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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indentation. Fig. 4a clearly shows that at a small depth H=R and a large probe shift L= 10 R the interaction has basically horizontal (lateral) character, that is, the vertical component has a small value. However, with the same shift L= 10 R , but a greater depth H>R (Fig. 4b), the vector of the force, which is the contribution from the presence of the inclusion in the material, increases its inclination. The vertical component, judging by the calculations, also increases, despite the fact that the modulus of the vector, obviously, becomes smaller.

Fig. 5. Dependence of the relative stiffness of the material K/K 0 on the probe displacement L/R . The color indicates the different depths of the inclusion. Inclusion radii R V =15 R and R V =30 R. For larger inclusions (Fig. 5), the same character of the K/K 0 ( L/R ) curves is observed and the same effects are observed when the probe is displaced larger than the radius of the inclusion (but due to the greater shift, the effect decreases). Another, more important question arises. Can we distinguish particles with different combinations of parameters? For example, if one of them is small and shallow, and the other is large and located at great depth. Let's compare the plots pairwise for particles with a radius of 5 R and 10 R at depths R and 10 R , as well as for particles with a radius of 10 R and 15 R at depths 2.5 R and 10 R (Fig. 6).

Fig. 6. Comparison of the K/K 0 ( L/R ) dependences for particles with different combinations of parameters and approximately the same stiffness value for central ( L/R =0) indentation. As you can see, despite the fact that with the central ( L/R =0) indentation the values of the relative stiffness are approximately the same, there are significant qualitative differences in the character of the curves. It is noticeable that the smaller the particle, and it is closer to the surface, the sharper the behavior of the curve we observe in the graphs. In practice, this means that we will see a similar picture on the hardness map of AFM data.