PSI - Issue 43

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

84 2

1. Introduction As a member of layered transition-metal dichalcogenide compounds (LTMDCs) of TX2 type (T = Mo, W, Nb, Re, Ti, Ta, etc., X = S, Se, Te, etc.) family, tungsten disulphide (WS 2 ), is composed of two-dimensional S-W-S sheets stacked on the top of one another. Each sheet is tri-layered with a W atom in the middle that is covalently bonded to six S atoms located in the top and bottom layers (Li et al. 2017). Understanding the mechanical properties of two dimensional (2D) TMDs is essential to harness their full potential for applications, such as in strain engineering and flexible field-effect transistors (FET). 2D WS 2 draw increasing attention due to its attractive properties deriving from the heavy tungsten and chalcogenide atoms, but its mechanical properties are still mostly unknown, as was reported in (Falin et al. 2021). In this work, using a complementary suite of experiments and theoretical calculations, volumetric Young modulus of high – quality monolayer WS 2 of 302.4±24.1 GPa and Poisson ratio of 0.22, were obtained. Falin et al. (2021) also have measured the ultimate strain for monolayer WS 2 and reported the impressive value of 19.8±4.3%. The most of the mechanically exfoliated atomically thin WS 2 and WSe 2 were found much more stable in the air-aging exposure than the chemical vapour deposition (CVD)- and Molecular beam epitaxy (MBE)-grown samples. Other researc hers obtained the 3D Young’s modulus and Poisson ratio of CVD -grown monolayer WS 2 measured by indentation as 272±18 GPa and 0.22 respectively, according to Liu et al . (2014). For one of the polytypes of WS 2 (with hexagonal symmetry) the calculated Young’s modulus and Poisson ratio at the ground state (0 K and 0 Pa pressure) were 133 GPa and 0.12, respectively (Li et al. 2017). In Wang (2017) the Young modulus of monolayer WS 2 was reported as 150-170 GPa, and in Wang et al. (2020) the value of 270 GPa is used, based by measured value of Liu et al. (2014). Regardless of the wide scattering in the data for elastic characteristics of WS 2 , with their superb mechanical properties, the WS 2 and WS 2 -like TMDs are promising candidates for reinforcing polymer materials (Wang 2017). Against the background of many experimental works on the properties of WS 2 , during the last years, only some research concerns modelling, predicting and controlling the stress transfer and/or strain mapping in WS 2 /polymer nanocomposites (Wang, 2017; Deng et al. 2018; Wang et al. 2020; Tang et al. 2021). In Zhang et al. (2016) a finite element (FE) model of WS 2 /PDMS sample under tensile strain has been investigated and strain relaxation with wrinkle formation is observed on the monolayer WS 2 triangular crystals at high tensile strain. Tang et al. (2021) have proposed more complex study on multiscale simulation, including density functional theory (DFT), molecular dynamic (MD) analysis, and finite element analysis (FEA), in order to analyse the WS2 mechanical properties, stress sensor and then fabricate and investigate the device for benchmarking. It was found that the proposed FEA model in this work can be used for further optimization of the device. In Wang (2017) and Wang et al. (2020) the stress transfer in exfoliated WS 2 has been examined in a model composite under uniaxial strain. It was demonstrated that the WS 2 can act as reinforcing phase in its nanocomposites and its behaviour can be predicted with shear lag theory. It was demonstrated that WS 2 still follows continuum mechanics on the microscale and that strain generates a non-uniform bandgap distribution even in a single WS 2 flake through a simple strain engineering. Our previous experience in this field (Kirilova et al. 2019, Petrova et al. 2022) have provided two analytical model solutions for the stress transfer in the graphene-polymer nanocomposites, based on the two-dimensional stress function method and minimization of complementary strain energy functional to the nanostructure. These studies include obtaining of solutions of governing fourth-order ordinary differential equation with constant coefficients for the 2D axial stress in the first layer of the structure, for two different graphene-polymer nanocomposites. The other 2D stresses in the structure’s layers are expressed and calculated as functions of this axial one and its derivatives. Now, in this work, the abovementioned method was used for modelling of stresses in three-layer WS 2 /SU-8/PMMA nanocomposite subjected t o a static extension load. Using two different geometries for the layer’s thicknesses, for the first time, the axial, shear and normal stresses in all layers of the considered nanocomposite are modelled and investigated. At the end, the model results for axial stress in WS 2 was compared with shear – lag results in Wang, 2017 and show very good agreement in elastic region of applied tension load.