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There are several possible mechanisms of failure of glassy polymers that can be activated by different states of stress in the material. They are reflected in the various failure criteria used to predict initiation of damage in the polymer based on the components of stress tensor. We investigated the applicability of several popular failure criteria (the von Mises, the Drucker-Prager, the parabolic stress, and the dilatational strain energy density) to predict processing-induced damage due to cooling after curing observed in 3D woven composites with high level of through-thickness reinforcement. We developed high-fidelity mesoscale finite element models of orthogonally reinforced carbon/epoxy composites and predicted their response to the uniform temperature drop from the curing to room temperature. Comparison of the simulation results with the X-ray computed microtomography indicates that matrix failure caused by the difference in thermal expansion coefficients of carbon fiber and epoxy resin is well predicted by the dilatational strain energy criterion. Initiation and propagation of this failure was numerically investigated using sequential deactivation of elements exceeding the allowable equivalent stress.