PSI - Issue 42

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Neha Duhan et al. / Procedia Structural Integrity 42 (2022) 863–870 Duhan et al./ Structural Integrity Procedia 00 (2019) 000 – 000

u x ,u y

y

b

x

L

d

L

(a)

(b)

Fig. 2. (a) Schematic of semi-infinite Si x Ge 1-x alloy domain with an edge type dislocation showing boundary conditions and (b) the meshed domain with enriched nodes shown by blue and magenta color along with outer boundary nodes shown by red color circles.

3.6

300 K 350 K 400 K 450 K 500 K

300 K 350 K 400 K 450 K 500 K

2.9

3.4

2.8

3.2

2.7

3.0

2.6

2.8

2.5

2.6

0.0 Normalized P-K force for heat flux along glide plane Si Concentration 0.2 0.4 0.6

0.0

0.2

0.4

0.6

0.8

1.0

0.8

1.0

Normalized P-K force for heat flux normal to glide plane Si Concentration

(b)

(a)

Fig. 3. The Peach-Koehler force in the normalized form by dividing the numerical values with the analytical elastic Peach-Koehler force for x = 0.5 is plotted against the Si concentration for (a) heat flux applied normal to the glide plane and (b) heat flux along the glide plane. The results of Peach-Koehler force obtained by using Eq. (16) are computed at different heat flux values acting in the x or y directions for different Si x Ge 1-x alloys. Here, fifteen alloys with different concentrations of Si i.e. ‘x Si ’ are considered along with five temperature values as seen in Fig. 3. For heat flux acting normal to the glide plane, the normalized Peach-Koehler force is plotted against Si concentration (x Si ) in Fig. 3(a) and that for heat flux along the glide plane is plotted in Fig. 3(b). The normalization of the Peach-Koehler force for both cases is done by using the elastic values of the Peach-Koehler force of an edge dislocation near the free surface. For ‘x Si ’ greater than 0.2, the force at any given heat flux increases with the increase in ‘x Si ’ . The force for values from 0 to 0.2 is showing a steep increase when ‘x Si ’ is increasing under the application of heat flux along the glide plane and is showing an initial increase and a sudden decrease for heat flux normal to the glide plane. The increasing values of the heat flux along the glide plane corresponding to an increase in temperature difference from 300 K to 500 K show a decrease in the normalized value of the Peach- Koehler force for all ‘x Si ’. Furthermore, for increasing values of the heat flux normal to the glide plane, the normalized Peach-Koehler force has an increasing trend opposite to the case of heat flux along

the glide plane. 4. Conclusion

The present work considered Si x Ge 1-x semiconductor alloy with an edge dislocation in it subjected to thermal loads in the form of external heat flux application and the electric field induced Joule heat along the dislocation line. The XFEM has been used to numerically model the glide plane discontinuity of the perfect edge dislocation. The material properties such as lattice constant, thermal and electrical conductivity along with thermal expansion coefficient of the