PSI - Issue 47

Ezio Cadoni et al. / Procedia Structural Integrity 47 (2023) 630–635 Author name / Structural Integrity Procedia 00 (2023) 000–000

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Fig. 6. Comparison between post-mortem specimen diameter for 5 and 15mm gauge length.

Fig. 7. Comparison between plastic strains in post-mortem analysis for 5 and 15mm gauge length.

nals were numerically reconstructed and compared with experimental ones following the propagation of the transient stress wave through input bar, specimen and output bar. As a result, the material model was tuned and the specimen’s deformation was calculated. For preliminary simulations, a mesh size of 0.46 mm was used for the specimen and 0.92 mm for the bars. In the case of long specimens, the mesh size allows for the highlighting of the deformation phases during the transition from elastic to plastic, uniform deformation, multiple plastic localisations in the initial phase of plastic deformation (see Fig. 8), and necking with high stress-strain localisation (see Fig. 9). It is observed that finite element simulation results are highly consistent with experimental results, whereas the reduction in plastic failure strain is due to the mediation e ff ect of finite elements. It is possible to prevent the latter by decreasing the mesh size and extending the computation time. The e ff ect of mesh size must be carefully considered when applying experimental results to actual structures, since real structures are generally modelled with larger elements. The spec imen was modelled using the DAMP model (Riganti and Cadoni (2014)), which takes yielding into account as the transient propagation of shear waves from initialisation points. According to the DAMP model, material strength is composed of two heterogeneous phases: intact and yielded. The upper yield strength is calculated as a function of the loading regime using the DAMP parameters (i) shear band propagation speed and (ii) number of initialisations. DAMP predicts the upper yield strength value well for two initialisations in the specimen cross-section and a shear band propagation velocity of 30 m / s for B500A steel in 10- and 15-mm-long specimens. According to the analytical formulae (from 12 to 15) from Riganti and Cadoni (2014), 40 MPa and 90 MPa are calculated above the dynamic yield stress for 10 and 15 mm, respectively. The strain rate dependent plasticity is then modelled in a similar manner to state-of-the-art rate dependent plasticity material models in LsDyna.

5. Concluding remarks

As a result of the experiments and simulations carried out, the following conclusions can be drawn: (i) the gauge lengths investigated permit to apply the simplified formulae (equation 7) for Split Hopkinson Bar; (ii) using di ff erent gauge length in SHTB for the same plastic strain rate the preload have to be adapted; (iii) the use of longer sample still allows to obtain uniform state of stress and strain; (iv) the use of shorter sample guaranties that the neck develops