20.15 Internal Friction Physics

Back

20.15.1 Basic Concepts

All damping derives from varying degrees of complexity because of the myriad interactions that are

present, either internal of nonconservative type or external involving the environment. This is true even

for systems that come closest to being governed by the textbook equations. For example, the author has

attempted to produce ideal harmonic oscillators using viscous liquids for damping. Even they are

complicated and do not strictly obey Stokes’ Law of drag force proportional to the velocity. The nonlinear

Navier – Stokes equation may be capable of describing them, but not in a simple form except to a first

approximation that is not really very good relative to the precision that is possible with modern sensors.

Perhaps the closest to being an ideal viscous damped oscillator is that in which the damping force derives

from eddy currents through Faraday’s Law. A magnet is attached to the oscillator and, as it moves in

proximity to a conductor, the time rate of change of magnetic flux gives rise to a retarding force that is

proportional to velocity. Because there really is a force involved, and because of Lenz’s Law, the damping

term makes sense physically. This case might be completely ideal except for one factor — the magnet is part

of a mechanical system that must possess structural integrity if it is to oscillate. Because of loads present in

the structure (reactionary normal forces to the various weights), there will always be some creep. The creep

is ultimately unavoidable, since there is apparently no stress threshold below which plastic deformation

ceases to exist. It is important to realize that forces associated with inertial mass (Newton’s Second Law) are

just as important as the weights. Systems designed around an elastic member (such as a spring, in contrast

to a simple pendulum) will experience damping in the weightlessness and the airlessness of space.

20.15.2 Dislocations and Defects

The extent to which mechanical defects, such as dislocations, have been ignored by large segments of

the scientific community is surprising. The surprise is even greater when one considers the importance

of defects in another field — that of electronics. Our present information age (world of computing)

came into existence only after widespread recognition of the importance of the defects called

impurities. The n-type and p-type semiconductor materials necessary to our modern age result from the

substitution of silicon atoms with others of pentavalent and trivalent type in surprisingly small

concentrations.

The strength of solids is very much less than as predicted by theories of an ideal (perfect) crystal.

Dislocations are the primary culprits. Their influence on materials used in engineering has prompted the

statement: “when mother nature fills the vacuum she abhors, she rarely does so with perfection.”

Unfortunately, few students exposed to fundamental science receive training in defect physics. Moreover,

it is difficult to provide a self-consistent fundamental description of their properties, so very few scientists

have more than a superficial knowledge of their importance.

“Viscoelasticity” is a misleading term. To combine the words viscous and elastic suggests that the state

variables vary smoothly in time, i.e., as a fluid in the viscous part. Unfortunately, this is not true of

hysteresis associated with either “domains” or with “grains.” In the case of magnetic domains, it is quite

easy to demonstrate nonsmooth (jerky) behavior that is called Barkhausen noise. Although the

phenomenon was demonstrated by Barkhausen in 1919, only recent studies have begun to understand

some of its complexities better (Urbach et al., 1995a,b).

A similar phenomenon, that must relate in some manner to the Barkhausen effect, is the PLC effect.

Under applied stress, alloys frequently display discontinuous strain increase (jumps). The author has

20-44 Vibration and Shock Handbook

© 2005 by Taylor & Francis Group, LLC

even demonstrated strain recovery of a similar type, catalyzed by “tapping.” The polycrystalline metals

that demonstrate these effects are obviously influenced by “granularity.” They differ from the “granular

materials” that have become a hot topic of recent research. Even pure polycrystalline metals exhibit these

features. The German word to describe the deformation of tin under large stresses is zinngeschrei

(¼tin cries). Anyone who has ever bent large-diameter tungsten wire has experienced this phenomenon,

since the nonsmooth strain can be both felt and heard.

There is still another type of material, thought to have great engineering potential in the future, that

shows “granular” behavior — that of shape memory alloys (SMA). If an SMA specimen is cycled in

temperature around the martensitic phase, it generates acoustic emissions (Amengual et al., 1987). For a

figure taken from their work and other good pages about hysteresis, refer to the webpages of Prof. Sethna

at http://www.lassp.cornell.edu/sethna/hysteresis/ReturnPointMemory.html. These emissions are probably

related to the PLC effect and are characterized by surprising reproducibilities in spite of their

complex behavior.

Thus, there is abundant experimental evidence against the overly simplistic view that hysteretic

damping can be meaningfully described by simple, linear differential equations. The nonlinear terms

necessary for a good mathematical treatment go beyond “chaos” to the world of “complexity.” Chaos of

deterministic type, though bewildering to many, is in many cases tractable (using equations that can be

integrated numerically). Damping problems are much more complex than deterministic chaos. The

challenges to our understanding derive in part from the long time that it has taken before there were any

serious investigations of the mesoscale, the place where defect structures abide. If, as with Zener, we use

the word anelasticity to describe systems that are “other than” elastic, then the term mesoanelastic

complexity is an appropriate label for this poorly understood physics that is important and yet mostly

unknown to many fields of both science and engineering.

Навигация