ICF100954OR DAMAGE EVOLUTION AND FRACTURE OF VISCOELASTIC COMPOSITES UNDER TIME-VARYING LOADS J. Varna 1 , A. Krasnikovs 2 and R. Talreja 3 1 Lule University of Technology, Lule, Sweden 2 Riga Technical University, Riga, Latvia 3 Georgia Institute of Technology, Atlanta, GA 30332-0150, USA 1. Introduction and Problem formulation Symmetric [0 n , 90 m ] s cross-ply laminate with transverse cracks in 90-layers is shown in Fig. 1. Layers in the (x,y,z) -system are homogeneous, orthotropic and linearly viscoelastic with constitutive relations given by, ( ) τ τ ε τ σ d d d t E t t i i i ∫ − = 0 ) ( (1) where the superscript i =0, 90 designate the layer and ε i , σ i and E i denote the strain, stress and stiffness tensors, respectively. In general, stresses and strains are functions of the position ξ characterized by dimensionless coordinates and . In the following, stress, strain and stiffness symbols without the superscript stand for averages over the entire laminate. Lower index, if given, specifies the component under consideration. For simplicity residual thermal stresses are not included in analysis. It is also assumed that all stresses arising during the formation of cracks have relaxed and the laminate before the displacement application is stress free. d x / d z / Plane stress formulation is used and the only applied loading is time dependent displacement in x-direction, see Fig.1, u . l t t x x 0 ) ( ) ( ε = l u o x x ε = 0° 90° b lo d z x Fig. 1 Schematic showing the cross ply-laminate with cracks in the 90-layers. For the assumed constant spacing of cracks the solution must satisfy: 1. Stress equilibrium equations 0 = ∂ ∂ xl i kl σ (2) 2. Strain-displacement relationships 1