PSI - Issue 68

Roman Vodička et al. / Procedia Structural Integrity 68 (2025) 212 – 218 Roman Vodicˇka / Structural Integrity Procedia 00 (2024) 000–000

216

5

Fig. 1: Relation between the shear stress quantity and normal stress quantity corresponding to triggering of either the phase-field damage or of the interface damage, denoting β = − Φ (0) > 0or β = − φ (0) > 0, respectively. The dashed lines are asymptotes.

3. An example

The computations show the influence of the interface and its particular property on cracks, and also of the loading and the parameter ω introduced to adjust processes of damage if the structure is exposed to compression. An interface is commonly a source for degradation processes, especially for multimaterial components. Thus, varying interface parameters leads to various scenarios for cracking close to the interface. The analysis in this example compares several such scenarios. The scheme of the analysed component is shown in Fig. 2. As long as the scenarios are di ff erent and they were intended to be compared for the same discretisation, the mesh was chosen more or less uniform, whose typical element size is h = 0 . 35mm.

(a)

(b)

g [μm]

g ( t )

29 . 55

0

40

t [μs]

40

80

− 24 . 67

x 2

x 1

Fig. 2: Description of the example: (a) A domain with with an inclusion; (b) Applied loading, tension or compression.

The parameters needed for the computations include the material values: the bulk modulus K p = 192 . 3GPa, the shear modulus µ = 76 . 9 GPa, density ρ = 7800 kgm − 3 for the inclusion, and K p = 22 . 0 GPa, µ = 12 . 3 GPa, density ρ = 2200 kgm − 3 for the matrix. The interface, considered as a thin adhesive layer is characterised by κ = 6 . 88 1 0 0 1 TPam − 1 , κ G = 1PPam − 1 . The fracture energy in the matrix domain is G I c = 0 . 25 Jm − 2 , for the shear mode a di ff erent value is considered: G II c = 5 G I c or 50 G I c to modify the influence of shear on the cracking process in the matrix. The length scale parameter of the phase-field model is = 1 mm. The degradation function is Φ ( α ) = α 2 α 2 + β (1 − α ) + 10 − 6 (see Wu (2017)), with β = 3. Degradation of the interface is controlled by the interface fracture energy, which takes one of two values, G I c = { 0 . 2 , 20 } Jm − 2 , to obtain alternative behaviour in crack formation process along the interface. The mode II interface fracture energy is adjusted so that the stress condition (11) is hardly a ff ected by its value. The interface degradation function is φ ( ζ ) = β (1 − ζ ) β + ζ for β = 0 . 1. The structural element is loaded by the displacement loading g ( t ) which is shown in Fig. 2(b) (it includes both tension or compression). This load is applied incrementally in time steps refined to 0 . 1 µ s. First, look at cracks which appear for tensional loading. In relation to interface, the crack either appears along it, or at its vicinity due to a stress concentration. Both cases occur depending on the choice of the interface fracture energy as seen in Fig. 3. For the small value, the interface itself is cracked (see the gap appearing between the matrix and the inclusion), and afterwards, at the tips of this crack, there appears a crack in the matrix material, shown in Fig. 3(a).