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Homogenization theories for periodic microstructures are introduced to investigate the crack initiation and propagation behaviours of the TP-650 titanium matrix composites. By adopting homogenization theories for periodical microstructures, the macroscopic material parameters are identified by solving the microscopic equations. A new fixed point iteration method for multi-particle unit cell’s boundary conditions of the microstructures is presented. The real displacement constrained conditions are obtained and applied to the multi-particle unit cell with this method. Finite element (FE) models containing some microstructure characteristics of the TP-650 composite are established and their fracture behaviors of the composites under tensile loading are simulated.