Existence of undulating fill and warp yarns in woven composite laminae introduce complex unit cell geometries and multi-scale interactions among the constituents. This coupled with high-strain-rate dynamic out of plane loading (such as blast or impact) induce damage to the lamina involving several micro and meso-scale complex failure modes that are challenging to model via conventional macro-scale damage models. Presented here is a semi-multi-scale approach viz. the microplane triad model, which can predict both the elastic and fracturing behavior of woven composite laminae, given the mesoscale constituent properties and the weave architecture. The model builds on the concept of microplane triads, which are imagined planes in sets of three, placed tangential to the yarn paths within the lamina microstructure. The various damage mechanisms are formulated in terms of stress-strain vectors on these microplane triads. Strain rate dependent phenomenon such as matrix viscoelasticity, and rate dependent damage evolution are incorporated within the formulation. The model is calibrated and validated with constituent and lamina level test data, and then used to predict the projectile impact behavior of twill woven lamina. Twenty-five different projectile impact velocity cases are considered, and the predicted residual velocities of the impactor are compared with corresponding experimental values. The model is demonstrated to predict very well the residual impactor velocities, as well as the failure modes of the lamina, its ballistic limit and deformation cone wave propagation speeds. Via sensitivity studies using the model, it is revealed that the fracture energy of the lamina is a crucial model input, necessary for accurate predictions of impact/blast loads. Future work involves application of the model to multi-layer laminates, enabling delamination analysis, which is a major mode of failure for stacked composites under out of plane impact.