Strength of adhesive contacts: Influence of contact geometry and material gradients
The strength of an adhesive contact between two bodies can strongly depend on the macroscopic and microscopic shape of the surfaces. In the past, the influence of roughness has been investigated thoroughly. However, even in the presence of perfectly smooth surfaces, geometry can come into play in form of the macroscopic shape of the contacting region. Here we present numerical and experimental results for contacts of rigid punches with flat but oddly shaped face contacting a soft, adhesive counterpart. When it is carefully pulled off, we find that in contrast to circular shapes, detachment occurs not instantaneously but detachment fronts start at pointed corners and travel inwards, until the final configuration is reached which for macroscopically isotropic shapes is almost circular. For elongated indenters, the final shape resembles the original one with rounded corners. We describe the influence of the shape of the stamp both experimentally and numerically.
Numerical simulations are performed using a new formulation of the boundary element method for simulation of adhesive contacts suggested by Pohrt and Popov. It is based on a local, mesh dependent detachment criterion which is derived from the Griffith principle of balance of released elastic energy and the work of adhesion. The validation of the suggested method is made both by comparison with known analytical solutions and with experiments. The method is applied for simulating the detachment of flat-ended indenters with square, triangle or rectangular shape of cross-section as well as shapes with various kinds of faults and to “brushes”. The method is extended for describing power-law gradient media.
Keywordsadhesion boundary element method (BEM) flat-ended indenters gradient media
Authors acknowledge the aßsistance of C. Jahnke in conduction of experiments and very useful discussions of adhesion with gradient media with M. Heß and E. Willert. This work has been conducted under partial financial support from DFG (Grant number PO 810/22-1).
Contributions of authors: R. Pohrt built the experimental setup and processed the experimental data. R. Pohrt and Q. Li executed the numerical simulations. Theoretical analysis was carried our primarily by V. L. Popov. All authors contributed equally to the writing of the manuscript.
- Landau L D, Lifshitz E M. Statistical Physics, Pt. 2, (Volume 9 of the Course of Theoretical Physics). Oxford: Pergamon Press, 1980Google Scholar
- Kendall K. Molecular Adhesion and Its Applications. New York (US): Springer Science & Business Media, 2001Google Scholar
- Pohrt R, Popov V L. Adhesive contact simulation of elastic solids using local mesh-dependent detachment criterion in Boundary Elements Method. Facta Universitatis, Series: Mechanical Engineering 13(1): 3–10 (2015)Google Scholar
- Hulikal S, Bhattacharya K, Lapusta N. A threshold-force model for adhesion and mode I fracture. arXiv:1606.03166.Google Scholar
- Rey V, Anciaux G, Molinari J-F. Normal adhesive contact on rough surfaces: efficient algorithm for FFT-based BEM resolution. Comput Mech, DOI: 10.1007/s00466-017-1392-5 (2017)Google Scholar
- Li Q, Popov V L. Boundary element method for normal non-adhesive and adhesive contacts of power-law graded elastic materials. arXiv:1612.08395 (2016)Google Scholar
- Argatov I I, Li Q, Pohrt R, Popov V L. Johnson-Kendall- Roberts Adhesive Contact for a Toroidal Indenter. Proceedings of the Royal Society of London, Series A 472(2191): (2016)Google Scholar
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