PSI - Issue 2_B

Koya Ueda et al. / Procedia Structural Integrity 2 (2016) 2575–2582 Author name / Structural Integrity Procedia 00 (2016) 000–000

2578

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(a) N=4000

(b) Before etching

(c) after etching

(d) crack initiation

Fig. 3. Photograph of crack initiation

3.1. Surface model

Ferrite pearlite steel consists of layered structure and each layer is made of grain. Modelling of ferrite-pearlite steel was based on model of Nemoto et al (2016), ferrite grains and pearlite particles are regarded as spheres and spheroids, respectively. From the observation, minor axis of pearlite is same as pearlite-band and major axis of that is as long as diameter of ferrite. These grains consist of the layered structure. Based on this modelling, ferrite grain is regarded as a circle and pearlite grain is regarded as an ellipse in this study. This is about modelling for the surface where cracks initiate. Surface of specimen is divided into square area elements and grains of ferrite and pearlite are filled in these area elements. These area elements are enough large to fill the biggest grain. The area rates of ferrite and pearlite are calculated and grains are filled into area element based on Monte Carlo method. First which grain is filled is decided according to ferrite area rate. Second the size of grain is decided according to the distribution of grain size. When grains are filled, random crystal orientations are added. This process is repeated till the sum of the area of filled grains is larger than the area element.

Surface Crack nucleation

Crack growth

(1)

(3)

(2)

(4)

Pearlit e (1)'

(5)

(6)

Fig. 4. Schematic diagram of grain arrangement

3.2. Inner specimen model

This is about modelling for the inner specimen where cracks propagate. In the modelling of inner specimen, ferrite grain is regarded as a circle and pearlite grain is regarded as an ellipse in the same way as surface model. To utilize two-dimensional modelling of small fatigue crack growth interacting with grain boundary, complex arrangement of grains is simplified. The arrangement of grains on the plate where cracks propagate is averaged into semi-circular lows of grains. The way to simplify the arrangement of grains is described below.

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