Lecture Problem 15.D5

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Lecture Problem 15.D5

• Richard Priddell
• E106

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Problem Statement

• It is necessary to fabricate an aligned and
  discontinuous glass fiber-epoxy matrix composite
  having a longitudinal tensile strength of 1200
  MPa using a .35 volume fraction of fibers.
  Compute the required fiber fracture strength
  assuming that the average fiber diameter and
  length are .015 mm and 5.0 mm respectively. The
  fiber-matrix bond strength is 80 MPa and the
  matrix stress at composite failure is 6.55 MPa.

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Formula

• Fibers aligned longitudinal so use formula
• scl sfVf smVm
• where
• scl longitudinal composite failure stress
• sf fiber failure stress
• Vf volume fraction of fibers
• Vm volume fraction of matrix

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Note About Formula

• Continuous Fiber Assumption assumes fiber length
  is at least 15 times greater than critical fiber
  length
• Will need to check this assumption after
  calculation using
• lc (sfd)/(2tc)
• Where d fiber diamater, tc fiber-matrix bond
  strength, and lc is critical fiber length

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Additional Notes

• If assumption invalid need to use long fiber, or
  short fiber equation
• Long fiber lc lt l lt 15lc
• scd sfVf(1- lc/(2l)) smVm
• Short fiber l lt lc
• scd (ltc/d)Vf smVm

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Givens

• scl sfVf smVm
• scl 1200 MPa
• Vf .35
• Vm 1 Vf .65
• sm 6.55 MPa
• d .015 mm
• l 5.0 mm

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Solve for sf

• (scl - smVm)/Vf sf
• sf 3.42 GPa

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Verify Assumption

• Require l gt 15lc
• lc (sfd)/(2tc)
• where
• sf 3.42 GPa
• d .015 mm
• tc 80 MPa

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Verify Assumption

• lc .32 mm
• l 5.0 mm
• l gt 15lc (15.625x bigger)
• Accept value of 3.42 GPa since assumption is
  valid

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Application

• Whenever working with composites it is
  insufficient to only know the properties of the
  constituents, need to calculate properties of the
  composite material
• Need to remember composites can have different
  properties in different directions, must take
  that into account when designing using composites