PSI - Issue 16

Jaroslaw Galkiewicz / Procedia Structural Integrity 16 (2019) 35–42 Jaroslaw Galkiewicz / Structural Integrity Procedia 00 (2019) 000 – 000

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mode are significant. Therefore, the largest challenge is to select parameters for the zone A modeling interactions between the inclusion and the matrix. Since in this case fracture according to mixed mode is possible, analysis of the influence of the parameters of the sliding mode on the fracture of a circular inclusion was carried out in the study Galkiewicz (2016). It was assumed that the fracture toughness according to the mode II in zone A changed in the range of a factor from 0.7 to 1.3 times that of the toughness for the opening mode. The obtained results demonstrate that the change in fracture toughness for the sliding mode does not significantly affect the process of cell damage.

a

b

Fig. 3. (a) parameters of the cohesive model in zone A and (b) in zones B and C located in the plane of symmetry.

Zones B and C are located in the plane of symmetry, which requires a slight correction to the entered parameters. The stiffness of the defined cohesive elements must be twice as large as the stiffness of the material in the surrounding continuum, while the magnitude of energy should be reduced by half (Fig. 3b). In the case of zone A, it is assumed that fracture may occur according to the mixed mode. In this case, it is assumed that the following condition indicates the critical moment after which a weakening of the element occurs:     2 2 max max / / 1 n n s s       (3) max is the maximum stress for mode II. Once the maximum stress of the cohesive element is reached, its gradual weakening begins. It is assumed that this process develops proportionally to the effective displacement computed according to the following equation: wherein σ n max is the maximum stress for mode I, and τ s It was also assumed that in the case of zone A, the mixed mode would be considered by using the Benzeggagh Kenane law (5) to determine the moment of damage of the element:    / ( ) TC IC IIC IC II I II G G G G G G G      (5) where: G TC is the critical strain energy release rate, G IC and G IIC are the critical energy release rate for mode I and II, and η=2.284. As was already mentioned, the conducted tests demonstrated that G IIC variation in the range of 0.7 – 1.3 G IC did not influence the obtained results. The critical moment in zones B and C was determined based on G IC . 2 n s      2 (4)

5. Parameters of the cohesive zones

The parameters characterizing the cohesive zone (maximum stress and fracture energy) are the most difficult elements of the model to determine. In the present study, the maximum stress characteristic for the inclusion material and the interface bonds between the inclusion and the matrix are variables.