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

676

3

The deformation can be divided into three stages according to the state of each phase. The first stage is the state before yielding of both phases, the second stage is the state where only one of the phases yields, and the third stage is the state where both phases yield. If the strain of the matrix phase and the volume fractions of each phase are determined in each stage, the stress and strain of the composite phase can be determined. The secant method is incorporated into the elasto-plastic FEM. If at least one of the two phases yields, the stress and strain of the composite phase can be obtained by the secant method assuming the strain of the matrix phase. The iterative calculations are continued until the values satisfy the equation (2). (2) " !" is the equivalent stress that would occur if the deformation considered in an increment were elastic. ∆ # is the variation of composite (total) equivalent plastic strain. $ means the yield stress. 4. In-situ neutron diffraction experiments during tensile deformation In order to use the elasto-plastic FEM module developed in this study, it is necessary to know the constitutive equation of the single-phase and the change of the volume fraction of each phase in response to deformation. Therefore, in-situ neutron diffraction experiments during tensile deformation were conducted. The temperature was adjusted to about 20 and 173K. Specimens used at 20K with a parallel diameter of 4 mm and a parallel length of 102 mm were cut from a 1/4 t section of a 50 mm thick SUS316L steel plate. Specimens used at 173K is with parallel section width of 5 mm, parallel length of 25 mm, and thickness of 1.5 mm. Table 1 shows the chemical composition of the specimens. The results at 173K are measured by Tsuchida et al (2021).

Table 1. Chemical composition of specimen. (mass%). C Si Mn Ni

Cr

Mo

Co

Fe

20K

0.011 0.015

0.42 0.56

0.83 0.92

12.1 12.2

17.6 17.6

2.08 2.06

0.33

Bal. Bal.

173K

-

In this experiment, the volume fractions and single phase stress can be obtained. The volume fractions can be obtained from the intensity of diffracted neutrons at specific wavelengths, which are strongly detected because of the Bragg rule. For the single-phase stress, the lattice plane displacement is obtained, and the lattice strain is obtained from the change in the displacement. Finally, the stress of a single phase can be obtained from the lattice strain. Fig. 1 shows the results of each phase volume fraction. Fig. 2 shows the results of total true stress, single phase stress and total equivalent plastic strain at 20K and 173K. At 20K, ε-martensite is also detected. But, it is difficult to distinguish between α and ε based on the neutron diffusion peak, and reducing the number of phase makes analysis easier, so α and ε were treated as the same phase in this study.

Fig. 1. Phase volume fraction in uniaxial tensile test at 173K (a) and 20K (b) in SUS316L steel