PSI - Issue 68

Roman Vodička et al. / Procedia Structural Integrity 68 (2025) 212 – 218

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Roman Vodicˇka / Structural Integrity Procedia 00 (2024) 000–000

(a)

(b)

Fig. 3: Cracking under tension: (a) Smaller interface fracture energy, time instants t = 16 µ s, and t = 58 µ s; (b) Bigger interface fracture energy, time instants t = 20 µ s, and t = 58 µ s.

The other variant demonstrated in Fig. 3(b), the crack nucleates in the matrix material in the neighbourhood of the interface and then propagates in the same direction perpendicular to the applied load. For compression, where the shear fracture energy is relevant, two its values are considered relatively to the value of the opening fracture energy. With the smaller one, the results are shown in Fig. 4. As above this value leads to an interface crack first, and then this crack may kink into the matrix. Depending on the parameter ω , the model may (a) (b)

Fig. 4: Cracking under compression G II

c = 5 G I c for the matrix domain, small interface fracture energy: (a) ω = 0 . 4, time instants t = 24 µ s,

and t = 31 µ s; (b) ω = 0 . 04, time instant t = 38 µ s.

provide di ff erent crack patterns. For the smaller value of ω in Fig. 4(b), the range of the load was unable to make further phase-field damage in the matrix. For the other value a crack patter appears above the inclusion due to a smaller (in absolute value, still may be negative) stress trace, presented in Fig. 4(a). With a higher ratio between G II c and G I c , damage still may first appear along the interface, if the interface fracture energy is small, see Fig. 5(a). As the strain energy travels across the whole body at a finite velocity, here, it caused

(a)

(b)

Fig. 5: Cracking in the domain with one inclusion under compression G II

c = 50 G I

c for the matrix domain: (a) ω = 20, time instants t = 60 µ s,

and t = 72 µ s, small interface fracture energy; (b) ω = 40, time instants t = 40 µ s, t = 79 µ s, big interface fracture energy.

damage triggering in the bottom part of the block, still having been initiated at the tips of the interface crack. For the case of the big interface fracture energy, no interface crack appeared in Fig. 5(b). Additionally as in the Fig. 4(a), the damage was initiated at the top face and the direction of the crack documents that shear was the phe nomenon which caused it.

4. Conclusion

Crack formation in multimaterial structural element exposed to tension or compression was studied by the devel oped computational model. We compared various crack patterns which may appear in a material with an interface due