PSI - Issue 7

A. Rotella et al. / Procedia Structural Integrity 7 (2017) 513–520 Antonio Rotella et al. / Structural Integrity Procedia 00 (2017) 000–000

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notable impact on the fatigue limit of the A357-T6 cast Aluminum alloy and this parameter has a primary role with respect to the defect morphology. The artificial and natural defects of the same size have a similar impact on the fatigue limit. 3.4. Finite elements simulations In order to better understand the impact of the defect morphology on the stress / strain fields around a natural pore, 3D finite elements simulations have been performed using the real geometry of a natural cavity shrinkage. The real defect geometry of four pores has been reconstructed. The 3D shape has been obtained after a µ-CT scan of the gage section of two specimens that initiated a crack on natural defects. Because of the geometry of the specimen (gage section with a diameter of 10 mm and a height of 20 mm) the final average voxel size is of about 7 µm. The choice to simulate only cavity shrinkages is dictated by the difficulties that can be encountered during the reconstruction and meshing of the sponge shrinkages because of the very low size of each porosity that compose the global sponge shrinkage structure. The segmentation of the pores, from the Aluminum matrix and the consequent surface mesh have been performed using the imaging software Avizo. The defect has been inserted as a cavity into a cylinder with the same size of the gage section of the specimen. The 3D meshing have been performed using the software GMSH. The final 3D mesh is imported in Abaqus to perform the finite elements simulations. The defects that have been chosen to be simulated are subsurface defects, this choice permits to simplify the meshing process and, as reported by Serrano Munoz et al. (2017), the difference between the stress concentration factor (K t ) of a surface defect and a subsurface defect can be neglected (if the ligament between the defect and the specimen surface is thin enough). The elastic-plastic behavior of the Aluminum matrix has been identified from the results of cyclic-hardening tests performed on the reference alloy (grade < 1). The cyclic behavior of the material is essentially a non-linear kinematic hardening and it has been modeled using the proposition of Lemaitre et al. (2009). The average element size on the defect surface has been fixed to 9 µm (after a convergence analysis) and is gradually coarser until a maximal value of 1 mm at the specimen extremes. The numerical simulations have been conducted for 10 load cycles, for a frequency of 1 Hz and for a positive load ratio (R=0.1). The choice of a load frequency equal to 1 Hz is not representative of the fatigue test but the material behavior, which have been used to model the Aluminum matrix, does not contain viscoplastic effects, thus the frequency is not to be considered as a parameter that influences the results. The simulations are conducted using parallel computing (8 nodes and 32 processors) and each simulation lasts 150h. For this reason the number of cycles has been fixed to 10 cycles, in order to not increase the simulation time. Nevertheless the stress distribution in the highly stressed zones starts to stabilize around the eighth load cycle, thus, after 10 cycles it can be supposed that the cyclic stress evolution is into a stable state. In order to define the severity of a defect, an indicator (K t pl ) has been defined as the ratio between the maximal principal stress and the applied stress (far from the defect) considering the plastic effects. The results obtained on the real shrinkage geometry have been compared with two equivalent geometries: a sphere and an ellipsoid. The equivalent sphere has the same volume of the shrinkage, the ellipsoid is chosen in order to have the same inertial distribution of the shrinkage (same volume and orientation in the space). Figure 6 shows the results obtained for the 4 tested defects. The diagram correlates the factor K t pl with the T/D parameter that is the ratio between the defect size and the minimal distance from the free surface. Globally the defects, which are close to the free surface, have higher values of the K t pl parameter. The approximation of the defect morphology with an equivalent ellipsoid is better than the sphere. The average absolute difference is respectively of about 3% for the equivalent ellipsoid and of about 11% for the sphere.

% difference

(b)

(a)

pl in function of the ratio T/D for three defect geometries (real geometry, equivalent sphere and equivalent ellipsoid),

Fig. 6. Evolution of the factor K t (b) error analysis over the K t

pl factor for the equivalent geometries.