PSI - Issue 13

Temma Sano et al. / Procedia Structural Integrity 13 (2018) 1154–1158 Author name / Structural Integrity Procedia 00 (2018) 000 – 000

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1. Introduction

Solute atoms are known to change the strengths of metals. Past studies on hydrogen revealed that it is localized in the vicinity of the crack tip and lowers the interatomic bonding force and facilitates plastic deformation in a material containing a crack when an external force is applied to open or close the crack. In addition, past studies confirmed hydrogen invasion and release from the material surface in hydrogen-exposed materials, apart from internal hydrogen diffusion. It is known that the strength of a material depends on the amount of hydrogen present. Therefore, it is necessary to know the influence of hydrogen on crack propagation, which is a factor determining material failure, and also, investigate the influence of the amount of hydrogen. In order to address these issues, our research group developed a static strength analysis method including hydrogen convection-diffusion for cracked materials by finite element method. (Sasaki 2015) The next objective is to make it possible to analyze fatigue crack propagation including hydrogen convection-diffusion using this method. When analyzing crack propagation based on finite elements, generally, the node release method is used. However, in the case of the node release method, the crack propagation length depends on the size of the element. In addition, in the static strength analysis method used in our previous study, the crack tip shape was modeled as a semicircle with a small radius to express the invasion and release of hydrogen from the face of the crack tip. Therefore, we cannot use the node release method, which is a conventional method. In this study, we proposed based on finite element method, a novel fatigue crack propagation analysis method that moves the stress field in the opposite direction to that of crack propagation by an equal amount in order to analyze crack propagation behavior without changing the analysis model of the crack tip. The concrete method is as follows. First, we performed a simple tensile load analysis on the model currently used for convection-diffusion analysis of hydrogen and output the displacements of all the nodes of the model at the maximum load. Then, the displacement was moved in the direction opposite to the crack propagation direction. Finally, the stress field was reproduced by forcibly moving all the nodes by the displacement amount. The proposed method was verified by the following method. By using the model used in our previous study, we compared the case of applying simple tension in the previous study with the case of moving stress field from simple tension by using the proposed method. For a comparison, we used the stress-strain distribution around the crack tip. If the stress-strain distributions for the two cases are the same, it can be said that the stress field can be reproduced by the proposed method. In this finite element analysis, we used Marc/Mentat 2017.0.0. Figure 1 shows a vertically symmetric two dimensional analytical model with a radius of 0.15 m. The model contains a crack with an initial tip radius of 5 μm. In this elastoplastic analysis, the model consists of 3706 nodes and 8-node quadrilateral 1776 elements. The crack length and loading condition were selected to satisfy small-scale yielding condition. The parameters used in the present analysis are listed in Table 1. The deformation was provided by the forced displacement to the boundary of the model, as shown in Fig. 1. The displacements in the x and y directions were obtained as follows. = I 1+ √ 2 cos 2 (3 − 4 − cos ) , (1) = I 1+ √ 2 sin 2 (3 − 4 − sin ) , (2) where u x and u y are the displacements along the x - and y -axes, respectively, E is Young's modulus, ν Poisson's ratio, and r the distance from the crack tip. The angle θ at the crack tip is set as shown in Fig. 1. The remote stress direction in the tensile simulation is the direction of the y -axis. In this study, the analysis was continued until unloading for simulating plastic zone evolution by cyclic loading. The unloading was realized by decreasing the remote stress applied on the model boundary to zero. 2. Analytical model and methods