PSI - Issue 2_A

M. Wicke et al. / Procedia Structural Integrity 2 (2016) 2643–2649 M. Wicke et al./ / Structural Integrity Procedia 00 (2016) 000–000

2647

5

Similar results were achieved for the first shrinkage pore. The maximum absolute deviation was 4.8 μm, ensuring the accurate conversion of the defect geometries into 3D volumetric models. Both pores were subsequently imported into a finite element model to identify regions of elevated stress on their contour in dependency of the load direction. 3.3. Stress concentration at casting pores Finite element analysis (FEA) was conducted with the commercial software ABAQUS 6.14 (Dassault Systèmes Simulia Corp.). While the morphology of the pores was accurately reconstructed, a homogeneous matrix with a linear elastic material behavior (i.e. modulus of elasticity: 70 GPa and Poisson’s ratio: 0.3) was used. After inserting the pore as a cavity in an FE model of a cylindrical volume representing the matrix material, a uniaxial displacement was imposed to the upper surface of the cylinder to simulate a quasi-static tensile test. The element type used for meshing was the eight-node quadratical tetrahedral element (C3D10) of the ABAQUS code. In order to correctly evaluate the local stress concentration, the region close to the pore was modelled with a refined mesh. The surface topology was first modified using virtual topology operations because of the quadrangular patches on the pore surface, which result out of the generation of the 3D volumetric models and may hinder the mesh generator creating an appropriate mesh. It is worth noting that the geometry is left undisturbed by this clean-up operation. In dependency of the size and tortuosity of the pore, the overall number of finite elements was 2.5 x 10 5 and 4 x 10 5 respectively. A typical pore surface mesh is shown in Fig. 5a. Three rotation angles ߶ , ߰ and ߯ around the ݔ -, ݕ - and ݖ -axis of the coordinate system centered in the pore center of gravity were defined as shown exemplarily in Fig 5a for the first shrinkage pore and each pore was rotated simultaneously around these axes from 0° to 360° in steps of 45°. A new FE model was thus generated for each configuration to be solved for the identification of critical regions in terms of local stress concentration. Fig 5b shows the computed stress distribution, which is mapped on the internal pore surface, and the peak von Mises value for the first shrinkage pore in the initial orientation.

Fig. 5. (a) Rotational angles around coordinate axes (z-axis parallel to loading direction) and (b) stress distribution on surface of a pore

These repeated analyses cover only few possible orientations of a pore with respect to the load direction. Nevertheless, they provide a relevant indication of local stress concentration and thus allow the identification of regions of elevated stress on the contour of each pore. Special emphasis is therefore put on an appropriate visualization of the simulation results in order to readily identify such hot spots. The approach developed here is based on an orphan mesh part of the pore analyzed with the same alignment as the initial orientation. After retransforming the coordinates of the integration point with the peak von Mises stress according to the previous rotation, an additional node was created on the orphan mesh part representing one of the 512 orientations investigated. Nodes within a certain region were collected in a node set and annotated, providing an exhaustive overview of the highly stressed regions as shown