PSI - Issue 77

Victor Rizov et al. / Procedia Structural Integrity 77 (2026) 382–388 Author name / Structural Integrity Procedia 00 (2026) 000–000

387

6

time (Fig. 3). It is seen also in Fig. 3 that the strain energy release rate rises when M increases which is an expected result. Results for the influence of the parameters, 1 f and 2 f , on the strain energy release rate are given in Fig. 4. The curves in Fig. 4 indicate that growth of 1 f causes a continuous reduction of the strain energy release rate. The same character has the influence of 2 f on the strain energy release rate (Fig. 4). We mention that the results given in Fig. 4 are also related to the time factor since 1 f and 2 f control the change of β E and γ η with time.

/ 0 0 = VS NS γ γ η η

0.5

VS NS E E 0 0 / β β ratio (curve 1 – at

Fig. 5. The strain energy release rate versus

, curve 2 - at

/ 0 0 = VS NS γ γ η η

1.0

/ 0 0 = VS NS γ γ η η

2.0

and curve 3 – at

).

VS NS E E 0 0 / β β and

NS 0 0 / γ γ η η

Figure 5 displays how the strain energy release rate is biased by

ratios. The

VS

growth of these ratios produces a continuous diminution of the strain energy release rate (Fig. 5). 4. Conclusions

A theoretical exploration of longitudinal fracture in functionally graded beam-like constructions with considering the time factor is carried-out. A non-linear viscoelastic mechanical model is used for treating the beams in the

analysis of the strain energy release rate. The analysis indicates that: 1) the strain energy release rate continuously grows with time; 2) the strain energy release rate rises when M increases;

3) the growth of 1 f and 2 f causes a continuous reduction of the strain energy release rate; 4) a continuous diminution of the strain energy release rate is observed at increase of

VS NS E E 0 0 / β β and

NS 0 0 / γ γ η η

VS ratios. The longitudinal fracture study approach presented in this paper can be used to prove the structural integrity of functionally graded beam-like constructions with nonlinear viscoelastic behavior. The approach is applicable also for evaluating the effect of time on the structural safety. References Hirai, T., Chen, L., 1999. Recent and prospective development of functionally graded materials in Japan. Mater Sci. Forum 308-311, 509-514. Mahamood, R.M., Akinlabi, E.T., 2017. Functionally Graded Materials. Springer. Marae Djouda, J., Gallittelli , D., Zouaoui, M., Makke, A., Gardan , J., Recho, N., Crépin, J., 2019. Local scale fracture characterization of an advanced structured material manufactured by fused deposition modeling in 3D printing, Frattura ed Integrità Strutturale, 14, 534-540. Nagaral, M., Nayak, P. H., Srinivas, H. K., Auradi, V., 2019. Characterization and Tensile Fractography of Nano ZrO2 Reinforced Copper-Zinc