Lecture 3 Flashcards
(14 cards)
State the 4 independent elastic constants of a ply.
E11 - Longitudinal modulus
E22 - Transverse modulus
G12 - Shear modulus
v12 - poissons ratio
What are the 5 independent strength values of a ply?
σ1T - Longitudinal tensile strength
σ1C - Longitudinal compressive strength
σ2T - Transverse tensile strength
σ2C - Transverse compressive strength
τ12 - In-plane shear strength
What are the two thermal coefficients of expansion in a ply?
α1 - longitudinal thermal coefficient of expansion (CTE)
α2 - transverse thermal coefficient of expansion (CTE)
Derive the rules of mixtures density formula for a composite.
Wc = Wf + Wm
Weight = density * volume W = ρV
ρcVc = ρfVf + ρmVm ρc = ρf (Vf/Vc) + ρm (Vm/Vc) ρc = ρfνf + ρmνm ρc = ρfνf + ρm(1 - νf)
(where ν is the volume fraction)
How would you find the weight fraction of a fibre and/or matrix?
Fibre:
wf = Wf / Wc = ρfVf/ρcVc
wf = (ρf/ρc)*νf
Matrix:
wm = Wm / Wc = ρmVm/ρcVc
wm = (ρm/ρc)*νm
Other than fibre and matrix, what else exists in real composites?
Voids: Vv and Wv
Thus the density formula becomes:
ρc = ρfνf + ρm(1 - νf - νv)
Voids typically appear in the matrix and reduce the volume fractions of the matrix
What is the deformation relation when a tensile force is applied in the longitudinal direction (fibre direction)?
εc1 = εm1 = εf1
Acts similar to a spring in parallel.
Derive the rules of mixtures longitudinal stress formula for a composite.
Fc = σc1*Ac Fc = Ff + Fm
Fc = σc1Ac = σf1Af + σm1*Am
σc1 = σf1(Af/Ac) + σm1(Am/Ac)
σc1 = σf1*νf+ σm1*νm σc1 = σf1*νf+ σm1*(1- νf)
Derive the rules of mixtures longitudinal modulus formula for a composite.
σc1 = σf1νf+ σm1νm
σ = Eε for linear elastic materials
Ec1εc = Ef1εfνf + Em1εmνm
εc1 = εm1 = εf1
Ec1 = Ef1νf + Em1νm Ec1 = Ef1νf + Em1(1-νf)
What is the deformation relation when a tensile force is applied in the transverse direction (opposing the fibre direction)?
Acts like springs in series (extension is different).
The transverse load acts equally on fibre and matrix.
Derive the rules of mixtures transverse modulus formula for a composite.
Transverse extension of the composite is equal to the sum of the extension of fibre and matrix.
εc Lc = εf Lf + εm Lm
εc = εf (Lf/Lc) + εm (Lm/Lc)
εc = εf νf + εm νm
σ = Eε for linear elastic materials
σc/Ec = σf/Ef νf + σm/Em νm
σc = σf = σm
1/Ec = 1/Ef νf + 1/Em νm 1/Ec = νf/Ef + νm/Em
Ec = E22 = EfEm/ νfEm + νmEf
(note the fibre transverse modulus should be used from property data)
Explain the modulus vs fibre volume fraction relationship for both longitudinal and transverse.
Longitudinal becomes linearly better with a higher volume fraction.
Transverse becomes exponentially better as the volume fraction increases.
Longitudinal is generally stronger than the transverse.
Explain why a volume fraction of 1 cannot be used?
Fibres are generally processed in circular shapes and therefore there are always small spaces between each fibre inserted.
State the 4 elastic constants of a ply (rules of mixtures).
E11 = Ec1 = Ef1νf + Em1νm
E22 = Ec2 = EfEm/ νfEm + νmEf
1/G12 = νf/Gf + νm/Gm
v12 = vf νf + vm νm
