PSI - Issue 23

Atsushi Kubo et al. / Procedia Structural Integrity 23 (2019) 372–377 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

374

3

(a)

(b)



 t

 t

t > 0







 t

wurtzite (2H)

zincblende (3C)

[0001] 4H

 t

[0001]

[001]

 t < 0



[010]

[2¯1¯10] [01¯10]

[100]

[2¯1¯10] [01¯10]

Fig. 1. (a) Examined crystal structures of SiC, GaN and AlN; (b) Schematic illustration of multiaxial deformation by uniaxial tensile strain  and transverse tensile/compressive stresses  t .

Tensile strain  was incrementally applied along one direction (typical crystal orientation listed in Table 1) under several transverse stress conditions  t [Fig.1(b)]. For each strain increment, atomic positions were relaxed until the total energy converged within 10  4 eV. Simultaneously, the transverse stress components were controlled to a predetermined target value  t by adjusting cell sizes perpendicular to strain direction, so that the deviations of transverse stresses from  t became less than 100 MPa. The ideal strength  c is determined as the maximum value of tensile stress  along tensile strain direction, where an unstable structural change is expected. Figure 2 shows tensile stress-strain relationships of SiC, GaN and AlN polytypes under uniaxial strain without transverse stresses (i.e.,  t = 0). The equivalent crystal orientations are indicated with a same symbol and color. For all the materials examined, similar tendencies are observed: 1. The ideal tensile strengths  c (the maximum point in the stress-strain curve) vary with the direction of tension, indicating a clear anisotropy in the ideal strength, while the elastic moduli E (the slope of the stress-strain curve) exhibit only slight variations. It is interesting that, all three materials with the zincblende (3C) structure have considerably high strengths  c against  100  tension, compared with those along other directions. Thus, fracture regarding  100  tension is unlikely to occur in the realistic systems; even if uniaxial tension is loaded along [100] direction, indeed other fracture modes may be activated before stress along [100] reaches  c . 2. The stress-strain behaviors of equivalent crystal orientations are similar to each other. For example, stress strain relationships of 2H-SiC under  2110  tension, 3C-SiC under  110  tension and 4H-SiC under  2110  tension are almost equal [shown with green points and curves in Fig.2(b)]. 3. Under no transverse stress  t applied (i.e., uniaxial stress condition), fracture occurs by bond breaking at the critical point in all the cases. Figures 3 show the ideal strengths  c as functions of the transverse stress  t for polytypes of SiC, GaN and AlN. Regardless of the material types, the whole trends of the  t -  c relationships are similar. The difference in crystal structure has only a marginal effect on  c if the deformation direction is crystallographically equivalent, as well as on the stress-strain relationships under uniaxial tension. In all the cases with high tensile transverse stress (  t > 0),  c decreases as  t increases, and all the  t -  c curves are expected to converge to the point (  t ,  c ) = (  c iso ,  c iso ), where  c iso denotes the ideal tensile strength under isotropic tension and all deformation types become equivalent. Under compressive transverse stress (  t < 0), there are two categories of fracture type as follows: 1. A fracture is caused by bond breaking in the similar manner to the case of uniaxial strain condition (  t = 0), typically found in  0001  -tension on wurtzite and  111  -tension on zincblende structures for all materials. In this case, the effect of  t on  c is relatively small (  c slightly increases as |  t | increases). 3. Results and Discussion