Rate-dependent constitutive equations for carbon fiber-reinforced epoxy

A rate‐dependent constitutive model for carbon fiber‐reinforced polymers was developed by assuming that the rate‐dependent characteristics of the composite could be described by stress relaxation of the polymer matrix. Relaxation functions in longitudinal, transverse, and in‐plane shear modes were derived in terms of separate matrix and fiber properties and the rules of mixture. The epoxy was represented as two Maxwell elements in parallel with a linear elastic spring, while the carbon was modeled as a linear elastic spring. The rate‐dependent, laminate stiffness matrix for a unidirectional IM6G/3501–6 carbon/epoxy laminate was found by fitting the rate‐dependent constitutive equations to material test data at constant strain rates ranging from 0.01 to 2,500 s−1. The transient deformation response of a [(08/908)2/08]s IM6G/3501–6 carbon/epoxy composite laminate under dynamic in‐plane loading could be predicted within 5% of experimental data using this laminate stiffness matrix. The rate‐dependent constitutive equations were also incorporated into LS‐DYNA3D via a user‐defined material subroutine and used to predict the transient response of a 32 ply AS4/3501–6 carbon/epoxy laminate under projectile loading. The maximum contact force between the projectile and laminate was found to be 7% higher than the experimental data. POLYM. COMPOS. 27:513–528, 2006. © 2006 Society of Plastics Engineers.