Periodic Reporting for period 4 - ShapingRoughness (Emergence of Surface Roughness in Shaping, Finishing and Wear Processes)
Reporting period: 2022-08-01 to 2023-01-31
Rough surfaces are everywhere in our environment. While we may perceive some as smooth when we look at them or touch them, there is hardly any natural or artificial surface that is not rough at some scale. The size of features varies drastically, from micrometer-sized asperities and cracks on polished surfaces of household devices, through millimeter scale bumps and pores on construction materials, up to several hundred meters high crags and crevasses in mountain ranges on the surface of the earth. A remarkable feature is that rough surfaces are often self-affine, meaning that if we zoom in on a part of the surface, we see similar features as on the full surface, but at a different scale. Self-affine scaling has been observed from atoms to mountains, spanning 15 orders of magnitude in length.
Since most of the surfaces around us appear self-affine, this opens the question how this self-affinity emerges. One plausible origin of self-affine roughness is plastic (irreversible) deformation during formation and processing of the body. Necessarily, as a body is deformed the surface of this body is deformed, too, and therefore stores the spatial signature of the microscopic mechanisms of deformation. It could then be spatial correlations in these deformation mechanisms which lead to a self-affine topography.
The central goal of this project was to investigate this connection between plastic deformation and roughening. A thorough understand of this connection would allow us to engineering surfaces with specific roughness – and hence specific function. Computer simulations that are idealized version of our reality were carried out to determine whether plastic deformation alone could cause self-affine roughening of the surface of a range of materials. The simulations itself were carried out at atomic scales (where the simulated object is an individual atom) and at “mesoscopic” scales, where an empirical law for plastic yielding of the material is prescribed. The idea is that atomic-scale models are proper representation of reality and can be regarded as a computer experiment, while mesoscale models allow us to test hypotheses on connections between deformation mechanism and roughness.
Since most of the surfaces around us appear self-affine, this opens the question how this self-affinity emerges. One plausible origin of self-affine roughness is plastic (irreversible) deformation during formation and processing of the body. Necessarily, as a body is deformed the surface of this body is deformed, too, and therefore stores the spatial signature of the microscopic mechanisms of deformation. It could then be spatial correlations in these deformation mechanisms which lead to a self-affine topography.
The central goal of this project was to investigate this connection between plastic deformation and roughening. A thorough understand of this connection would allow us to engineering surfaces with specific roughness – and hence specific function. Computer simulations that are idealized version of our reality were carried out to determine whether plastic deformation alone could cause self-affine roughening of the surface of a range of materials. The simulations itself were carried out at atomic scales (where the simulated object is an individual atom) and at “mesoscopic” scales, where an empirical law for plastic yielding of the material is prescribed. The idea is that atomic-scale models are proper representation of reality and can be regarded as a computer experiment, while mesoscale models allow us to test hypotheses on connections between deformation mechanism and roughness.
To understand the formation of roughness from plastic deformation, we used a simple model system: A periodic slab of material with two free surfaces that is biaxially compressed. In atomic scale models, the simplest realization is a pure single crystal, but we also studied a high-entropy alloy and a metallic glass to introduce different amounts of disorder. The atomic-scale calculations were carried out on systems in excess of 50 million atoms, with lateral dimensions on the order of 100 nm. Calculations of this size are at the limit of what is possible on present-day computers but were necessary to extract information on the statistical properties of the emerging roughness. These molecular simulations of biaxial compression showed the emergence of roughness for these three materials under various loading conditions. In particular, roughness emerged at atomically flat interfaces beyond the yield point of the material. The rough topography is imprinted at yield and is reinforced during subsequent deformation. Crucially, these simulations not only allow evaluation of the emerging surface topography, but they also allow a detailed inspection of the subsurface displacement field. We were able to show that the topography is nothing but a fingerprint of the structure of the larger subsurface deformation during flow of a solid body.
These atomic-scale simulations are like an experiment and do not intrinsically tell us why the specific self-affine structure of roughness emerged. However, they do allow insights into subsurface deformation fields that are difficult to obtain experimentally, and allowed us to connect this deformation to surface roughness. In order to gain further understanding about the origin of self-affinity, the proposal suggested mesoscale continuum models where the mechanism behind the individual plastic flow event can be controlled. Those continuum models require efficient solvers for large simulation domains, that we developed within this project. We carried out two-dimensional and three-dimensional calculations of this character. The marked difference between these is that in two dimensions, we see clear emergence of shear bands. The ensuing surface roughness does look self-affine, but with a Hurst exponent much smaller than 0.5. In contrast, the three-dimensional calculations do not emerge shear bands and the surface topography that emerges is not self-affine. The reason for the suppression of shear banding in three dimensions is that the percolation of deformation events is more difficult in three than in two dimensions.
