Entropy in Tribology: in the Search for Applications
<p>Heat flow away from the frictional interface.</p> "> Figure 2
<p>Hidden energy density <span class="html-italic">vs</span>. the number of cycles [<a href="#B29-entropy-12-01345" class="html-bibr">29</a>].</p> "> Figure 3
<p>(a) Self-organized protective film at the interface of a composite material (b) The coefficient of friction as a function of film thickness for various values of the microstructure parameter <span class="html-italic">ψ</span>. Sub-critical values of <span class="html-italic">ψ</span> < <span class="html-italic">ψ<sub>cr</sub></span> result in the positive slope (no layer formed), whereas <span class="html-italic">ψ</span> < <span class="html-italic">ψ<sub>cr</sub></span> results in the instability and self-organization of the protective layer. The slope depends on the ratio of the bulk and layer values of μ, which allows finding composite microstructure that provides the self-organization of the layer.</p> "> Figure 4
<p>A significant wear and friction reduction with decreasing particle size in Al-Al<sub>2</sub>O<sub>3</sub> nanocomposite (based on [<a href="#B31-entropy-12-01345" class="html-bibr">31</a>]) can be attributed to surface self-organization</p> "> Figure 5
<p>(a) Variation of the steady state and stick-slip friction with sliding distance [<a href="#B35-entropy-12-01345" class="html-bibr">35</a>]; (b) a typical decrease of friction during the running-in.</p> "> Figure 6
<p>A feedback loop (a) model and (b) its presentation in Simulink. Two simultaneous processes (adhesion and deformation) affect surface roughness in different manners. (c) Total friction is the sum of the deformational and adhesional components and the equilibrium value of roughness R corresponds to the minimum value of friction. Consequently, an equilibrium value of roughness exists, which corresponds to minimum friction [<a href="#B36-entropy-12-01345" class="html-bibr">36</a>].</p> "> Figure 7
<p>The time-dependence of the coefficient of friction and roughness parameter during the running-in simulated with Simulink for A = B and A ≠ B. For A = B, while roughness reaches its equilibrium value, the coefficient of friction always decreases. Therefore, self-organization of the rough interface results in the decrease of friction and wear. For A ≠ B the coefficient of can decrease or increase depending on the initial value of roughness [<a href="#B36-entropy-12-01345" class="html-bibr">36</a>].</p> "> Figure 8
<p>The change of the coefficient of friction and the surface roughness in Cu substrate with the number of cycles during a ball-on-disk test with a tungsten carbide (WC) ball [<a href="#B36-entropy-12-01345" class="html-bibr">36</a>].</p> "> Figure 9
<p>Elastic waves radiated from the frictional interface between two elastic half-spaces. The bodies are shown pre-stressed with the pressure <span class="html-italic">p</span><sup>*</sup> and shear <span class="html-italic">q</span><sup>*</sup> applied at infinity [<a href="#B45-entropy-12-01345" class="html-bibr">45</a>].</p> "> Figure 10
<p>Positive feedback leading to the friction-induced instabilities [<a href="#B22-entropy-12-01345" class="html-bibr">22</a>]</p> "> Figure 11
<p>Friction reduction due to propagating stick-slip zones. The shear force <span class="html-italic">F</span> is smaller than the force needed to initiate friction μ<span class="html-italic">W</span>; however, due to many propagating slip regions the two contacting bodies shift relative to each other in what is observed as friction at the reduced apparent coefficient of friction μ<sub>ap</sub> = <span class="html-italic">F/W</span><μ.</p> "> Figure 12
<p>Normal (<span class="html-italic">y</span>) and tangential (<span class="html-italic">x</span>) degrees of freedom during friction.</p> "> Figure 13
<p>Schematics of self-healing using (a) precipitation (figure provided by Mr. J. M. Lucci, from the UWM) (b) reinforcement with shape-memory alloy (c) embedding of a healing agent (e.g., low melting point solder).</p> "> Figure 14
<p>Block diagram of the healing process. Deterioration is caused by an external force. The deteriorated system is brought out of equilibrium so that the restoring (“healing”) force is created, which is coupled with the degradation flow through the parameter <span class="html-italic">M</span>.</p> "> Figure 15
<p>Self-healing observed at the macroscale (healed cracks and increased orderliness) and microscale (ruptured microcapsules and decreased orderliness) [<a href="#B23-entropy-12-01345" class="html-bibr">23</a>].</p> "> Figure 16
