PSI - Issue 32

R.I. Izyumov et al. / Procedia Structural Integrity 32 (2021) 87–92 Author name / Structural Integrity Procedia 00 (2019) 000–000

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The subject of this work was filled polymer nanocomposites. The aims of the work were: 1) to simulate the process of indentation of an AFM probe into a structurally inhomogeneous material, 2) to obtain data on the force required for penetration, 3) in an attempt to relate this response to the parameters of inclusions and their location in the surface layer of the material. The solution of this problem will make it possible to study not only the surface of the nanocomposite, but also the subsurface structure. As a result, it becomes possible to significantly expand information on the structure of the material on the same base of experimental data obtained using atomic force microscopy. 2. Finite element model The model describes the interaction of a rigid parabolic probe with a nonlinear elastic material. The material was considered incompressible ( λ 1 λ 2 λ 3 = 1). The mechanical properties were described by the Neo-Hookean potential w = E /6( λ 1 + λ 2 + λ 3 – 3), where E is the initial modulus of elasticity of the material. The inclusion was rigid, and its size was determined by the radius R v . At the interface between the probe and the sample, the condition of complete adhesion without slipping during loading was specified. The lower boundary of the sample was rigidly fixed. The nonlinear elastic problem was solved by the finite element method in a two-dimensional formulation for the case of generalized plane deformations. The calculations were carried out using the ANSYS software package. Convergence research work was carried out, as a result of which we chose a FE mesh, consisting of approximately 30,000 elements and 100,000 nodes. An irregular mesh was used, the elements of which near the probe and inclusion particles had a size of 0.2R-0.3R. 8-node biquadratic elements were used.

Fig. 2. The model consists of three elements: a rigid parabolic AFM probe with a tip curvature radius R, an incompressible nonlinear elastic sample with height 150 R and width 400 R , a rigid inclusion of radius R v located at a depth H and with a horizontal displacement L relative to the probe axis. The probe geometry is described by the equation y=x 2 /2 R , where R is the curvature radius of the probe tip. For the probe, vertical displacements were specified towards the material u= 10 R . The inclusion position was determined by the parameters: H is the distance from the surface of the material to the upper point of inclusion, L is the shift of the indenter position relative to the center of inclusion (Fig. 2). The following combinations of parameters were considered: 3 cases of the probe position relative to the center of inclusion ( L= 0, L= 5 R , L= 10 R ), 2 cases of the inclusion size ( R v =5 R and R v =10 R ); 2 cases of inclusion depth ( H= 5 R and H= 10 R ).