{"id":651,"date":"2015-09-06T23:03:47","date_gmt":"2015-09-07T03:03:47","guid":{"rendered":"http:\/\/tasharp.com\/?p=651"},"modified":"2017-10-09T18:30:42","modified_gmt":"2017-10-09T22:30:42","slug":"651","status":"publish","type":"post","link":"https:\/\/tasharp.com\/index.php\/651\/","title":{"rendered":"Contact properties of rough solids: all about the Gap"},"content":{"rendered":"

Essentially all materials have rough surfaces at small scales. This can be a problem for engineers designing electrical contacts, thermal contacts, or seals to prevent leaks, since the roughness creates gaps between the two contacting surfaces. By increasing the pressure, the two solids can be forced closer together, reducing the gaps somewhat, but some space between the surfaces usually still remains.<\/p>\n

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Two blocks in compression may appear to be in full contact, but there is nearly always microscopic roughness that leads to gaps. \u00a0For randomly-rough geometries, only \"\nabla, the root-mean-squared slope of the surface, determines the microscopic contact area, for an applied force on the block, \"F_N\", made of material with Young’s modulus \"E\".<\/figcaption><\/figure>

Work with Mark O. Robbins quantified how surprisingly resilient the gaps are, and how important they are in determining the contact properties. To analyze the problem, we had to overcome technical challenges related to the large range of length scales of random-rough geometry on typical material surfaces, usually millimeters down to atomic scales. \u00a0The rough geometry can be modeled using the mathematics of random (self-affine) fractals. \u00a0Large-scale parallel processing on a computing cluster is required to simulate and analyze contact between many random realizations of rough 3D cubes of length 1000 atoms on a side. \u00a0We worked with Lars Pastewka to write C++ code for GPUs to do fast simulations using lattice Greens functions and continuum-elastic Greens functions, which will be described in a later post.<\/p>\n

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Small example region of contact at the atomic scale for two similar surfaces, a bent lattice and a stepped lattice. \u00a0If the material can yield, stepped surfaces produce more plasticity and lead to increased contact area (dark atoms).\u00a0 The amount of increase is given by \"\nabla.\u00a0 However, \"\nabla must be very large to enter the limiting plastic regime, where the contact area is the applied force over the material yield stress.<\/figcaption><\/figure>

We found that the large-scale features of the material’s surface get flattened more easily, but the small-scale roughness cannot be squeezed away even at considerable pressures; we found that the fraction of the surface that is in contact is well-defined and at common pressures is less than 20%. \u00a0Within this regime the fractional contact area obeys a simple law: \"f_A, where \"p\" is the confining pressure, \"E'=E\/(1-\nu^2)\" is the material’s contact modulus, \"\nu\" is the effective Poisson ratio, \"E\" is the material’s Young’s modulus, and \"\nabla is the root-mean-squared slope of the original roughness profile[1]. \u00a0\"\kappa\" is a dimensionless constant with value about 2.2.<\/p>\n

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Atoms on the surface of a solid are colored red if they experience a repulsive force from the opposing surface. The statistical properties of the contact and pressure spatial distributions change with atomic scale features.<\/figcaption><\/figure>

We considered this problem with both continuum-scale and atomic-scale simulations. \u00a0We found that the continuum results can often be applied to small scales, meaning that continuum analyses are often appropriate for nanotechnology applications[2]. \u00a0At the atomic-scale, the concept of contact area gets replaced by the number of atoms that exert repulsive forces on the other surface. \u00a0However, for very rough or crystalline surfaces, atomic-scale plasticity causes the value of \"\kappa\" in the above equation to increase, up to a value of 10.0. \u00a0We went on to analyze the transition from elastic to plastic contact with roughness.<\/p>\n

