Residual Strength and Fatigue Lifetime of ... - Solid Mechanics
Residual Strength and Fatigue Lifetime of ... - Solid Mechanics Residual Strength and Fatigue Lifetime of ... - Solid Mechanics
of contact elements (CONTACT173 and TARGET170), and displacement controlled geometrical non-linear analysis was conducted. To simulate the boundary conditions in the experimental setup, nodes on the top side of the columns, in contact with the top ending plate of the test rig, were displaced uniformly in the direction of loading. Furthermore, the nodes in contact with the lateral clamp surfaces were constrained to have zero lateral displacement. Symmetry boundary conditions were applied to the symmetry plane. Hence, displacements of the nodes on the symmetry plane were assumed to be zero in the loading direction, see Figure 2.16. Due to the need of a high mesh density at the crack front when performing the fracture mechanics analysis, a submodelling technique was developed, where displacements calculated on the cut boundaries of the global model with a coarse mesh were specified as boundary conditions for the submodel. Submodelling is based on St. Venant's principle, which states that if an actual distribution of forces is replaced by a statically equivalent system, the distributions of stresses and strains are altered only near the regions of load application. The approach assumes that the stress concentration around the crack tip is highly localised; therefore, if the boundaries of the submodel are sufficiently far away from the crack tip, reasonably accurate results may be obtained in the submodel. Interpolated displacement results at the cut boundaries in the global model were used as boundary conditions in the submodel at different load steps. A 20-node isoparametric element (solid 95) was used in the finite element model. The finite element model and submodel are shown in Figure 2.17. In the global model and the submodel, the size of the elements along the crack flanks near the crack tip is 0.2 and 0.01 mm, respectively. The energy release rate and the mode-mixity are determined on the basis of relative nodal pair displacements along the crack flanks obtained from the finite element analysis and the CSDE method as explained in the introduction. Figure 2.16: Applied boundary conditions in the finite element model of the columns. 30
Figure 2.17: Finite element models. (a) Half-model showing the mesh in the global model. The smallest element size is 0.2 mm. (b) Submodel showing the refined mesh. The element size close to the crack tip is 10 m. 2.6 Comparison of Numerical and Experimental Results Results from the experimental testing and numerical modelling presented above are compared. The focus is divided into three parts: The effect of imperfections on the instability behaviour, the through-width variation of energy release rate and mode-mixity and, finally, the influence of imperfections on the debond propagation. In order to examine the effect of initial imperfection on the instability behaviour of the specimens, columns with initial imperfection amplitudes of 0.1, 0.2 and 0.4 mm were analysed numerically and compared with test results. The columns tested had in average an imperfection magnitude of 0.2 mm. Figure 2.18 shows the deformed shape of a debonded sandwich column with H100 core containing a 50.8 mm face/core debond and 0.2 mm initial imperfection amplitude. The imperfection resembles a half-sine wave with the maximum deflection at the centre, consistent with DIC measurements described above. Figure 2.19 shows load vs. out-of-plane deflection for columns with H100 core and 25.4, 38.1 and 50.8 mm debonds determined from numerical analysis at imperfection amplitudes of 0.1, 0.2 and 0.4 mm and testing (two or three replicates are shown). The numerical and the test results show that 31 (a) (b)
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<strong>of</strong> contact elements (CONTACT173 <strong>and</strong> TARGET170), <strong>and</strong> displacement controlled<br />
geometrical non-linear analysis was conducted. To simulate the boundary conditions in the<br />
experimental setup, nodes on the top side <strong>of</strong> the columns, in contact with the top ending plate <strong>of</strong><br />
the test rig, were displaced uniformly in the direction <strong>of</strong> loading. Furthermore, the nodes in<br />
contact with the lateral clamp surfaces were constrained to have zero lateral displacement.<br />
Symmetry boundary conditions were applied to the symmetry plane. Hence, displacements <strong>of</strong> the<br />
nodes on the symmetry plane were assumed to be zero in the loading direction, see Figure 2.16.<br />
Due to the need <strong>of</strong> a high mesh density at the crack front when performing the fracture<br />
mechanics analysis, a submodelling technique was developed, where displacements calculated<br />
on the cut boundaries <strong>of</strong> the global model with a coarse mesh were specified as boundary<br />
conditions for the submodel. Submodelling is based on St. Venant's principle, which states that if<br />
an actual distribution <strong>of</strong> forces is replaced by a statically equivalent system, the distributions <strong>of</strong><br />
stresses <strong>and</strong> strains are altered only near the regions <strong>of</strong> load application. The approach assumes<br />
that the stress concentration around the crack tip is highly localised; therefore, if the boundaries<br />
<strong>of</strong> the submodel are sufficiently far away from the crack tip, reasonably accurate results may be<br />
obtained in the submodel. Interpolated displacement results at the cut boundaries in the global<br />
model were used as boundary conditions in the submodel at different load steps. A 20-node<br />
isoparametric element (solid 95) was used in the finite element model. The finite element model<br />
<strong>and</strong> submodel are shown in Figure 2.17. In the global model <strong>and</strong> the submodel, the size <strong>of</strong> the<br />
elements along the crack flanks near the crack tip is 0.2 <strong>and</strong> 0.01 mm, respectively. The energy<br />
release rate <strong>and</strong> the mode-mixity are determined on the basis <strong>of</strong> relative nodal pair displacements<br />
along the crack flanks obtained from the finite element analysis <strong>and</strong> the CSDE method as<br />
explained in the introduction.<br />
Figure 2.16: Applied boundary conditions in the finite element model <strong>of</strong> the columns.<br />
30