Properties for Design of Composite Structures. Neil McCartney

in the x₃-direction. When the plate is uniaxially loaded in the x₂-direction, the parameter νt is the Poisson’s ratio determining the transverse through-thickness deformation in the x₃-direction.

      It is useful, first, to show the form of the stress-strain equations (2.196) when the material is transverse isotropic about the x₃-axis, so that they may be used when considering the properties of unidirectional plies in a laminate where the fibres are aligned in the x₃-direction of the ply, and so that use can be made of analysis given in the previous section. It follows from (2.196) that when the material is transverse isotropic about the x₃-axis, the stress-strain relations are of the form

(2.197)

      As S11=1/υT, S12=−νt/υT and S66=1/μt it follows from (2.189) that for a transverse isotropic solid the following condition must be satisfied:

(2.198)

      In Chapter 4 considering fibre-reinforced materials, stress-strain relations are required for the cylindrical polar coordinates (r,θ,z) corresponding to the relations (2.197), which are given by

      (2.199)

      When the fibres are aligned in a direction parallel to the x₁-axis, as required in Chapters 6 and 7 concerning laminates and their plies, the transverse isotropic stress-strain relations, resulting from the orthotropic form (2.196), are given by

(2.200)

      where, again, the relation (2.198) must be satisfied.

      For plane strain conditions such that ε11≡0, it follows from (2.200) that

      (2.201)

      When ΔT=0, the term ε22+ε33 is the change in volume per unit volume ΔV/V for the plane strain conditions under discussion when an equiaxial transverse stress σ is applied such that σ2=σ3=σ. It then follows that a plane strain bulk modulus kT can be defined by

      

Скачать книгу