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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3. Results And Discussion 3.1. The Metal Matrix Composite

The numerical simulation has shown that rigid silicon carbide particles clamp a thin matrix layer. Clamping leads to the emergence of local plastic strain regions. On the other hand, stiff silicon carbide inclusion particles distributed in the ductile matrix make tensile stress areas in their proximity. This has been shown by computing the stress stiffness coefficient k in the finite element nodes pertaining to the matrix of the composite. Maximum k values caused by inclusion proximity appear to occur in distinctive microcrack initiation areas observed in experiments. It is known that severe tensile stresses contribute to intensive plastic dilatancy and accelerate the fracture process (Kolmogorov (2001)). This conclusion is confirmed by numerical simulations of damage  accumulation in the matrix metal within an MMC microvolume. The fracture locus of commercially pure aluminum (the composite matrix material) for 300 °C has been taken from the experimental investigation reported in (Smirnov et al. (2016)). The fracture locus determines the dependence of ultimate shear strain f  at fracture on the stress state parameters k and   ,   , f f k      . The ultimate strain at fracture was calculated as follows: / 3 f f    . It has been found that the most possible regions of failure initiation (i.e. the regions where equation 1 holds true) are strain localization regions where adverse tensile stresses prevail. As an example, Fig. 4 depicts accumulated damage distribution in the central cross section xy of the metal matrix within the microvolume depending on equivalent macroscopic strain for uniaxial tension. The results of MMC damage simulation were discussed in more detail in (Smirnov et al. (2017)). 3.2. The Complexly Alloyed Brass The experimental investigations have shown that (Fe;Mn) 5 Si 3 particles of any geometry, which are on the average larger (10 to 80 µm) and contain iron, are more prone to fracture than smaller manganic Mn 5 Si 3 particles (10 to 20 µm) under identical deformation c onditions. Besides, a negative effect is exerted by the non-uniform stress-strain state of the material at the mesoscale, whereas the geometry of silicides scarcely affects their ability to fracture. Therefore, in the subsequent discussion our consideration is restricted to the ultimate plasticity of acicular iron containing (Fe;Mn) 5 Si 3 silicides. The features of the fracture of silicides in brass were discussed in more detail in (Smirnov et al. (2016)). The analysis of the calculation results has revealed the non-uniformity of the stress-strain state of silicides at the microscale at a fixed moment of loading. A fairly wide range of the values of the stress stiffness coefficient k and its variation in the course of specimen upsetting enables us to use the identification procedure for determining the diagram relating the amount of ultimate equivalent strain preceding silicide fracture sil f  to the stress stiffness coefficient k . The description of such diagrams by the exponential function is the most commonly used for metal alloys (Kolmogorov (2001)); therefore, to describe the diagram of the ultimate equivalent strain of (Fe;Mn) 5 Si 3 silicides, it is also reasonable to use the function of the form   exp sil f a bk    , where a and b denote empirical coefficients obtained by identification. Let the mean value of   be constant on every step of upsetting under plate strain conditions. Then the fracture criterion (1) can be used to compute damage in every node of the finite element mesh of silicides, at every computation step. It is assumed in the calculation that a silicide will fracture when the above-mentioned fracture condition is fulfilled on the average over the nodes belonging to this silicide. The number of fractured silicides at each stage of deformation was determined similarly. The model was identified from the condition of the best agreement between the experimental and calculated data, reasoning from the minimization of the value of the quadratic residual. For the quadratic residue S = 0.22, the following empirical coefficients were obtained: a = 0.005, b = 6.1.