Abstract
The incorporation of the saturation of the tangential contact stress with the increase of the normal contact stress is required for the analysis of the friction phenomenon of solids and structures subjected to a high normal contact stress, which cannot be described by the Coulomb friction condition, in which the tangential contact stress increases linearly with the increase of the normal contact stress. In this article, the subloading-friction model, which is capable of describing the smooth elastic—plastic transition, the static—kinetic transition, and the recovery of the static friction during the cease of sliding, is extended to describe this property. Further, some numerical examples are shown, and the validity of the present model will be verified by the simulation of the test data on the linear sliding of metals.
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Abbreviations
- ū, ū n, ū t :
-
Sliding displacement vector and its normal part and tangential part
- ū e, ū en , ū et :
-
Elastic sliding displacement vector and its normal part and tangential part
- ū p, ū pn , ū pt :
-
Plastic sliding displacement vector and its normal part and tangential part
- ū t :
-
Tangential component of sliding displacement vector to contact surface
- t ū :
-
Unit tangential sliding vector
- f, f n, f t :
-
Contact stress vector and its normal part and tangential part
- f n , f t :
-
Normal and tangential components of contact stress vector to contact surface
- t f :
-
Unit tangential contact stress vector
- w e :
-
Elastic sliding work
- φ(ū e):
-
Elastic sliding energy function
- Ē :
-
Elastic sliding modulus tensor
- α n,α t :
-
Elastic sliding coefficient in normal and tangential directions
- f(f):
-
Sliding-yield function of sliding stress vector
- n :
-
Unit outward-normal vector to contact surface
- n t :
-
Unit direction vector of plastic sliding rate, which is the tangential component of outward-normal vector to sliding subloading surface
- r :
-
Sliding normal-yield ratio
- Ū(r):
-
Function in evolution of r
- μ :
-
Sliding hardening function
- μ s,μ k :
-
Material constant specifying the maximum (static) and minimum (kinetic) values of μ
- κ ξ :
-
Material constant designating the decrease of hardening function by plastic sliding and recovery of hardening function by time-elapse
- \(\mathop {\overline \lambda }\limits^ \cdot ,\,\,\mathop {\overline \Lambda }\limits^ \cdot \) :
-
Positive plastic multiplier in terms of stress rate and strain rate
- m p, m c :
-
Sliding plastic modulus and creep modulus
- Ē ep :
-
Elastoplastic sliding modulus tensor
- g n :
-
Function describing dependence of normal contact stress on contact stress ratio
- c n :
-
Material constant dominating inclination of sliding-yield surface at null normal contact stress
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Koichi HASHIGUCHI. He received his Ph.D. degree from Tokyo Institute of Technology, Japan, in 1976. After that he served as assistant professor, associate professor, and professor at Kyushu University, Japan. He is currently an emeritus professor at Kyushu University, member of the Engineering Academy of Japan, and the technical adviser of MSC software Ltd., Japan. His research area covers the elasto-plastic deformation and the friction phenomena of solids, proposing the subloading surface model.
Masami UENO. He received his Ph.D. degree of agriculture from the University of Tsukuba, Japan, in 1983. He has worked in the Department of Agricultural Engineering, University of the Ryukyus, Japan. He is currently an emeritus professor at the University. His research covers the solid mechanics, smart farming, and systems engineering for agriculture.
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Hashiguchi, K., Ueno, M. Subloading-friction model with saturation of tangential contact stress. Friction 11, 1107–1120 (2023). https://doi.org/10.1007/s40544-022-0656-z
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DOI: https://doi.org/10.1007/s40544-022-0656-z