PSI - Issue 13

Hiroaki Ito et al. / Procedia Structural Integrity 13 (2018) 1105–1110 Author name / Structural Integrity Procedia 00 (2018) 000–000

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two-dimensional problemwith two steps based on Tanaka’s theory. (Shibanuma et al., 2018) For ferrite-pearlite steels, the predicted fatigue lives and limits showed good agreement with experimental results. Shibanuma’s simplification considers characteristic features of a fatigue crack such that a crack generally initiates at a surface and the crack growth direction is approximately orthogonal to that of maximum principal stress. However, Shibanuma’s model doesn’t consider either the crack closure or stress distribution. Long fatigue cracks under constant amplitude loading generally remain closed during a part of loading cycle, especially when compressed. Crack opening stress becomes higher as the crack grows, and even short fatigue cracks are affected by the crack closure. For configurations with non-uniform stress fields, stress distribution must be considered. Shibanuma’s model uses only the normal stress on the surface of the specimens, although the specimens are notched and the normal stress distributions exist. In this study, an extended model for predicting fatigue life and limit is proposed by considering the effects of the crack closure and stress distributions. Although these new factors are considered, this model aims to predict fatigue properties only with mechanical properties and microstructural information. 2. Model development 2.1. Modeling of spatial distributions of ferrite grains and pearlite colonies on the inside plane Three-dimensional crack growth is simplified as a two-dimensional phenomenon on the inside plane. This model considers the effect of microstructures by modeling spatial distributions of grains on the inside plane. A fatigue crack generally becomes semi-elliptical as it propagates. Anai et al. showed that the aspect ratio is affected by the crack depth (Anai et al., 2015), expressed as � � � �0.0� � 0.���0.5 � � 0 � . 0 5 � � � � 0.5 � � � 0� � �� (1) where is the short diameter (crack depth), is the long diameter and � � is the normal stress distribution. The spatial distributions of grains on the inside plane are defined corresponding to the modeling of crack initiation and growth. Each grain is assigned randomly by the Monte Carlo method. In this model, the modeling of crack growth is different from that of Shibanuma. The procedure of this modeling is shown in Fig. 1, and presented as follows.

Fig. 1 Modeling of spatial distributions of ferrite grains and pearlite colonies 1. The crack initiating grain is assumed to be a semi-circle with diameter � and is assigned on surface plane (Fig. 1 (0)) 2. The grain with the major axis � and the minor axis � is assigned adjacent to the crack initiating grain (Fig. 1 (1)) 3. The grains keep being assigned on the plane to make a grain line until ����� reaches the length of the semi-elliptical arc with the minor axis � � � � � . L is the length of a semi-elliptical arc with a certain length of major axis. (Fig. 1 (2)) 4. Steps 1-3 are repeated so that the next grain line is defined. (Fig. 1 (3))