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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operated in such a cryogenic environment. The final objective of this study is to calculate in detail the loads and deformations applied to a large size liquefied hydrogen storage tank and to evaluate the safety of the tank under the severe environment of 20 K when a huge earthquake occurs. Although metastable austenitic stainless steel SUS316L is the most suitable material for the tank from the viewpoints of cost and fracture toughness, it has been found that the matrix austenite transforms hard martensite in cryogenic environments with deformed. It is called strain induced martensitic transformation (SIMT). The SIMT may reduce the fracture toughness at cryogenic temperatures. We believes that the SIMT is not sufficiently taken into account in the conventional elasto-plastic finite element analysis, which is often used to determine the fracture toughness of structures. Therefore, this study describes a new method for elasto-plastic finite element analysis with sufficient consideration of SIMT. 2. Martensitic transformation of metastable austenitic stainless steels In metastable austenitic stainless steels, body-centered cubic α' martensite and hexagonal ε-martensite are formed by plastic deformation below the Md temperature. Using a homogenization method called the secant method proposed by Weng (1990), Tsuchida et al. (2000, 2021a, 2021b) developed a method to determine the dual phase metal stress strain relationship during uniaxial tensile transformation from the stress-strain relationship of a single phase. These studies focused only on the uniaxial tensile state and paid little attention to the effect of the stress field on the SIMT. However, the studies by Lebedev et al. (2000), Polatidis et al. (2021), Beese et al. (2011), and Morohoshi (2022) show that this phase transformation is highly influenced by the stress field. Structural and fracture mechanics analyses that take these transformation behaviors into account are necessary for accurate prediction of deformation and stress concentration. However, in order to make these findings truly available to structural designers, it is necessary to formulate them in a form suitable for the finite element method. However, this has not yet been realized. In this study, we attempt to develop an FEA method that takes into account the SIMT behavior, which depends on the stress field, and to calculate the fracture mechanics parameters more accurately.

3. Theory of elasto-plastic FEM considering SIMT 3.1. Problems with conventional elasto-plastic FEM

In elasto-plastic FEM, a material constitutive equation describing the stress-strain relationship of a material is required as input data. There are several ways to express this constitutive equation, but in this study, it is expressed in the form of Equation (1).

(1)

is yield stress. is material constant. The results of uniaxial tensile tests are usually used for this constitutive equation. This is because in uniaxial tensile conditions, the true stress in the tensile direction is same as the equivalent stress. However, this method is inappropriate for metastable austenitic stainless steels because of the stress triaxiality dependence of SIMT. Since SIMT accelerates in high stress triaxiality situations compared to uniaxial tension, the value of equivalent stress should be larger at the same amount of equivalent strain. The volume fraction of martensite changes depending on the stress triaxiality, as a results the constitutive equation also changes. This change is not taken into account in the conventional elasto-plastic FEM. This study addresses the solution of this problem. 3.2. Theory of elasto-plastic FEM incorporating secant method The secant method is one of the homogenization methods proposed by Weng (1990). This theory derives the constitutive equation of dual phase metal from the single-phase constitutive equations and the volume fractions of each phase using a composite model in which spherical inclusions are assumed to be embedded in the matrix phase. is equivalent plastic strain.