Background
Traditional laminate stiffness involves predicting and measuring four elastic constants: longitudinal stiffness (ExE_xEx), transverse stiffness (EyE_yEy), shear modulus (EsE_sEs), and Poisson’s ratio (νx\nu_xνx). While measuring ExE_xEx is straightforward, predicting and testing for EyE_yEy and EsE_sEs are challenging.
Our breakthrough
We discovered TRACE, a single parameter that simplifies stiffness representation. Trace, the sum of the diagonal components of the stiffness matrix, represents the total elastic stiffness capability of a composite ply. It’s easier to use, understand, and determine experimentally.
Benefits
- Simplified Stiffness Ranking: Composite materials can now be ranked by stiffness, much like metals (e.g., aluminum at 70 GPa, titanium at 110 GPa, and steel at 210 GPa).
- Universal Laminate Partitioning: Laminate stiffness ratios remain constant across materials. For example:
- For a [90/0] laminate:
- E1=E2=0.47×Trace
- E6=0.03×Trace
- These values are consistent for carbon, Kevlar, glass, and even flax composites.
- For a [90/0] laminate:
Material Comparisons Made Simple:
If Material A’s trace is 20% higher than Material B, all laminates of Material A are 20% stiffer than those of Material B.
Applications
- Streamlined Testing:
- Only ExE_xEx needs to be tested to determine trace. For carbon/epoxy composites, Trace=Ex/0.88
- Testing can be approximated using the rule-of-mixtures: Ex=Vf . Ef
- Effortless Deflection Calculations:
- Deflections in beams and tubes can be directly compared using relative trace values, with no recalculations needed.
- Broader Implications:
- Trace links directly to other composite constants, such as U2, making stiffness properties more accessible and comprehensible.