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The gap (here quantified by the mean surface separation \"\bar{u}\") approaches zero as the log of applied force \"F\". When \"\bar{u}\" is normalized by surface rms height \"h_{rms}\" and \"F\" is normalized by the product of macroscopic contact area and contact modulus, \"A_0, the result collapse for different symbols, corresponding to continuum and atomistic simulations with varying roughness parameters.\u00a0 The lowest forces correspond to effects from our simulations having limited size, while the regime with slope \"\gamma\" corresponds to an exponential relationship between applied pressure and the gap size.<\/figcaption><\/figure>

Even if the contacting materials are very stiff, they can seem much less so because of the gap from roughness at the contacting surface; the rough topography can be compressed more easily than the solid material. \u00a0For both atomic and continuum analyses, the average gap width, \"\bar{u}\" decreases slowly with force. \u00a0We quantified this and showed that at large confining force, \"F\", it follows \"\bar{u} where \"h_{rms}\" is the root-mean-squared height of the original surface, \"A_0\" is the apparent surface area. \u00a0As a result, the stiffness of the interface is \"k_I. \u00a0The stiffness of the interface is extremely low when there is no confining pressure, and so the surface roughness dominates the mechanical response of the whole two-block system.<\/p>

References:
\nChapter 5 of my thesis<\/a>\u00a0(papers in preparation)<\/p>

Sampling of the related work that helped build up this picture:<\/p>\n

 Hyun, S., et al. \"Finite-element analysis of contact between elastic self-affine surfaces.\"\u00a0Physical Review E<\/i>\u00a070.2 (2004): 026117.\r\n Pei, L., et al. \"Finite element modeling of elasto-plastic contact between rough surfaces.\"\u00a0Journal of the Mechanics and Physics of Solids<\/i>\u00a053.11 (2005): 2385-2409.\r\n Cheng, S. & Robbins, M.O. \"Defining contact at the atomic scale.\"\u00a0 Tribol Lett (2010) 39: 329. https:\/\/doi.org\/10.1007\/s11249-010-9682-5\r\n C Yang and B N J Persson 2008\u00a0J. Phys.: Condens. Matter<\/em>\u00a020<\/b>\u00a0215214\u00a0http:\/\/iopscience.iop.org\/article\/10.1088\/0953-8984\/20\/21\/215214\/\r\n Persson, B. N. J. \"Relation between interfacial separation and load: a general theory of contact mechanics.\"\u00a0Physical review letters<\/i>\u00a099.12 (2007): 125502.\r\n Mo, Yifei, Kevin T. Turner, and Izabela Szlufarska. \"Friction laws at the nanoscale.\"\u00a0Nature<\/i>\u00a0457.7233 (2009): 1116.<\/pre>\n","protected":false},"excerpt":{"rendered":"
Essentially all materials have rough surfaces at small scales. This can be a problem for engineers designing electrical contacts, thermal contacts, or seals to prevent leaks, since the roughness creates gaps between the two contacting surfaces. By increasing the pressure, the two solids can be forced closer together, reducing the gaps somewhat, but some space […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[11,14],"tags":[],"class_list":["post-651","post","type-post","status-publish","format-standard","hentry","category-physics","category-tribology"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/s5Yxym-651","jetpack-related-posts":[],"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/tasharp.com\/index.php\/wp-json\/wp\/v2\/posts\/651","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/tasharp.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/tasharp.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/tasharp.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/tasharp.com\/index.php\/wp-json\/wp\/v2\/comments?post=651"}],"version-history":[{"count":54,"href":"https:\/\/tasharp.com\/index.php\/wp-json\/wp\/v2\/posts\/651\/revisions"}],"predecessor-version":[{"id":790,"href":"https:\/\/tasharp.com\/index.php\/wp-json\/wp\/v2\/posts\/651\/revisions\/790"}],"wp:attachment":[{"href":"https:\/\/tasharp.com\/index.php\/wp-json\/wp\/v2\/media?parent=651"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/tasharp.com\/index.php\/wp-json\/wp\/v2\/categories?post=651"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/tasharp.com\/index.php\/wp-json\/wp\/v2\/tags?post=651"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}