Structural design against brittle fracture: Optimizing energy release rate and experiment

Despite substantial advancements in optimizing structural designs for stiffness, the field of design against fracture is still in its early stages. This paper introduces a fundamental and standardized paradigm for structural design against brittle fracture, achieved through the minimization of the energy release rate G within the framework of linear elastic fracture mechanics (LEFM). By leveraging the Griffith criterion expression and the total potential energy in LEFM, we propose an efficient approach for structural optimization that enhances the toughness of architected materials. The energy release rate G is evaluated a synergistic application of finite element analysis and finite difference methods, yielding a precision of 0.6% compared to benchmarks in published handbooks. We demonstrate significantly reduced G values compared to standard stiffness and stress-oriented topology optimization, which directly contributes to increased toughness. To comprehensively analyze the fracture process encompassing damage, crack initiation, propagation, and failure, we employ post-processing phase field fracture modeling on the optimally designed architected materials. By performing multi-objective optimization of the stiffness and energy release rate G, the toughness and extreme load-bearing capacity can be simultaneously improved. The resulting perforated architecture effectively outperforms homogeneous structures in both toughness and peak load. Additionally, we extend our analysis to various configurations, such as non-center cracks, pure shear loading, and adherence to the standard 3D compact tension ASTM E-399-72. The designed structures are additively manufactured and experimentally validated, demonstrating a toughness increase of over 10 times compared to stress-based design. These contributions offer promising prospects for advancing the design of future engineering structures and materials with a favorable balance of critical fracture resistance characteristics.