Second Order Defeaturing Error Estimator of Porosity on Structural Elastic Performance in Manufactured Metallic Components

Manufactured metallic components often contain non-uniformly distributed pores of complex morphologies. Since such porosity defects have significant influence on material behaviors and affect the usage in high-performance applications, it is significant to understand the impact of porosity characteristics on the behaviors of components. In this work, a gradient-enhanced porosity defeaturing estimator, which allows for the modeling of pore geometry and spatial distribution, is proposed within a general elastostatic framework. In this approach, the first order shape sensitivity is implemented to account for the change in elastic quantity of interests with respect to variations of pore sizes and shapes, which is then supplemented by a second order shape sensitivity whose mixed partial derivative quantifies the interactions between pores in proximity. The efficacy of the proposed method comes from its posterior manner that it only relies on field solutions of reference models where pores are suppressed. In this context, meshing difficulty and solution convergence issue are avoided, which would otherwise arise in a direct finite element analysis on porous structures. The impact of porosity on structural elastic performance is approximated using a second order Taylor expansion where the topological difference between the porous and reference domains is estimated by topological sensitivity; the field variables on pore boundaries are approximated as explicit functions of design variables using exterior formulations. Numerical results show that the elastic performances of components are influenced by the existence of pores. The pore-to-pore interactions are significant when pores are close by.