Micromechanics Approach to Failure

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Micromechanics Approach to Failure

• James C. Iatridis

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Strength of composite materials

• References
• RM Jones Mechanics of Composite Materials, 2nd
  Edition, Taylor Francis, 1999 Sections 2.9,
  3.5, 4.5
• SW Swanson Advanced Composite Materials,
  Prentice Hall, Inc., 1997 Chapter 4
• Barbero -- class text

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Tensile strength in the fiber direction

• As the load increases several things occur1)
  Both fibers and matrix deform elastically2)
  Fibers continue to deform elastically, but matrix
  deforms plastically3) Both fibers and matrix
  deform plastically4) Fibers fracture followed by
  fracture of the composite material

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Schematic of tensile failure
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Mixture theory approach to tensile strength

• Assuming parallel orientation of fibers and
  matrix (this is a good approximation for tension
  in the fiber direction).
• Assuming fibers all have the same strength, are
  relatively brittle compared to the matrix, and
  that the composite has more than a certain
  minimum volume fraction of fibers, then
• ecmaxefmax

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Failure stress in tension
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Failure in tension
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Failure in tension

• Assumption that fiber failure causes composite
  failure breaks down for low volume fractions. The
  critical volume fraction where fibers increase
  strength of composite is
•  
•  
• Microstructural model of tensile failure in the
  fibers is described for a single fiber break as
  the Model for bridging around a fiber break and
  several breaks can be combined together using a
  statistical approach

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Compressive failure of composites

• Compressive Strength in the Fiber Direction
• Rosens Microstructural model for fiber buckling
  in extensional and shear modes is given in
  Barbero, Section 4.42, Swanson, ch4.4, and Jones
  3.5.3

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Fiber buckling

•  

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Fiber misalignment

• Buckling probability increased with fiber
  misalignment

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Misalignment

• Probability of fiber misalignment is a normal
  distribution

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Compressive microfailure

• related to misalignment

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Compressive failure of composites

• Note that in Jones Figure 3-61 that extensional
  mode is favored at low Vf and shear mode favored
  at more typical values for Vf

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Next steps

• Now lets look analytically at bridging around a
  broken fiber in tension and also at microbuckling
  in compression.