PSI - Issue 61

Enes Günay et al. / Procedia Structural Integrity 61 (2024) 34–41

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E. Gu¨nay et al. / Structural Integrity Procedia 00 (2024) 000–000

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3. Numerical Examples

3.1. Single Crystal Copper Model Validation

A finite element model is constructed for single-crystal copper to validate the model parameters with the literature. The validation model is based on , where single crystal copper experiments are conducted, and a finite element model is created to examine elastic rotations in detail, which would not be possible through experiments (see e.g., Kareer et al. (2020)). The experiments in the said work apply force-controlled indentation and scratching to the copper sample, followed by a deformation-controlled FEM simulation. The magnitudes of normal and lateral forces on the indenter are found to match with the experiments. The FEM model of the single crystal copper uses the same material parameters as the polycrystal one, given in Table 2. The sample is indented by 0.247 µ m and scratched by 10 µ m with a friction coe ffi cient of 0.15 using the same Berkovich indenter geometry. Fig. 2 shows that the normal and lateral forces on the indenter are in agreement with the literature.

4

3

F N Experiment (Kareer et al., 2020) F N Simulation (Kareer et al., 2020) F N Current Study

F L Experiment (Kareer et al., 2020) F L Simulation (Kareer et al., 2020) F L Current Study

3.5

2.5

3

2

2.5

1.5

2 Force (mN)

1 Force (mN)

1.5

0.5

1

0

40

42

44

46

48

50

40

42

44

46

48

50

Scratch distance ( m)

Scratch distance ( m)

(a) Normal Force

(b) Lateral Force

Fig. 2: Reaction forces on the indenter from numerical simulations of single crystal copper, compared with Kareer et al. (2020)

3.2. Polycrystal Examples

In this section, we present a comparative analysis of numerical simulations involving specimens characterized by three distinct average grain diameters: 5 µ m , 15 µ m , and50 µ m . The indentation and scratching pattern is set to be the same in every case, such that the grain size e ff ects can be examined while mitigating the influence of other factors. Fig. 3 shows the normalized normal and lateral forces, F N and F L , on the indenter. The normalization is done by dividing the net reaction forces on the indenter by total surface area of the Berkovich indenter. It is found that the specimens with smaller grain diameters create a larger load on the indenter, hence, are stronger and harder to deform. Notably, the specimen with a 5 µ m average grain diameter, on average, imparts a load 62% greater on the indenter in the normal direction compared to its 50 µ m counterpart during the scratching step (between t = 1 and t = 1.75). Similarly, this increase in load on the indenter is 57% in the lateral direction. These results align with the anticipated behavior that metallic materials with smaller grains show a stronger constitutive response due to intrinsic size e ff ects, and shed some light into the e ff ect of grain size on nanoscratching tests under conditions where the only variable is the average grain diameter. The apparent friction coe ffi cient, which is the sum of ploughing friction coe ffi cient and adhesive friction coe ffi cient, is calculated from the ratio of normal and lateral forces on the indenter using the following relation (see e.g. Subhash and Zhang (2002), Chamani and Ayatollahi (2018)),

F L F N

(9)

µ app = µ pl + µ ad =