Normal Contact Analysis Between Two Self-affine Fractal Surfaces at the Nanoscale by Molecular Dynamics Simulations

Abstract

This work attempts to investigate contact between two self-affine fractal surfaces with one being of a rigid solid and other of a FCC deformable body. A normal contact model between two self-affine fractal surfaces at the nanoscale is established. Effects of surface morphology on contact force, atomic structure, dislocation with normal displacement are investigated by simulating the contact process of self-affine surfaces. Results show that the normal force for rougher surfaces at initial contact yields the larger negative extremum due to effects of surface morphology on interatomic repulsion and attraction. Furthermore, the atomic structure change proportion varies monotonically with normal displacement whereas effects of surface morphology can be approximately ignored. However, the phase transition generated by too large atomic slip leads to a non-monotonic variation between total dislocation lines length and normal displacement. Differences in contact ratio-separation dependence between the classical micro-asperity model and the established model are compared.

Graphical Abstract

Appendix A

A system of two contacting rough surfaces can be considered as an equivalent system of a flat deformable surface with an effective elastic modulus E*. The effective elastic modulus E* can be written as,

$$E^{*} = \left[ {\left( {1 - \nu_{1} } \right)^{2} /E_{1} + \left( {1 - \nu_{2} } \right)^{2} /E_{2} } \right]^{ - 1},$$

(A1)

where v₁, v₂, and E₁, E₂ are the Poisson’s ratios and elastic modulus of the two interacting surfaces, respectively.

In the contact analysis of fractal surfaces, the real contact area A_r depends on the contact state, which is judged according to the relationship between the critical micro contact area a_c' and the largest truncated micro contact area a_L'. When a_L' ≤ a_c', all microcontacts are in the fully plastic contact state, thus,

$$A_{r} = \left( {\frac{D - 1}{{3 - D}}} \right)a_{L}^{\prime }$$

(A2)

when a_L' > a_c', both elastic and fully plastic microcontacts exist at the interface, and the real contact area A_r is given by,

$$A_{r} = \left( {\frac{D - 1}{{6 - 2D}}} \right)\left[ {1 + \left( {\frac{{a_{c}^{\prime } }}{{a_{L}^{\prime } }}} \right)^{{\left( {3 - D} \right)/2}} } \right]a_{L}^{\prime }$$

(A3)

The critical micro contact area a_c' is expressed as follows,

$$a_{c}^{\prime } = \left[ {\frac{{2^{{\left( {11 - 2D} \right)}} }}{{9\pi^{{\left( {4 - D} \right)}} }}G^{{\left( {2D - 4} \right)}} \left( {\frac{{E^{*} }}{H}} \right)^{2} \ln \gamma } \right]^{{1/\left( {D - 2} \right)}}$$

(A4)

The largest truncated micro contact area a_L' at a given mean surface separation distance d can be determined from the total truncated area S' of the equivalent rough surface, by

$$S^{\prime} = \left( {\frac{D - 1}{{3 - D}}} \right)a_{L}^{\prime }$$

(A5)

The total truncated area S' can be determined from numerical integration of the truncated areas of the rough surface. The material properties are listed in Table 2.

Table 2 Materials properties used in Komvopoulos's model