<p>The paradigm of Green Tribology: renewable energy, biomimetic surfaces, and biodegradable lubrication [<a href="#B61-entropy-12-01345" class="html-bibr">61</a>,<a href="#B62-entropy-12-01345" class="html-bibr">62</a>,<a href="#B63-entropy-12-01345" class="html-bibr">63</a>].</p> ">
Abstract
:1. Introduction
2. Entropy During Friction and Wear
2.1. Friction and Dissipation
2.2. Wear and Entropy
Process | Entropy change |
---|---|
Adhesion | , where γ is surface energy, A area |
Plastic deformation | , where Up is the work per volume, V volume |
Fracture | , where is the energy release rate, a is crack length |
Phase transition | , where H is enthalpy |
Chemical reaction | , where Ni are numbers of molecules and μi are chemical potentials for reactants and products. |
Mixing | , where Ni are numbers of molecules and R is the universal gas constant |
Heat transfer | , where T1 and T2 are temperatures of the two bodies |
3. Entropic Methods of Study of Self-organized Tribological Systems
3.1. Self-organization in Tribology
Effect | Description of the state or evolution | Features of synergism | Self-regulated parameter | Target function and/or governing principle |
---|---|---|---|---|
Auto-hydrodynamic effects (wedges, gaps, canyons) | Equations of motion, competing processes for entropy and negentropy production | Bifurcation; self-excited vibrations and waves; feedback and target functions | Gap thickness, temperature, and microtopography distributions | Minimum friction |
Self-reproducing micro-topography, waviness | Equations of motion or kinetics | Bifurcations; self-excited vibrations and waves | Rough surface microtopography | Minimum energy dissipation; pressure or heat flow distribution |
Steady state microtopography of worn surfaces (“natural wear shape”) | Competing processes for entropy and negentropy (information) production | Feedback and target function | Shape of the profile | Minimum energy dissipation |
Self-excited vibrations of wear, electric resistance, stresses, etc. | Measurements of a parameter of the system (friction force, electrical resistance, wear rate, etc) | Instabilities and self-excited oscillations of the measured parameter | Corresponding parameter | Minimum entropy production |
Spatial or periodic chemical pattern | Molecular, atomic, or dislocation structure | Large-scale ordered structures | Secondary heterogeneity at the surface | Dissipative principles |
Periodic or concentric structures, such as Bénard cells | Molecular, atomic, or dislocation structure; Entropy is measured | Large-scale order structures; a sudden decrease in entropy production | - | Minimum entropy production |
Decrease in macrofluctuation of temperature, particle size and other parameters | Order-parameter dependent on generalized coordinate, Measurements of a parameter of the system | Microfluctuations; phase transitions; instabilities and self-excited vibrations of the measured parameter | - | Sub-minimal friction |
Effect | Mechanism/ driving force | Condition to initiate | Final configuration |
---|---|---|---|
Stationary microtopography distribution after running in | Feedback due to coupling of friction and wear | Wear affects microtopography until it reaches the stationary value | Minimum friction and wear at the stationary microtopography |
In situ tribofilm formation | Chemical reaction leads to the film growth | Wear decreases with increasing film thickness | Minimum friction and wear at the stationary film thickness |
Slip waves | Dynamic instability | Unstable sliding | Reduced friction |
Self-lubrication | Embedded self-lubrication mechanism | Thermodynamic criteria | Reduced friction and wear |
Surface-healing | Embedded self-healing mechanism | Proper coupling of degradation and healing | Reduced wear |
3.2. Thermally Activated Self-organization
3.3. The Concept of “Selective Transfer”
3.4. The Concept of “Tribofatigue”
4. Frictional Dynamical Systems: Self-Organization and Entropy
4.1. Frictional Adjustment During the Running-in
4.1.1. Feedback Loop Model for the Running-in
4.1.2. Shannon Entropy and Entropy Rate of a Random Process as Measures of Surface Roughness
Information | Energy | Mass | |
---|---|---|---|
Surface roughness | Friction (dissipation) | Wear (mass flow) | |
Entropic description | Shannon entropy and entropy rate for a stochastic process | Thermodynamic entropy | Entropy of mixing (configurational) |
