ME 257 Intro to Micromechanics

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ME 257 -- Intro to Micromechanics

• Prof. James C Iatridis

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Composite types
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Fabrics
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Composite coordinate frame

• This class will focus on analysis of continuous
  fiber laminated composites with miscellaneous ply
  numbers and orientations

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Coordinate frame

• To begin lets define a coordinate frame

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Material Properties

• The material properties we will be concerned with
  for plane stress (to be defined soon)
  formulations are E1, E2, n12, n21, and G12

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Longitudinal modulus
What material properties can we calculate here?
E1s1/e1 or E11s1/e1
n12-e2/e1
note that I will often avoid the use of
subscripts when using powerpoint for ease in
typing
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Transverse modulus

• What material properties can we calculate here?

E2s2/e2 or E22s2/e2
n21-e1/e2
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Reciprocity relationship

• n21n12E22/E11
• Is it better to calculate n21 using direct
  experimental measurement or using reciprocity
  relationsip?

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In-plane Shear Modulus G12
G12t12/g12
pure shear
Iosipescu shear test
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Examples of laminated composites

• Human intervertebral disc annulus fibrosus

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Tensile behavior of annulus fibrosus
Why is value of poissons ratio unusual?
Nonlinear elasticity and anisotropy are apparent!
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Shear behavior of annulus fibrosus

• Non-linear shear stress-strain behavior
• Strain-softening material

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Shear behavior of carbon-epoxy

• Carbon/epoxy AS4/3501-6 has similar
  strain-softening effect in shear

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Next steps

• Now that we have a general idea of composite
  material behavior, lets figure out how to
  calculate stresses, strains and strengths in them

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Micromechanics

• macromechanics
• The study of composite material behavior where
  material is assumed homogeneous
• Obtain aberage apparent properties of the
  material
• Micromechanics
• The study of composite material behavior where
  interactions of constituent material is examined
  in detail
• Emphasize heterogeneity

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Definitions

• Heterogeneous -- material properties vary from
  point to point
• Homogeneous -- material properties are the same
  everywhere
• Isotropic -- material properties are the same in
  every direction
• Anisotropic -- material properties depend on
  direction
• GE/2(1n)

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Homogenization

• Establish material properties from
  micromechanical considerations
• Homogenize and analyze macromechanically

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Representative volume element (RVE)