| Abstract Scope |
This work introduces a 3D Fatigue State Matrix (3D-FSM) for multi-scale fatigue life prediction in metal additive manufacturing (AM), integrating residual stress, microstructure, and process-induced anomalies in a unified active block matrix tensor framework. Surpassing Goodman-based and crystal-plasticity models, the 3D-FSM provides spatially resolved, multi-scale fatigue life mapping with mechanism-specific attribution of fatigue degradation. Each 3D-FSM element stores a 2D state matrix combining: (i) deterministic fields (e.g., residual stress) from elastoplastic simulations, (ii) nonlocal interaction (e.g., stress redistribution) through active element communication via a pseudodifferential operator (ΨDO), (iii) stochastic anomaly weighting, and (iv) a neural-network-based microstructure-dependent term capturing grain orientation and size effects. Weighted damage contributions quantitatively decompose fatigue life, identifying dominant mechanisms such as residual tensile stress, defect clusters, or microstructural weaknesses. The 3D-FSM, formally a rank-5 tensor with active element interaction, combines multi-scale physics to generate interpretable fatigue life maps, supporting digital twin applications in fatigue-critical AM components. |