### 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: E_{x}= E_{y} = E_{θ. }Quantitatively this can be described using a *general **rule **for a **quasi-isotropic** layup. Simply **apply the following equation** that defines the angle between the plies for a symmetric laminate having an identical number of plies at each orientation**:*

**Equation: π/n → n≥3**

In its simplest form, an engineer could design a tri-directional laminate having only 3-plies [e.g., 0/±60] to achieve a quasi-isotropic laminate. Note however, 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 quasi-isotropic laminate stacking sequences 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 practiced all too often in the industry is the formulation of a laminate design that stacks a negative 45-degree ply adjacent to a positive 45-degree ply…what’s wrong with that picture? Clearly, the angle formed between the two 45-degree plies equals 90-degrees, ostensibly a clear violation of the general rule. More troubling is when laminate designs are considered superior to all others because they provide properties similar to metals…in other words, the all too familiar “Black Aluminum” designs. Yet, quasi-isotropy should be considered a baseline design not the final design. Huh? Yes…I know it’s counterintuitive and atypical given industry trends. Nevertheless, it’s a reasonable guideline given the anisotropic advantages inherent with composites. From the Handbook of Composites by S.T. Peters an excerpt that draws attention to this consideration reads as follows:

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 midplane, balanced (equal quantity of-θand+θplies), 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.

Finally, what would a discussion about composites be if it did not include my favorite topic the ABD matrix. If you are concerned whether or not you have a quasi-isotropic laminate, simply refer to the A-terms that characterize the extensional stiffnesses. Each of the A-terms must satisfy the following conditions:

A_{11}=A_{22}, A_{16}=A_{26}=0 and A_{66} = (A_{11}-A_{12})/2

What’s convenient here is that a designer can quickly ascertain if in fact the laminate is compliant by simply examining the ABD matrix…a procedure that can be performed prior to any analysis. To illustrate, an example showing the A-matrix that satisfies the criteria above is shown below.

As a reminder, the isotropy in these laminates only applies in-plane; that is why the laminate is described as a “quasi” laminate. The term “quasi” refers to the fact that both the B and D terms generally do not behave like an isotropic material. In closing, consider quasi-isotropy as a baseline design during preliminary development. Carefully weigh the options before committing to a less than optimal design (Black Aluminum that is...). Start by considering the advantages of anisotropic laminates that provide superior performance along with optimal (and in some cases significant) strength/weight and stiffness/weight ratios. As always, I have briefly touch on the topic of quasi-isotropy by covering the salient subject matter. Therefore, your comments are always welcome.