Estimation of Elastic Behavior of Cast Metal Components Containing Process Induced Porosity

Significant progress has been made for assessing the influence of porosity on the performance metrics for cast components through various modeling techniques. However, a computationally efficient framework to account for porosity with various shapes and sizes is still lacking. The main contribution of this work is to address this limitation. Specifically, a novel porosity sensitivity method is proposed, which integrates the merits of topological sensitivity and shape sensitivity. While topological sensitivity approximates the first order change on the quantity of interest when an infinitesimally small spherical pore is inserted into a dense (no pore) structure, shape sensitivity estimates the subsequent change in the quantity when the small pore boundary is continuously perturbed to resemble the geometry reconstructed from tomography characterization data. In this method, an exterior problem is solved to explicitly formulate pore stress and strain fields as functions of shape scaling parameters. By neglecting higher order pore-to-pore interaction terms, the influence of multiple pores can be estimated through a linear approximation. The proposed method is first studied on a benchmark example to establish the impact of different pore parameters on the estimation accuracy. The method is then applied onto case studies where the pore geometry is either from tomography reconstruction or computer-generated representations. Efficiency and accuracy of the method are finally demonstrated using a commercial 3D application. The proposed method can be extended to other manufacturing (e.g., additive manufacturing) induced porosity problems.