PSI - Issue 28

Mingyang Li et al. / Procedia Structural Integrity 28 (2020) 472–481 Author name / Structural Integrity Procedia 00 (2019) 000–000

474

3

j  y y x x x x i j   

i

(4)

s



j

i

If the stretch exceeds a critical stretch value, 0 s , then the bond is broken.

Fig. 1. PD model for a polycrystalline material when the orientation of the crystal is 0° (Li et. al., 2020).

As shown in Fig. 1, there are two different bond constants that are used to represent cubic crystals, which are considered in this study. Bonds represented by dashed lines, d c , are in all directions whereas bonds represented by solid lines, s c , are in particular directions with an angle of   2 1 , ( 1, 2, 3, 4) 4 i i     with respect crystal orientation. Bond constants for these two types of bonds can be expressed in terms of components of the stiffness matrix of a cubic crystal, 11 c and 12 c , as   2 11 11 12 3 11 12 d c c c c h c     (5a)   2 2 11 12 12 11 4 3 2 c c c c

11 c   

(5b)

c



s

N

1 j V      ij j

where

, ij  is the bond length between material points i and j , and  is the horizon size.

Fig. 2. Randomly generated polycrystals (Li et. al., 2020).