Computational solid mechanics has become an indispensable approach in engineering, and numerical investigation of fracturing in composites is essential, as composites are widely used in structural applications. Crack evolution in composites is the path to elucidating the relationship between microstructures and fracture performance, but crack-based finite-element methods are computationally expensive and time-consuming, which limits their application in computation-intensive scenarios. Consequently, this study proposes a deep learning framework called Crack-Net for instant prediction of the dynamic crack growth process, as well as its strain-stress curve. Specifically, Crack-Net introduces an implicit constraint technique, which incorporates the relationship between crack evolution and stress response into the network architecture. This technique substantially reduces data requirements while improving predictive accuracy. The transfer learning technique enables Crack-Net to handle composite materials with reinforcements of different strengths. Trained on high-accuracy fracture development datasets from phase field simulations, the proposed framework is capable of tackling intricate scenarios, involving materials with diverse interfaces, varying initial conditions, and the intricate elastoplastic fracture process. The proposed Crack-Net holds great promise for practical applications in engineering and materials science, in which accurate and efficient fracture prediction is crucial for optimizing material performance and microstructural design.