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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 that follows the 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:  π/n → n≥3

Using an n value (defined as the number of lamina) equal to 3, an engineer could design a tri-directional laminate with orientations of  [0/±60] only and remain compliant with the quasi-isotropic definition. Note...the angle between each ply must remain equal to or less than 60-degrees, a key condition to achieve quasi-isotropy. Below are some possible π/4 quasi-isotropic laminates that satisfy the general rule:

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

A mistake I see all too often in industry is the development of a laminate stacking sequence that places a negative 45-degree ply adjacent to a positive 45-degree ply…what's wrong with that picture!? Clearly, the total angle between the 45-degree plies equals 90-degrees...a clear violation of the general rule. Even more troubling is when a laminate design with a quasi-isotropic layup is considered superior to all others simply because it behaves similar to an isotropic material…in other words, the all too familiar "Black Aluminum" designs. Yet, quasi-isotropy should be considered as a baseline design, not the final design. Huh? Yes…I know it's counterintuitive given industry perception; nevertheless, it's a reasonable guideline given the anisotropic advantages inherent with composites. To put it another way, one should contemplate the following passage: 

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 a discussion about composites be if it did not include my favorite topic the ABD matrix. If you want to quickly ascertain whether or not you have a quasi-isotropic laminate, simply refer to the A-terms in the ABD matrix and apply the following definitions: 

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

As a reminder, the isotropy in these laminates only applies to 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. Consider quasi-isotropy as a baseline design only-not a final design! Carefully weigh the other composite options before committing to quasi-isotropic design; such as, balanced and symmetric anisotropic laminate designs that provide both superior structural performance and optimal strength-to-weight and stiffness-to-weight ratios.  


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