PSI - Issue 43

Elisaveta Kirilova et al. / Procedia Structural Integrity 43 (2023) 282–287 Author name / Structural Integrity Procedia 00 (2022) 000 – 000

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3. Results and discussion The geometrical and mechanical parameters of the considered nanocomposite structure (Fig. 1) WS 2 /SU-8/PMMA are: l =10 μm , E (1) =270 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 ISS noted as Case 1 (real roots) – Eq. (8) and Case 2 (complex roots) – Eq. (10), depend on the thicknesses of the substrate and adhesive layer (see Table 1). For model stress calculation and graphics representation, 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 parameters of the layers for the both Cases. Table 1. Values of geometrical parameters of the obtained model ISS in the adhesive layer of the considered WS 2 /SU-8/PMMA structure. Case h 1 , (m) h a , (m) h 2 , (m) Discriminant of the quadratic equation Roots of the biquadratic characteristic equation Case 1 0.65x10 -9 2x10 -8 1x10 -7 1.095x10 31 ±5.919 x10 7 ; ± 1.395x10 7 Case 2 0.65x10 -9 2x10 -8 1x10 -5 -8.43x10 24 1.009x10 6 ± i 7.196x10 5 ; -1.009x10 6 ± i 7.196x10 5 Firstly, the ISS values, when varying the magnitude of the applied static tension load at constant values of the geometric properties of the materials have been calculated. The obtained results for both cases are presented in Fig. 2 and Fig. 3. For both Cases the considered length of the nanocomposite structure is 10 μ m and the critical value of shear strength for the adhesive – 30 MPa (red lines in Fig. 2 and Fig. 3).

Fig. 2. Influence of the magnitude of applied load σ 0 on the

Fig. 3. Influence of the magnitude of applied load σ 0 on the ISS in the adhesive layer, for Case 2.

ISS in the adhesive layer, for Case 1.

For the Case 1, when applying mechanical load lower than σ 0 ≤ 5 GPa, a delamination of the tungsten disulphide layer does not appear, (Fig. 2). For the Case 2 with the thicker PMMA layer, a delamination of the WS 2 layer occurs when apply mechanical load of σ 0 ≥ 1.175 GPa, (Fig. 3). The obtained value for debond length for this case by Eq. (11) is 1 μm . Then a parametric analysis has been performed at a fixed mechanical load, calculating the values of the ISSs varying the length of the considered nanocomposite structure. The results obtained for the critical values for the magnitudes of the applied mechanical load, over that a delamination occurs (Case 2), are listed in Table 2.

Table 2. Critical values for the magnitudes of applied mechanical load, over which a delamination occurs at different length of the nanocomposite structure. l, (μm) 5 10 15 20 25 30 σ 0 , (GPa) σ 0 ≥ 1.165 σ 0 ≥ 1.175 σ 0 ≥ 1.17 σ 0 ≥ 1.175 σ 0 ≥ 1.27 σ 0 ≥ 1.455

It can be seen from Table 2 that for case 2 (structure with thicker PMMA layer) with increasing length of WS 2 , delamination occurs at increasingly higher values of the applied external load. In the next Fig. 4 is presented how the debond length value changes with increasing length of the considered nanostructure for Case 2. It can be concluded that the value of debond length slightly increases with increasing the structure length, at fixed applied load.