Indentation of a plastically deforming metal crystal with a self-affine rigid surface: A dislocation dynamics study

Although indentation of elastic bodies by self-affine rough indenters has been studied extensively, little attention has so far been devoted to plasticity. This is mostly because modeling plasticity as well as contact with a self-affine rough surface is computationally quite challenging. Here, we succeed in achieving this goal by using Green's function dislocation dynamics, which allows to describe the self-affine rough surface using wavelengths spanning from 5 nm to 100 micron. The aim of this work is to gain understanding in how plastic deformation affects the contact area, contact pressure and hardness, gap profile and subsurface stresses, while the roughness of the indenter is changed. Plastic deformation is found to be more pronounced for indenters with larger root-mean-square height and/or Hurst exponent, and to be size dependent. The latter means that it is not possible to scale observables, as typically done in elastic contact problems. Also, at a given indentation depth (interference) the contact area is smaller than for the corresponding elastic contact problem, but gap closure is more pronounced. Contact hardness is found to be much larger than what reported by classical plasticity studies. Primarily, this is caused by limited dislocation availability, for which the stiffness of the deforming crystal is in between that of a linear elastic and an elastic-perfectly plastic material. When calculating hardness and nominal contact pressure, including very small wavelength in the description of the surface is not necessary, because below a given wavelength the subsurface stresses become invariant to a further decrease in true contact area. This is true for both elastic and plastic materials. Considering small wavelengths is instead required to capture accurately roughening and contact stress distribution.