PSI - Issue 40

N. Kondratev et al. / Procedia Structural Integrity 40 (2022) 239–244 N. Kondratev et. al. / Structural Integrity Procedia 00 (2022) 000 – 000

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(a)

(b)

Fig. 1. The scheme of grain structure for the modified statistical model (a), grain structure in three-dimensional Euclidean space, obtained by Neper (b) 3. Identification of a grain structure based on experimental data and results analysis To solve the problem of generating a grain structure in the statistical model, it is necessary to establish distribution laws for relative grain size d eq and sphericity S , which characterizes the shape of the grains. For polycrystalline copper based on the literature data (Suresh K. S., Rollett A. D., Suwas S. (2013)) these distributions were digitized and shown in Fig. 2. The resulting polyhedral grain structure for this data is shown in Fig. 1 (b).

(a)

(b)

Fig. 2. The relative grain size experimental distribution d eq (a) and sphericity S (b) of polycrystalline copper. Digitized data defined on the basis of (Suresh K. S., Rollett A. D., Suwas S. (2013))

As the result, the generated by Neper grain structure of a copper polycrystal had characteristics shown in Table 1. The following notation is used below: d av , d min , d max are average, minimum and maximum grain sizes, s av , s min , s max are average, minimum and maximum facets areas, N av , N min , N max are average, minimum and maximum number of neighbor grains.

Table 1. Formed grain structure geometric characteristics of a copper polycrystal

d av , µm

d min , µm 1,14

d max , µm 10,14

s av , µm 2 3,48

s min , µm 2 0,02

s max , µm 2

N av

N min

N max

3,00

129,37

11,68

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