Trace theory applied to composite analysis: A comparison with micromechanical models

Abstract Composite materials design is a challenging topic, and its first step is the estimation of the macromechanical elastic properties. Usually, this analysis is carried out applying micromechanical models that use constituent properties as input. Alternatively, according to Tsai's trace theory, the trace of stiffness matrix is invariant. In other words, it is independent of fibers and matrices used, as well as their volume fractions. The main advantage of trace-based approach is that the properties can be normalized by trace and only one test is required to compute all elastic properties, resulting in considerable saving of cost and time. On the other hand, the original proposal is limited to in-plane properties of carbon fiber laminates. In the present study, the trace-based methodology is compared with a set of 138 experimental data compiled from the literature for carbon fiber reinforced polymers (CFRP) and glass fiber reinforced polymers (GFRP). An extension of trace theory is proposed to compute the out-of-plane shear modulus. Trace theory is compared with 10 micromechanical models establishing a comparative discussion. Results show that average error of Tsai's trace approach is smaller than 20% for all the properties for both fiber types. Especially for the in-plane Poisson's ratio, trace-based estimation results in a smaller error than all other micromechanical models. The main goal of this paper is to compare Tsai's trace approach with classical micromechanical models. Although other models are useful in some cases, Tsai's trace approach is advantageous due to a considerable reduction of the design cost and time.