Validating a micromechanical modelling scheme for predicting the five independent viscoelastic constants of unidirectional carbon fibre composites

Abstract

In this paper we experimentally validate a new micromechanical modelling scheme for predicting the five independent viscoelastic constants of a unidirectional carbon fibre epoxy resin composite. This study has built on a number of previous papers by these authors, where extensive finite element calculations were used to validate a much more easily implemented, classical analytical micromechanical approach for predicting the viscoelastic properties of composite materials. For formulating the viscoelastic predictions, the elastic-viscoelastic correspondence principle is used to convert the static elastic solutions to their complex steady state viscoelastic forms simply by replacing static elastic moduli of the matrix and the fibers by their complex viscoelastic moduli.To formulate accurate micromechanical predictions for comparison and validation by experimental measurements, appropriate values for the five independent elastic constants of the reinforcing carbon fibres in the experimental materials are required. To obtain them, we have used the ultrasonic immersion method (UIM) and an inverse modelling scheme as previously described by Smith. The UIM allows the full stiffness tensor to be determined for both the carbon fibre composite and the epoxy resin matrix at a frequency of 2.25 MHz. The validated Hashin–Rosen composite cylinders micromechanical model was then used to determine the best fit elastic constants of the carbon fibres. Once these were determined, the ‘viscoelastic properties’ of both the pure epoxy matrix and the carbon fibre composite were studied using low frequency measurements (1 Hz). The results showed that for the two viscoelastic constants that can be routinely measured experimentally, namely the in-plane longitudinal and transverse Young's moduli, these are very well predicted by the same micromechanical model. Most importantly, following this validation, the micromechanical model can then easily provide all of the five independent viscoelastic composite stiffness constants. These values are critical for accurate vibration damping and noise cutting design of advanced engineering composite parts exposed to oscillatory loading such as aircraft wings and tails or wind turbine blades.