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TECHNICAL PAPERS

Thermoelastic Dynamic Instability (TEDI) in Frictional Sliding of a Half-Space Against a Rigid Non-Conducting Wall

[+] Author and Article Information
L. Afferrante, M. Ciavarella

 CEMEC-PoliBA-Centre of Excellence in Computational Mechanics, Politecnico di Bari, V.le Japigia 182, 70125 Bari, Italy

However, the TEI critical speed is only due to the displacement constraint in the normal direction and could be removed by considering a force control in normal direction (Afferrante and Ciavarella (27)).

These curves remind the single curve in the dimensionless plot of Azarkhin and Barber (33).

J. Appl. Mech 74(5), 875-884 (Oct 16, 2006) (10 pages) doi:10.1115/1.2712232 History: Received April 07, 2006; Revised October 16, 2006

In the sliding of half-spaces with constant friction coefficient, two classes of instabilities are well known: thermoelastic instability (TEI), which occurs for sufficiently long wavelengths and Dynamic Instability (DI), which happens at sufficiently high friction coefficient, and whose growth factor increases linearly with wave number. Although the two phenomena look therefore quite distinct, their coupling is discussed here for an elastic and conducting half-space sliding against a rigid and non-conducting wall. The coupling between thermal and dynamic effects is not always negligible. In fact, surprisingly, new areas of instability are found, called thermoelastic dynamic instabilities (TEDI), similar to TEI at high speeds and DI at low speeds. TEDI lowers the critical speed and friction coefficient in many conditions even to zero. At low speeds, TEDI is ill-posed as DI at small wavelengths, and hence a regularized friction law like the Rice-Ruina one would probably be needed to correct the results.

Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Elastic half-plane sliding against a rigid wall

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Figure 2

Some example results for Dynamic Instability (DI): variation of the real part of the dimensionless growth rate b̃ with the friction coefficient f for different ν

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Figure 3

Some example results for Dynamic Instability (DI): variation of the imaginary part of the dimensionless growth rate b̃ with the friction coefficient f for different ν

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Figure 4

Some example results for the TEI: variation of the real part of the dimensionless growth rate b̂=bk∕ω2 with the dimensionless wave number γ=ωk∕c1 for different friction coefficient f (V̂0=10−3, H=1).

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Figure 5

Map of instability in terms of V̂0 for ν=0.3, p̂0=10−3 and γ=3×10−2

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Figure 6

Map of instability in terms of V̂0 for ν=0.3, p̂0=10−3 and γ=10−3

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Figure 7

Map of instability in terms of p̂0 for ν=0.3, V̂0=10−3 and γ=3×10−2

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Figure 8

Map of instability in terms of p̂0 for ν=0.3, V̂0=10−3 and γ=2.5×10−4

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Figure 9

Variation of the exponential growth rate R(z) with the friction coefficient f for different value of H, ν=0.3, p̂0=V̂0=10−3, γ=2

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Figure 10

Variation of the exponential growth rate R(z) with the sliding speed V̂0 for different wave numbers γ and H=1, f=0.5, ν=0.3, p̂0=10−3

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Figure 11

Variation of the characteristic speed V̂1 with the pressure p̂0 for different frction coefficients (ν=0.3)

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Figure 12

Variation of the exponential growth rate R(z) with γ for different values of the friction coefficient f, p̂0=10−3, V̂0=10−3<V̂1, H=1 and ν=0.3

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Figure 13

Dependence of γcr on V̂0 for p̂0=10−3, H=1, f=0.5, and ν=0.3

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Figure 14

Dependence of γcr on p̂0 for V̂0=10−3, H=1, f=0.5, and ν=0.3

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Figure 15

Variation of the exponential growth rate R(z) with γ for different values of the friction coefficient f, p̂0=10−3, V̂0=2×10−3>V̂1, H=1 and ν=0.3

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