Properties for Design of Composite Structures. Neil McCartney
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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
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:
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
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
where, again, the relation (2.198) must be satisfied.
For plane strain conditions such that ε11≡0, it follows from (2.200) that
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