PSI - Issue 42

Roman Vodička et al. / Procedia Structural Integrity 42 (2022) 927 – 934

933

R. Vodicˇka / Structural Integrity Procedia 00 (2019) 000–000

7

G II

I c = 10

II c / G

I c = 1

II c / G

I c = 10

II c / G

I c = 1

c / G

G

G

G

Fig. 6. Stress (trace) distribution causing initiation and propagation of cracks ( left ), and displaying the cracks as distribution of the phase-field variable after application of the given load ( right ), di ff erent values of mode dependent fracture energies, no inclusion.

iI c / G

I c = 10

iI c / G

I c = 1

G

G

t = 0 . 172 s

t = 0 . 182 s

t = 0 . 165 s

t = 0 . 172 s

Fig. 7. Stress (trace) distribution at the selected instants, check di ff erences close to the interface for various fracture energy ratios.

G iI

I c = 10

iI c / G

I c = 1

iI c / G

I c = 10

iI c / G

I c = 1

c / G

G

G

G

× 10 − 3

Fig. 8. Equivalent shear strain at the instant t = 0 . 172 s with magnified (100 × ) deformations ( left ), and crack propagation as distribution of the phase-field variable at the instant t = 0 . 200 s.

such a crack appears for the option with large interface fracture energy. Though, in the form of arising material cracks there is no substantial di ff erence between these two cases. Anyhow, the crack appears in the material due to the same reason as in the sample without the inclusion and also the form of the crack is the same. Additionally, crack appears also at the interface, either by initiating directly at an interface crack if the interface fracture energy and pertinent critical stress at the interface are small, see the strain plot in Fig. 8 in the option G iI c = G I c , or due to a stress concentration close to such an interface between matrix and a sti ff inclusion. The di ff erence (though not principal) between cracks that finally develop in both cases is seen in left part of the same figure. Finally, if the mixed mode fracture is not taken into account by putting G II c = G I c , the character of fracture is di ff erent as documented in Fig. 9. Similarly to the case without the inclusion in Fig. 6, the crack appears during the phase of lateral loading and seams to have a shear character. It is attracted by the inclusion, though due to low energies, no interface crack appears, even for the lower value of the interface fracture energy.

5. Conclusions

A mixed fracture mode computational model is presented for quasi-static loading of quasi-brittle materials. The inclusions in material required to formulate the model which allows for cracking along interfaces. These two forms of flaws in material may appear simultaneously and compete in computational procedures which of them is physically attainable. It is clear that the model needs several parameters related to crack formation processes. The influence of