PSI - Issue 42

Pauline Herr et al. / Procedia Structural Integrity 42 (2022) 498–505 P. Herr et al. / Structural Integrity Procedia 00 (2019) 000–000

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we observed void growth and coalesence as a dominant failure mechanism in our simulations, which was also found in experiments using computer tomography under similar loading conditions, cf. Dumont al. (2019).

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Fig. 2. (a) Comparison of TSLs from FFT-based homogenization and the proposed model; (b) Unloading behavior of the ML-based model demon strated by one element tests.

For all volume fractions, a one-element test was performed in Abaqus in order to evaluate the capabilities of our ML-based model. Furthermore, Figure 2a shows the comparison with the TSLs obtained from FFT-based homoge nization and the response of the model during unloading is demonstrated in Figure 2b . At the onset of plasticity, the model deviates slightly from the FFT simulation, but nevertheless the curves show a good agreement in general. Thus, the surrogate model is able to represent the mechanical response of the RVE well for the volume fractions included in the training data. However, we observed that the model is not yet well suited for volume fractions, which were not part of the training data. This can probably be corrected by increasing the amount of training data, but it is not clear at this point how many di ff erent volume fractions must be considered to improve the interpolation and extrapolation capabilities of the ML-based model. The slight deviations at the onset of plasticity emerge owing to the immediate increase of the slope in the plastic separation-separation relation at the transition from the elastic to the plastic region, which causes a kink in the corre sponding curve. It was observed that this kink could not be captured well by the FFNN and thus leads to deviations of the model response, see 3a. This issue might be eliminated by using a criterion for the initiation of plasticity instead of fitting the FFNN to the full plastic separation-separation relation; however, the deviations are still negligible in comparison to expected experimental scattering. Furthermore, a FEM simulation of a DCB test was performed with the ML-based model for a volume fraction of 5 % as an exemplary simple structural simulation on the component scale, see Figure 4, where the macroscopic damage field is shown. The J integral in pure mode I for a cohesive zone (Rice (1968)), and for the DCB test (Paris and Paris (1988)) is given by J = u t 0 σ ( u ) d u = 2 P θ b . (9) where P denotes the force applied on the DCB specimen, θ denotes the rotational angle of the load introduction points, and b is the width of the adhesive layer. The Crack Opening Displacement (COD) u t corresponds to the separation at the crack tip. It is expected that the J integral in the DCB simulation at crack propagation equals the critical ERR ( = J c ) calculated by integration of the TSL from FFT -based homogenization. The good agreement, as shown in Figure 3b, indicates reasonable results of the simulation using the ML-based model. Up to a certain point, the simulations still converged during crack propagation, which is indicated by the large J plateau. Indeed, the computational time of the DCB simulation was also of the same order of magnitude as expected