Abstract
A model is proposed herein to investigate the incipient sliding of contacts in the presence of both friction and adhesion, where the interfacial response is modeled based on traction-separation laws. A Maugis-like parameter is defined to characterize the response in the tangential direction. Subsequently, the model is used to investigate the contact between a smooth cylinder and a flat body, where adhesion-friction interactions are strong. A range of behaviors are observed when a tangential displacement is imposed: When the parameter is low, the contact pressure exhibits a relatively constant profile; when it is high, a pressure spike is observed at the edge of the contact. This difference is caused by a significant interface compliance in the former case, which limits the amount of slip. The results for the mid-range values of the Maugis-like parameter can qualitatively replicate various experiments performed using polydimethylsiloxane (PDMS) balls.
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Abbreviations
- δ :
-
Characteristic length of adhesion (m)
- p :
-
Pressure (Pa)
- u :
-
Displacement (m)
- φ :
-
Work of adhesion (N/m)
- σ max :
-
Maximum interface stress in normal direction (Pa)
- τ fit :
-
Fitting for the tangential stress at onset of sliding (Pa)
- τ max :
-
Maximum interface stress in tangential direction (Pa)
- τ m :
-
Tangential stress at infinite separation (Pa)
- G :
-
Green’s functions
- a r :
-
Contact area (m)
- E :
-
Elastic modulus (Pa)
- E* :
-
Equivalent elastic modulus (Pa)
- g :
-
Gap between surfaces (m)
- H 1 :
-
Height of the elastic block (m)
- H 2 :
-
Height of the rigid block (m)
- L :
-
Length of periodic cell (m)
- R :
-
Radius of cylinder (m)
- w :
-
Load between the two bodies (N/m)
- x :
-
Coordinate in tangential direction (m)
- λ n :
-
Maugis parameter
- λ t :
-
Maugis-like parameter in the tangential direction
- \({\tilde G_{ij}}\) :
-
Dimensionless Green’s functions
- G :
-
Gap between surfaces
- P :
-
Contact pressure
- U :
-
Deformation at contact surface
- W :
-
Load
- X :
-
Coordinate in tangential direction
- o:
-
Point at which onset of sliding occurs
- S:
-
Contact surface
- app:
-
Applied
- dmp:
-
Damping
- el:
-
Elastic
- int:
-
Interface
- n:
-
Normal direction
- r:
-
Reference parameter used for scaling
- total:
-
Total
- t:
-
Tangential direction
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This work is funded by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant No. 681813).
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Francesc PÉREZ-RÀFOLS. He received his B.S. and M.S. degrees from Polytechnic University of Catalonia, Spain, and his Ph.D. degree in machine elements from the University of Lulea, Sweden. Later, he was awarded a postdoc position at the University of Padova, Italy. Currently, he is a lecturer at Polytechnic University of Catalonia.
Lucia NICOLA. She received her M.S. degree in materials engineering from the university of Trento, Italy, and her Ph.D. degree in mathematics and physics from the university of Groningen, the Netherlands. In 2017, she became a professor of computational materials science at Delft University of Technology, the Netherlands. Currently, she is a professor of metallurgy at the University of Padova, Italy.
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Pérez-Ràfols, F., Nicola, L. Incipient sliding of adhesive contacts. Friction 10, 963–976 (2022). https://doi.org/10.1007/s40544-021-0546-9
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DOI: https://doi.org/10.1007/s40544-021-0546-9