62. 1) T 300/5208 graphite/epoxy = 0. 6 (*) vf 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 glass/epoxy = 0. 45 (*) Evf 160 (1103) 90 (621) 4. 0 (27. 6) 20. 0 (138) 12. 0 (82. 7) E-glass/470 -36 -glass/vinylester = 0. 30 (*) E vf 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 Stress Representative stress-strain curves for typical fiber, matrix and composite materials (matrix failure strain greater than fiber failure strain) Stress Fiber Composite (a) Fiber Failure Mode Typical of polymer matrix composites Matrix Strain

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 Composite Typical of ceramic matrix composites Matrix Strain

Longitudinal Tensile Strength a) Fiber failure mode (ef 1(+)<em 1(+)); polymer matrices Rule of mixtures for longitudinal stress: (3. 22) when (4. 22) (only valid if vf is large enough)

Longitudinal Tensile Strength Critical fiber volume fraction, vfcrit when (4. 23) Once fibers fail, when vf <vfcrit (4. 24)

Longitudinal Tensile Strength This defines (4. 25) In most of the cases, vfcrit is very small, so (4. 22)

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

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

Longitudinal Tensile Strength (b) Matrix Failure Mode; ceramic matrices (4. 26) Fibers can withstand ef 1(+)>em 1(+) and remaining area of fibers is such that (4. 27) which applies for practical vf (see Fig. 4. 13 – previous two slides)