PSI - Issue 43

Tatyana Petrova et al. / Procedia Structural Integrity 43 (2023) 83–88 Author name / Structural Integrity Procedia 00 (2022) 000 – 000

86 4

3. Results and discussion The geometrical and mechanical parameters of the considered nanocomposite structure (Fig. 1) WS 2 /SU8/PMMA are: l =7.10 -6 (m), E (1) =272 (GPa), E (a) =2 (GPa), E (2) =3.5 (GPa), v (1) =0.22, v (a) =0.22, v (2) =0.35. The model solutions for the axial stress Case 1 (real roots) – Eq. (1) and Case 2 (complex roots) – Eq. (2), depend on the layer’s thickness (see Table 1). For the model stress calculation and figures preparation, Mathcad Prime v.6.0 and Sigma Plot, v.13.0 have been used. The discriminant of quadratic equation and its roots are listed in Table 1 along with the geometrical characteristics for the both Cases. Table 1. Values of geometrical parameters and other characteristics of the obtained model solutions Case 1 and Case 2 of the considered nanocomposite structure. Case h 1 , (m) h a , (m) h 2 , (m) ± (1.009*10 6 ± i 7.196*10 5 ) In Fig.2 the plots (2D and 3D) of calculated axial, shear and peel (normal) stresses for Case 1 are presented in each of the layers of considered nanocomposite – at first row for WS 2 , at second for adhesive SU-8, and at third one – for substrate PMMA, all at constant axial tension load 0 3 GPa  = . One of the model assumption suggests that axial stress in the adhesive layer is smallest in respect to the axial stresses in other layers and it is taken to be 0. All axial stresses are functions of x only, shear and peel are functions of x and y. To the best of the author's knowledge, this type of graphics is published for the first time for the WS 2 /SU-8/PMMA nanostructure. 11-05-2022, stresses WS2/SU8/PMMA/ POSITIVE ROOTS l=7 microna, h1=0.65e-09m, ha=2e-08 m, h2=5e-07, sigma0=3e+09 Pa, 12-05-2022, stresses WS2/SU8/PMMA/ POSITIVE ROOTS l=7 microna, h1=0.65e-09m, ha=2e-08 m, h2=5e-07, sigma0=3e+09 Pa, 12-05-2022, stresses WS2/SU8/PMMA/ POSITIVE ROOTS l=7 micron , h1=0.65e-09m, ha=2e-08 m, h2=5e-07, sigma0=3e+09 Pa, Discriminant of the quadratic equation Roots of the biquadratic characteristic equation Case 1 Case 2 0.65*10 -9 0.65*10 -9 2*10 -8 2*10 -8 1*10 -7 1*10 -5 4.855*10 28 -8.43*10 28 ± 1.65*10 7 ; ± 7.212*10 6

6e+6

2.5e+11

-1e+6 0 1e+6 2e+6 3e+6 4e+6 5e+6 6e+6

-1.5e+8 -1.0e+8 -5.0e+7 0.0 5.0e+7 1.0e+8 1.5e+8

1.5e+8

5e+6

2.0e+11

1.0e+8

4e+6

5.0e+7

3e+6

1.5e+11

yy , Pa

0.0

1 xy , Pa

2e+6

1

1 , Pa

1.0e+11

-5.0e+7

1e+6

-1.0e+8

5.206e-7

0

5.0e+10

5.206e-7

5.205e-7

5.205e-7

5.204e-7

5.204e-7

5.201e-7 12-05-2022, stresses WS2/SU8/PMMA/ POSITIVE ROOTS l=7 microna, h1=0.65e-09m, ha=2e-08 m, h2=5e-07, sigma0=3e+09 Pa, 5.202e-7 5.203e-7 Y1, m -1e+6 1e-6 2e-6 3e-6 4e-6

-1.5e+8 12-05-2022, stresses WS2/SU8/PMMA/ POSITIVE ROOTS l=7 microna, h1=0.65e-09m, ha=2e-08 m, h2=5e-07, sigma0=3e+09 Pa, 1e-6 2e-6 3e-6 4e-6

5.203e-7

5.202e-7

Y1, m

5.201e-7

0.0

5e-6 6e-6

5.200e-7

5e-6 6e-6

5.200e-7

7e-6

0

2e-6

4e-6

6e-6

7e-6

x, m

x, m

x, m

1.5e+8

4e+8

-1e+8 0 1e+8 2e+8 3e+8 4e+8

1.0e+8

3e+8

X-7microna vs sigma1, s0=3e+09

5.0e+7

2e+8

0.0

a xy , Pa

a yy , Pa

1e+8

-5.0e+7

0

-1.0e+8

5.2e-7

5.1e-7 12-05-2022, str sses WS2/SU8/PMMA/ POSITIVE ROOTS l=7 microna, h1=0.65e-09m, ha=2e-08 m, h2=5e-07, sigma0=3e+09 Pa, 5.2e-7

6e-6 12-05-2022, stresses WS2/SU8/PMMA/ POSITIVE ROOTS l=7 microna, h1=0.65e-09m, ha=2e-08 m, h2=5e-07, sigma0=3e+09 Pa, -1e+8 1e-6 2e-6 3e-6 4e-6

0 12-05-2022, stresses WS2/SU8/PMMA/ POSITIVE ROOTS l=7 microna, h1=0.65e-09m, ha=2e-08 m, h2=5e-07, sigma0=3e+09 Pa, 2e-6 4e-6 -1.5e+8

YA, m

5.1e-7

5e-6 6e-6

5.0e-7

7e-6

x, m

x, m

3.05e+9

1.5e+8

-1.5e+8 -1.0e+8 -5.0e+7 0.0 5.0e+7 1.0e+8 1.5e+8

1.4e+9

-2.0e+8 0.0 2.0e+8 4.0e+8 6.0e+8 8.0e+8 1.0e+9 1.2e+9 1.4e+9

3.00e+9

1.2e+9

1.0e+8

1.0e+9

2.95e+9

5.0e+7

8.0e+8

2.90e+9

6.0e+8

0.0

yy , Pa

xy , Pa

, Pa

2.85e+9

4.0e+8

-5.0e+7

2.0e+8

2.80e+9

0.0

5e-7

5e-7

-1.0e+8

2.75e+9

4e-7

4e-7

3e-7

3e-7

-2.0e+8

2e-7

1e-6 2e-6

2e-7

-1.5e+8

1e-7

2.70e+9

Y2, m

Y2, m

3e-6 4e-6

1e-6 2e-6 3e-6

1e-7

4e-6 5e-6 6e-6

0

0

2e-6

4e-6

6e-6

5e-6

7e-6

6e-6

x, m

7e-6 0

x, m

x, m

Fig. 2. Visualization of the model stresses in the layers of considered WS 2 /SU-8/PMMA, for Case 1.