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Quasi-Isotropy…wait…what is that?

What is it you ask…well, this is one of my favorite meals. A large quasi-isotropy with a side of fries and coke. LOL…but of course is isn't…actually, this is a laminate, that when constructed correctly, emulates a metallic material having an isotropic relationship defined as: Ex= Ey = Eθ

A general rule for describing a quasi-isotropic layup is to apply the following equation that defines the angle between the plies for a symmetric laminate having an identical number of plies at each orientation using the following ratio:  π/n → n≥3

By using an n value (defined as the number of lamina) equal to 3, an engineer could design a tridirectional laminate with orientations of  [0/±60] only while complying with the quasi-isotropic definition. Note...the angle between each ply must be equal to or less than 60-degrees: a key condition to achieve quasi-isotropy. Quasi-isotropic laminates below that satisfy the general rule:

[0/±45/90]s or [0/+45/0/-45/90]s or [0/±30/±60/90]s  

An oversight that I see all too often during the development of a laminate stacking sequence (using tape), is the placement of a negative 45-degree ply adjacent to a positive 45-degree ply ahh, what's wrong with that picture!? Crucially, the total angle between the 45-degree plies equals 90-degrees...a clear violation of the general rule stated above. Even more troubling is when a quasi-isotropic layup is considered "superior" to all others because it acts like an isotropic material…you know the "Black Aluminum" design. Yet, quasi-isotropy should be considered as a baseline design, not a final design. Huh? Yes…I know it's counterintuitive, given industry perception. Nevertheless, it's a reasonable expectation given the anisotropic advantages inherent with composites. One should contemplate the following passage before accepting a quasi-isotropic layup:

Quasi-isotropic laminates have been used because they give properties like those of metals, and predictable responses that are familiar, although they are not optimal in strength-to-weight or stiffness-to-weight ratios. Many laminates used today on aircraft structures tend to be of this type. In general, however, the more directional the loading, the bigger the payoff possible with anisotropic tailoring.

To improve on the performance obtained with a quasi-isotropic laminate, the cost to design and analyze the anisotropic part is unfortunately often thought not to be worth the additional weight savings. This attitude is commonly rationalized by worry about holes, increase in work associated with more complicated fiber placement (preform assembly), etc. In practice, laminate designs, if not quasi isotropic, are certainly still symmetric about the mid-plane, balanced (equal quantity of -θ and +θ plies), and orthotropic. [Unfortunately] capitalizing on the benefits of anisotropy will probably occur in other industries first before being adopted by the more conservative aircraft industry.

by Handbook of Composites by S.T. Peters

Finally, what would this discussion be if I did not include my favorite topic...the ABD matrix. If you want to quickly determine whether or not you have a quasi-isotropic laminate, simply refer to the A-terms in the laminates ABD matrix and apply the following definitions: 

  A11=A22, A16=A26=0 and A66 = (A11-A12)/2

Remember, the "isotropy" for these laminates only applies to the in-plane behavior...hence the term "quasi". Specifically, the prefix "quasi" emphasizes the fact that both the B and D terms generally do not behave like an isotropic material. So, consider quasi-isotropy as a baseline only...not a final design! Carefully weigh other anisotropic options before committing to a quasi-isotropic design. For instance, balanced and symmetric anisotropic laminate designs that provide both superior structural performance and optimal strength-to-weight and stiffness-to-weight ratios.  

Content Updated: 2/26/19 - Grammatical Changes

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