Parameterization of arbitrary hole shapes using non-destructive testing and resulting stress concentration in a 2D plate with finite dimensions
Air void inclusions are mostly unavoidable in many different materials resulting from manufacturing processes or environmental conditions. In this contribution, non-destructive testing (NDT) like computer tomography (CT) is used for air void detection and quantification. The air voids lead to stress concentrations around them which influence significantly the structural integrity and at worst, lead to structural failure. By nature, air voids exhibit arbitrary shapes on which circular, elliptical, slotted and rounded rectangular holes are fitted by a least-square optimization algorithm to reduce the amount of necessary shape parameters. The mentioned shapes are compared in relation to the arbitrary one and with regard to the resulting stress concentration factor as well as the location of the maximum first principal stress in a 2D plate with finite dimensions under uniaxial tension. Finally, aleatory and epistemic uncertainties are derived from the conducted CT analysis which leads to a problem under polymorphic uncertainties. The problem is solved by a surrogate model based on cubic spline interpolation and points out the importance of the consideration of different hole shapes for analyzing the stress concentration.