PSI - Issue 28

Paul Seibert et al. / Procedia Structural Integrity 28 (2020) 2099–2103 Seibert et al. / Structural Integrity Procedia 00 (2020) 000–000

2101

3

3. Experimental Data Reported in the Literature

Ahmed and Susmel [2] recently reported an experimental campaign with failure results for notched FDM-produced PLA specimens together with the corresponding TCD predictions. The filaments were deposited in a woven orthog onal structure at a certain angle to the specimen orientation, θ p . Di ff erent θ p led to di ff erent tensile strengths σ UTS , Young’s moduli E and fracture thoughnesses K Ic , which were determined from separate experiments. Note that the definition of the printing angle is slightly di ff erent as θ p = 0 ◦ denotes diagonal fiber loading and θ p = 45 ◦ is parallel and orthogonal. Their campaign covered many geometries, but the preliminary results presented herein are confined to the configurations shown in Table 1 together with their average failure loads for each printing angle. For the TCD predictions, the length scale L was calibrated from notched specimens and not from the measured fracture toughness. The emergent material strength σ 0 di ff ered significantly from σ UTS , indicating that the material ductility can not be neglected. Amongst other e ff ects, the complicated mesostructure and other subtleties of the manufacturing process triggered a zigzag crack path with local mixed-mode propagation, a θ p -dependent degree of ducility, and crack ini tiation at a distance from the notch root. Despite these and other complex phenomena, the Point and Area Method yielded good predictions, whereas the Line Method was not applicable due to 2 L exceeding the specimen geometry. Further information can be taken from the reference paper [2].

Table 1. Considered configurations together with their average failure loads as reported by Ahmed and Susmel [2].

θ p = 30 ◦ f, avg (N)

θ p = 45 ◦ f, avg (N)

0 ◦ f, avg (N)

F θ p =

2 α ( ◦ )

r (mm)

F

F

30

0 . 05

1040 1000

829 754 693 722

875 649 642 744

135 135 135

0 . 4 1 . 0 3 . 0

927 899

4. Failure Prediction Results and Discussion

The strain energy density fields were obtained from linear elastic Finite Element simulations. ABAQUS was chosen for both meshing and solving with quadratic plane strain elements and a simple linear elastic (isotropic) material model. The simulations were made with di ff erent material parameters for each printing angle as well as using the properties averaged over θ p in order to test the robustness of the method. When applying the ASED criterion to the reported data, the standard approach is using Equation (2) to estimate R 0 . Note that in [2], two very di ff erent sets of fracture toughnesses were reported. Obviously, the radii computed from them also di ff er, as can be seen in Table 2. Both sets of K Ic values led to a large scatter and very conservative predictions. However, in their analyses, Ahmed and Susmel [2] did not use K Ic to obtain the material length scale L , they used the more robust approach, where L is calibrated from a part of the notched specimens. In order to create comparable conditions, an analogous procedure is applied to the ASED criterion: For the smallest notch root radius, ψ ( x ) can be obtained from an FE computation with the boundary conditions from the failure experiment and averaged over control volumes with di ff erent radii R 0 . Then, the intersection point W ( R 0 ) = W c defines the choice of R 0 for the subsequent analyses. This idea was already presented for cyclic loading in [12], but is not commonly used for the ASED criterion. The procedure is shown in Figure 2 and the obtained R 0 are listed in Table 2. As can be seen in Figure 3, the predictions of the ASED criterion using the more robust length scale calibration method are satisfactory. The predictions based on average material properties and one single R 0 and W c for all data demonstrate the robustness of the method. The scatter is similar to what Ahmed and Susmel reported for the TCD, but slightly shifted towards the conservative side. This is most likely because they did not use the smallest but the second smallest notch geometry for calibration, although the stress concentration factor was around three times lower, leading to less conservative predictions.