PSI - Issue 40

Sergey Smirnov et al. / Procedia Structural Integrity 40 (2022) 378–384 Sergey Smirnov, Marina Myasnikova / Structural Integrity Procedia 00 (2022) 000 – 000

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Fig. 4. Distribution of damage  in the matrix; the central xy cross-section of metal matrix microvolume, tension simulation: (a)  = 0.04; (b)  = 0.2.

With the obtained diagram and the linear model of damage accumulation (Kolmogorov (2001)), the simulation of the deformation and fracture of silicides in the course of specimen upsetting was performed. The fragment of brass microstructure, sized about 70×80 µm, was used as a structurally heterogeneous microcell. Fig . 5a shows the simulation results at the equivalent macroscopic strain  = 0.04 in upsetting. It shows the areas corresponding to the zones of the most probable fracture of silicides. It is possible to reduce the probability of silicide fracture, i.e. to increase the durability of the brass, through the use of “milder” stress schemes offering a higher level of compressive stresses, suffici ent for minimizing the “adverse” tensile stress zones. Fig . 5b shows the results of the simulation of damage accumulation in silicides prior to fracture at the equivalent macroscopic strain  = 0.25 in upsetting under plane strain with an additional external hydrostatic pressure of 850 MPa. The simulation demonstrates that this loading condition enables brass to be deformed with a fairly high value of strain and minimum internal fractures (with only slight spalling at the silicide edges).

Fig. 5. Damage distribution among silicides at equivalent macroscopic strain in upsetting: (a)  = 0.04; (b)  = 0.25 (b); additional hydrostatic pressure of 850 MPa is applied in (b). 4. Conclusion Both two- and three-dimensional computational models of inhomogeneous material deformation have been developed. The two-level structural-phenomenological approach has been used to couple the macroscopic boundary condition and the microscopic model. The model takes into account the complex rheological properties of its components. The developed models have been implemented numerically on the example of simulating the loading of the random microstructure subvolume of an aluminum matrix composite with silicon carbide reinforcement for uniaxial tension and compression, as well as for simulating the loading of a random microstructure portion of complexly alloyed brass in upsetting under the plane strain state. The principal applicability of the phenomenological damage theory to simulating damage accumulation in materials under loading has been demonstrated. The evolution of stress-strain parameters (the stress stiffness coefficient and the Lode-Nadai coefficient) has been taken into account. A technique has been proposed for relating the ultimate strains of brittle