PSI - Issue 40

Artyom A. Tokarev et al. / Procedia Structural Integrity 40 (2022) 426–432 Artyom A. Tokarev, Anton Yu. Yants / Structural Integrity Procedia 00 (2022) 000 – 000

430

5

Fig. 1. FE partition of the specimen. Different grains are shown in colors.

The loading of the specimens was carried out as follows: for all nodes of the lower A 1 B 1 C 1 D 1 (z = -0.5 unit) and upper ABCD (z = 0.5 unit) polycrystal faces were given vectors of constant displacement velocity   5 0, 0,5 10    V and   5 0,0, 5 10      V unit/s respectively, and the rest of the faces were free. The length of the edge of the cube was 1 unit, grain size – 1/ k unit, crystallite size – 0.2/ k unit. Integration step was about 0.1s for each realization. Elastic modules of crystalline material Al in the basis of the crystallographic coordinate system were assumed equal to: п iiii = 108 GPa, п iijj = 61.3 GPa, п ijij = 28.5 GPa, where i , j = 1...3. The mean values, standard deviations of the stress in the polycrystal after compression by 0.1% and also mean value change rate were calculated (fig. 2, 3). Damping of fluctuations in mean values can be tracked by the following measure of the relative change rate

 

 

    3 3

 

 

3

1

m n m n

 

 

2

,

(8)

C n



3

1

m n m n

 

where n 3 – the number of grains for which the change rate is calculated, m – mean values of the average stress intensity as a function of the number of grains (curve in fig. 2). In essence   C n is a relative (relative to the middle of the interval) interval of variation of the curve of mean values of the stress intensity.