4.2. The Problems of Combining Friction with Dynamics and Linear Elasticity
4.2.1. Paradoxes
4.2.2. Frictional Dynamic Instabilities
4.2.3. Self-organized Elastic Structures
System | Single half-space | Two half-spaces, no friction | Two welded half-spaces | Two half-spaces, finite friction | |
---|---|---|---|---|---|
slightly dissimilar | significantly dissimilar | ||||
Waves | Surface (Rayleigh) waves | Interface (generalized Rayleigh) waves (GRW) | Stoneley waves | Instabilities confined at the interface (GRW with growing amplitude) | Radiated waves |
Derivative waves | Non-linear stick-slip waves | Linear slip waves |
4.3. Non-linear Models
5. Non-equilibrium Thermodynamic Approach to Friction, Wear and Self-healing
5.1. Linear Equations of the Non-equilibrium Thermodynamics and Friction
5.2. Linear Equations of the Non-equilibrium Thermodynamics and Wear
5.3. Self-healing
Mechanism | Precipitation | SMA reinforcement | Healing agent encapsulation |
---|---|---|---|
Type (according to [56]) | Damage prevention | Damage management | |
Type (according to [57]) | Solid-state | Solid-state (possibly also liquid assisted) | Liquid-assisted |
Matrix Material | Al-Cu, Fe-B-Ce, Fe-B-N, etc. | Sn-Bi, Mg-Zn | Al |
Reinforcement Materials | - | NiTi | Sn-Pb |
Microstructure parameter, | Solute fraction | Concentration of microwires | Concentration of microcapsules or low-melting point alloy |
Degradation measure, | Volume of voids | Volume of voids | Volume of voids |
Healing measure, | Amount of precipitated solute | SMA strain | Amount of released healing agent |
Characteristic length of degradation | Void size (microscale) | Void/crack size (macroscale) | Void/crack size (macroscale) |
Characteristic length of the healing mechanism | Atomic scale (atomic diffusion) | Microwires diameter (macro or microscale) | Microcapsule size (microscale) |
Phase transition involved | Solute precipitation | Martensite/austenite | Solidification of the solder |
Healing temperature | Ambient | Martensite/austenite transition | Melting of the low-melting point alloy |
Property improved | Creep resistance | Restored strength | Restored strength and fracture toughness |
6. Future Directions
Phenomena | Principle | Application |
---|---|---|
Wear (friction-induced) | Proportionality of the wear rate and entropy flow | Wear reduction for various applications [15,16] |
Running-in | Microtopography adjustment observed as Shannon entropy and roughness reduction | Friction and wear reduction in the stationary regime [20,30] |
Formation of in-situ tribofilms | Friction-induced diffusion of the film-material to the interface due to the destabilization of the stationary state. | Friction and wear reduction due to protective tribofilm [12,13,22,25,31,32,33,34] |
Slip waves | Elastic waves at the interface which can result in friction reduction. Can result in self-organized critical behavior and stick-slip. | Novel ways of ultrasonic motors, etc. [43,44,45]; new theories of dislocation-assisted sliding [47]; geomechanical applications [17,18,19,20] |
Friction-induced instabilities | Coupling of friction with wear, thermal expansion, etc. Usually leads to the “negative viscosity” and similar types of frictional instabilities | Eliminating friction-induced vibrations and noise [39,42,43,44,45,46] |
Self-healing by embedding microstructures | A mechanism, which provides the coupling of healing with another relevant thermodynamic force, is embedded into material. Healing can occur due to the deterioration of embedded microstructure (e.g., microcapsules). | Self-healing materials and surfaces [22,23,24,30, 53, 56,57] |
Damage prevention | A mechanism to heal voids as they appear is embedded into material (e.g., nucleation of a solute at void points in supersaturated solid solution). | Wear-resistant and self-healing materials and surfaces [56,57] |
Self-lubrication | Various mechanisms, including embedded microstructure, to reduce friction and wear. | Self-lubricating materials [30,53] |
7. Conclusion
Acknowledgements
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Nosonovsky, M. Entropy in Tribology: in the Search for Applications. Entropy 2010, 12, 1345-1390. https://doi.org/10.3390/e12061345
Nosonovsky M. Entropy in Tribology: in the Search for Applications. Entropy. 2010; 12(6):1345-1390. https://doi.org/10.3390/e12061345
Chicago/Turabian StyleNosonovsky, Michael. 2010. "Entropy in Tribology: in the Search for Applications" Entropy 12, no. 6: 1345-1390. https://doi.org/10.3390/e12061345