PSI - Issue 68

Rintaro Tsuda et al. / Procedia Structural Integrity 68 (2025) 674–680 R. Tsuda et al. / Structural Integrity Procedia 00 (2025) 000–000

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Fig. 2. Phase volume fraction in uniaxial tensile test at 173K (a) and 20K (b) in SUS316L steel

5. Obtaining an equation expressing the stress triaxiality dependency of volume fraction and the single phase constitutive equation 5.1 Equation expressing the stress triaxiality dependency of volume fraction As an expression of the transformation rate as a function of the amount of plastic strain, the equation proposed by Matsumura et al. (1987) was used in the previous study. However since it is necessary to express the dependence of the volume fraction on the stress triaxiality, a new equation (3) is used in this study. This equation is assumed based on the previous study by Lebedev (2000). (3) ̅ #%$$ is effective equivalent plastic strain excluding the untransformed region observed in the initial stage of plastic deformation, &' is initial volume fraction of martensite. Coefficient b means the effect of temperature and chemical composition and coefficient c expresses the effect of stress triaxiality. Fitting parameters based on Levedev's study, we can determine b= 14.02 , = 2.74, ̅ #%$$ = ̅ # −0.05 . In this study, the volume fractions are measured only for the case of stress triaxiality, η =1/3. Therefore, based on the previous work of Lebedev (2000), the coefficient c is assumed to be constant regardless of temperature and chemical composition, and only the coefficient b is fitted. As a result, c is 2.74 and b= 4.04 , ̅ #%$$ = ̅ # −0.0614 at 173K, b= 9.27 , ̅ #%$$ = ̅ # −0.01 at 20K. 5.2 Single phase constitutive equations In order to obtain the single phase constitutive equation, it is necessary to determine the single-phase strain in addition to the single-phase stress. However, the strain of a single phase cannot be obtained directly from experiments. Therefore, we attempted to determine the strain of a single phase by the algorithm shown in Fig. 10. First, we assume α to be the ratio of the inclusion strain and the composite strain. Based on this α , the strain of the single phase is determined, and the constitutive equation of the single phase is also obtained at the same time. However, since it is necessary to confirm that the assumed α is correct, the secant method is solved based on the constitutive equation of the single phase obtained in the previous step to obtain α . When the obtained α and the assumed α are in sufficient agreement, α and the single phase constitutive equation are judged to be correct. We can say that we have performed a convergence calculation for α . A 3DFEM model with a sufficient amount of spherical inclusions is developed to simulate a two-phase steel with spherical inclusions simply. The model was subjected to uniaxial tensile deformation to verify the relationship between the equivalent strain of the total dual metal and the equivalent strain of the inclusion phase. As a result, it is confirmed