# 6.9: Out--of-plane Stresses and Symmetric Laminates

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So far we have only considered in-plane stresses within a given ply and within the laminate, but when plies are bonded together there are also through-thickness (or coupling) stresses, which are difficult to quantify, between the plies. These arise from the differences in the Poisson contractions of each individual ply and can lead to microstructural damage and distortions of the laminate.

Consider the simple case of a uniaxially loaded cross-ply laminate, shown in the animations below.

The strains of the two plies parallel to the loading direction are equal, but the Poisson contraction, ν12 , for the parallel ply is greater than that for the transverse ply, ν21 (See page on Off-axis loading ). The result of this is that there are coupling stresses that try to deform the flat laminate into the shape shown in animation iii). Extending this to a random stacking sequence, it is clear that the Poisson ratio for a single ply will vary with the fibre direction (See model in Stiffness page) and therefore, coupling stresses are present in a laminate if the plies have different constituents or if the laminae are not aligned.

## Symmetric laminates

If the laminate has a mirror plane in the laminar plane, i.e. the laminate is symmetric, the coupling forces cancel out and the distortions are significantly reduced, even though local coupling stresses still exist.

For these reasons balanced symmetric stacking sequences are preferred, but this might not always be possible when performance requirements are taken into account.