Friction

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# Friction - PowerPoint PPT Presentation

Friction. Why friction? Because slip on faults is resisted by frictional forces. In the coming weeks we shall discuss the implications of the friction law to: Earthquake cycles, Earthquake depth distribution, Earthquake nucleation, The mechanics of aftershocks, and more... .

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## PowerPoint Slideshow about 'Friction' - Samuel

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Presentation Transcript

Friction

Why friction? Because slip on faults is resisted by frictional forces.

• In the coming weeks we shall discuss the implications of the friction law to:
• Earthquake cycles,
• Earthquake depth distribution,
• Earthquake nucleation,
• The mechanics of aftershocks,
• and more...

Question: Given that all objects shown below are of equal mass and identical shape, in which case the frictional force is greater?

Question: Who sketched this figure?

Da Vinci law and the paradox

Leonardo Da Vinci (1452-1519) showed that the friction force is independent of the geometrical area of contact.

Movie from: http://movies.nano-world.org

The paradox: Intuitively one would expect the friction force to scale proportionally to the contact area.

Amontons’ laws

Amontons' first law: The frictional force is independent of the geometrical contact area.

Amontons' second law: Friction, FS, is proportional to the normal force, FN:

Movie from: http://movies.nano-world.org

Bowden and Tabor (1950, 1964)

A way out of Da Vinci’s paradox has been suggested by Bowden and Tabor, who distinguished between the real contact area and the geometric contact area. The real contact area is only a small fraction of the geometrical contact area.

Figure from: Scholz, 1990

where p is the penetration hardness.

where s is the shear strength.

Thus:

Since both p and s are material constants, so is .

The good news is that this explains Da Vinci and Amontons’ laws.

But it does not explain Byerlee law…

Beyrlee law

Byerlee, 1978

Static versus kinetic friction

The force required to start the motion of one object relative to another is greater than the force required to keep that object in motion.

Ohnaka (2003)

The law of Coulomb - is that so?

Friction is independent of sliding velocity.

Movie from: http://movies.nano-world.org

Velocity stepping - Dieterich

Dieterich and Kilgore, 1994

• A sudden increase in the piston's velocity gives rise to a sudden increase in the friction, and vice versa.
• The return of friction to steady-state occurs over a characteristic sliding distance.
• Steady-state friction is velocity dependent.

Slide-hold-slide - Dieterich

Dieterich and Kilgore, 1994

Static (or peak) friction increases with hold time.

Slide-hold-slide - Dieterich

• The increase in static friction is proportional to the logarithm of the hold duration.

Dieterich, 1972

Dieterich and Kilgore, 1994

• The dimensions of existing contacts are increasing.
• New contacts are formed.

Dieterich and Kilgore, 1994

• The real contact area, and thus also the static friction increase proportionally to the logarithm of hold time.

The effect of normal stress on the true contact area - Dieterich and Kilgore

Dieterich and Kilgore, 1994

• Upon increasing the normal stress:
• The dimensions of existing contacts are increasing.
• New contacts are formed.
• Real contact area is proportional to the logarithm of normal stress.

The effect of normal stress - Dieterich and Linker

• Changes in the normal stresses affect the coefficient of friction in two ways:
• Instantaneous response, whose trend on a shear stress versus shear strain curve is linear.
• Delayed response, some of which is linear and some not.

Instantaneous

response

linear

response

Summary of experimental result

• Static friction increases with the logarithm of hold time.
• True contact area increases with the logarithm of hold time.
• True contact area increases proportionally to the normal load.
• A sudden increase in the piston's velocity gives rise to a sudden increase in the friction, and vice versa.
• The return of friction to steady-state occurs over a characteristic sliding distance.
• Steady-state friction is velocity dependent.
• The coefficient of friction response to changes in the normal stresses is partly instantaneous (linear elastic), and partly delayed (linear followed by non-linear).

The constitutive law of Dieterich and Ruina

• were:
• V and  are sliding speed and contact state, respectively.
• A, B and  are non-dimensional empirical parameters.
• Dc is a characteristic sliding distance.
• The * stands for a reference value.

The set of constitutive equations is non-linear. Simultaneous solution of non-linear set of equations may be obtained numerically (but not analytically). Yet, analytical expressions may be derived for some special cases.

• The change in sliding speed, V, due to a stress step of :
• Static friction following hold-time, thold:

The evolution law: Aging-versus-slip

Aging law (Dieterich law):

Slip law (Ruina law):

Slip law fits velocity-stepping better than aging law