These calculations allow a key insight into the formation of surface roughness: A discrete carrier of deformation (the shear band) is necessary for self-affinity to emerge. In the molecular calculations, this discrete carrier is either a dislocation (for crystals) or a shear transformation (for glasses). Conversely, a discrete microscopic event is intrinsically absent in most continuum models such as the one used by us. The deformation is assumed to be of a laminar nature, and this only leads to self-affine topographies and if the deformation self-organizes into shear bands. The fact that self-affine topographies are observed even on geological scales (the earth’s surface) could therefore also be related to the fact, that deformation of rocks also proceeds in shear bands - albeit at much larger (macroscopic) scales than the effects studied by us.
These atomic-scale simulations are like an experiment and do not intrinsically tell us why the specific self-affine structure of roughness emerged. However, they do allow insights into subsurface deformation fields that are difficult to obtain experimentally, and allowed us to connect this deformation to surface roughness. In order to gain further understanding about the origin of self-affinity, the proposal suggested mesoscale continuum models where the mechanism behind the individual plastic flow event can be controlled. Those continuum models require efficient solvers for large simulation domains, that we developed within this project. We carried out two-dimensional and three-dimensional calculations of this character. The marked difference between these is that in two dimensions, we see clear emergence of shear bands. The ensuing surface roughness does look self-affine, but with a Hurst exponent much smaller than 0.5. In contrast, the three-dimensional calculations do not emerge shear bands and the surface topography that emerges is not self-affine. The reason for the suppression of shear banding in three dimensions is that the percolation of deformation events is more difficult in three than in two dimensions.
These calculations allow a key insight into the formation of surface roughness: A discrete carrier of deformation (the shear band) is necessary for self-affinity to emerge. In the molecular calculations, this discrete carrier is either a dislocation (for crystals) or a shear transformation (for glasses). Conversely, a discrete microscopic event is intrinsically absent in most continuum models such as the one used by us. The deformation is assumed to be of a laminar nature, and this only leads to self-affine topographies and if the deformation self-organizes into shear bands. The fact that self-affine topographies are observed even on geological scales (the earth’s surface) could therefore also be related to the fact, that deformation of rocks also proceeds in shear bands - albeit at much larger (macroscopic) scales than the effects studied by us.
The most significant scientific outcome is our atomic-scale simulation results on the emergence of surface roughness in plasticity. Our simulations clearly show that self-affine roughness emerges because of the intrinsic non-affine nature of plastic flow in materials. We showed that this is independent of whether the material is ordered (crystalline) or disordered (in the extreme case amorphous). This debunks the common hypothesis that roughness is due to material heterogeneity. Heterogeneity is clearly not necessary for self-affinity to emerge. Indeed, our continuum calculations clearly show that heterogeneous materials that flow in a laminar fashion do form roughness on exposed interfaces, but that roughness is not of a self-affine nature.
The most significant nonscientific (infrastructural) outcome is a central cloud-based database for topography data. Within this project, we were able to build this database using modern web technologies and mold the underlying code base into a sustainable development effort. The code is available under an open-source license at https://github.com/ContactEngineering/(opens in new window) and the cloud service itself is deployed at https://contact.engineering/(opens in new window). The service supports publication of topography data under the assignment of a digital object identifier (DOI). This cloud service is not just a data management tools (and a place to publish topography data) but also an analysis/analytics platform. The platform makes a range of analysis methods available to non-experts. This includes complex boundary element simulations for estimating functional properties of the rough topography, such as the real area of contact and the contact stiffness.
The most significant nonscientific (infrastructural) outcome is a central cloud-based database for topography data. Within this project, we were able to build this database using modern web technologies and mold the underlying code base into a sustainable development effort. The code is available under an open-source license at https://github.com/ContactEngineering/(opens in new window) and the cloud service itself is deployed at https://contact.engineering/(opens in new window). The service supports publication of topography data under the assignment of a digital object identifier (DOI). This cloud service is not just a data management tools (and a place to publish topography data) but also an analysis/analytics platform. The platform makes a range of analysis methods available to non-experts. This includes complex boundary element simulations for estimating functional properties of the rough topography, such as the real area of contact and the contact stiffness.