PSI - Issue 14

Ashish Mishra et al. / Procedia Structural Integrity 14 (2019) 544–548 A.Mishra, A. Alankar / Structural Integrity Procedia 00 (2018) 000–000

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3.2. Count of various dislocation reactions The current work addresses the junction count for Hirth, glissile, sessile and collinear junctions. The basis for tracking scheme implemented in 3D-DDD package for identifying particular type of junctions is taken from the work of Groh et al. (2009). We implemented the counting scheme to determine the number of occurrences of different dislocation reactions in the MDDP package developed by Zbib et al. (1998). Fig. 2(a) shows the variation of stress with the formation and annihilation of dislocation reactions in a single crystal. It can be observed from Fig. 2(a) that when formation of junctions occurs, then stress rises whereas unzipping of junction results into decrease in stress. Fig. 2(b) illustrates the occurrences of different dislocation reactions as a function of strain when the copper crystal is loaded along [1 1 1] direction.

Fig. 2. (a) Variation of stress and total number of junction nodes formation w.r.t strain; (b) Evolution of different reactions with increase in strain in a crystal.

3.3. Influence of dislocation interactions on stress evolution The strength of various dislocation interactions provides strength to the crystal. Therefore, the stress in material can be predicted by the summation of strength contributed by Hirth lock, glissile junction, sessile junction, collinear reaction and cross slip event individually using the expression Eq. 1. (1) where � , � , � , ��� and �� are fractions of occurrences of Hirth locks, glissile junctions, sessile junctions, collinear reactions and cross slip events respectively out of total number of reaction events during the deformation process. � , � , � , � , ��� and �� denotes pierls stress, stress due to Hirth lock, glissile junction, sessile junction, collinear reaction and cross slip respectively. Strength increase due to individual dislocation reactions can be obtained by minimizing the error between predicted stress value and that obtained by DD (Eq. 2). 0 pred H H G G S S            col col CS CS f f f f f  

error DD pred     

(2)

As the strength of collinear reaction is maximum, thus the effectiveness of each interaction had been calculated w.r.t the collinear reaction. The values thus obtained are listed in Table 2.