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In the paper, we present an integrated data-driven modeling framework based on process modeling, material homogenization, mechanistic machine learning, and concurrent multiscale simulation. We are interested in the injection-molded short fiber reinforced composites, which have been identified as key material systems in automotive, aerospace, and electronics industries. The molding process induces spatially varying microstructures across various length scales, while the resulting strongly anisotropic and nonlinear material properties are still challenging to be captured by conventional modeling approaches. To prepare the linear elastic training data for our machine learning tasks, Representative Volume Elements (RVE) with different fiber orientations and volume fractions are generated through stochastic reconstruction. More importantly, we utilize the recently proposed Deep Material Network (DMN) to learn the hidden microscale morphologies from data. With essential physics embedded in its building blocks, this data-driven material model can be extrapolated to predict nonlinear material behaviors efficiently and accurately. Through the transfer learning of DMN, we create a unified process-guided material database that covers a full range of geometric descriptors for short fiber reinforced composites. Finally, this unified DMN database is implemented and coupled with macroscale finite element model to enable concurrent multiscale simulations. From our perspective, the proposed framework is also promising in many other emergent multiscale engineering systems, such as additive manufacturing and compressive molding.