Statistical Characterization of Viscoelastic Modulus using a Spectrum Function Approach

Previous experiments have shown a high degree of variation in viscoelastic creep strain measurements of polymer matrix composites (PMCs). Engineering design involving material properties of PMCs should be performed with this variability in consideration. Therefore, this paper presents an approach to characterize the longitudinal relaxation modulus of a vinyl ester polymer (DERAKANE 441-400) with variations in its material properties. A spectrum approach is used to describe viscoelastic material functions; a distribution function with two parameters is selected. Short-term tensile creep experiments were conducted at four temperatures below the glass transition temperature. In-plane longitudinal and transverse strain-time histories were measured using a digital image correlation technique. The variation in the relaxation modulus was described by formulating the probability density functions (PDFs) and the corresponding cumulative distribution functions (CDFs) of the moduli using a two- parameter Weibull distribution. Both Weibull shape (γ) and scale (β) parameters of the relaxation moduli distributions were shown to be time and temperature dependent. Two-dimensional quadratic Lagrange interpolation functions were used to characterize the Weibull parameters to obtain the PDFs and subsequently the CDFs of the creep compliances for the complete design temperature range (24°C ≤ T ≤ 60°C) during steady state creep (t ≥ 1000 s). At each test temperature, relaxation modulus curves were obtained for constant CDF values and compared with the experimental data. The predicted relaxation moduli of a vinyl ester polymer in the design space are in good agreement with the experimental data.