Re: Hardness/restitution

[brian whatcott <inet@intellisys.net>]

At 14:37 11/17/97 -0500, you wrote:
> > I am puzzled by the following problem
> >
> > G Barnes (Am Journal of Physics, 1958,vol26, p7) defines coefficient of
> > restitution as follows:
> >
> >        e=3D (ae1 +be2)/(a+b)
> >
> > e1 and e2 are Young coefficient of colliding bodies 1 and 2.
> > a and b are realtive hardness of substances 1 and 2.
> >
> > How establish and explain the dependance of the coefficient of restitution
> > upon the hardness of bodies?
> > What is the link between hardness and rebound?
> >
> > All comments are  highly welcomed.
> >
> > D. Ismael Youssouf.
>
> This is a puzzlement!  A rubber ball might have a good coefficient of 
> restitution (rebound) and fail miserably on a hardness test;  whereas a 
> hard steel ball might do well on both (?).  Must find somebody who knows 
> about these things.  Any help out there?  I'm curious.
>
> -Bob
>
> Bob Sciamanda 

On the understanding that fools rush in...

The idea of a coefficient of restitution as a measure of the proportion
of energy retained through successive cycles, involves the idea of a 
dissipative mechanism.
 Young's modulus - a measure of stiffness - is certainly to do with
'elasticity', being the stress which would double the length of a
specimen if fracture did not supervene.

'Hardness' then must be some measure of loss?
  You will share my difficulty in seeing the connection, I am sure.

Instrumentally, we might use a diamond cone indenter with a fixed force
and measure the 'crater' size, or modulate an indenter's force to produce a
fixed depression... These are among the methods used to measure 'hardness'.

It is the case that an indentation has stressed a material locally beyond 
its power to resist eleastically so that it yields permanently - an energy
consuming process to be sure.

But you can see that it is not necessary to employ forces which are at all
likely to provide permanent deformation, so (I speculate), we must be
witnessing an indirect mechanism for energy loss. 

One that comes to mind is the lateral expansion of a contact patch during a
bounce - given that two materials expand laterally by different amounts, or
that one material does, and the other does not, this is a plausible
mechanisn for external energy loss
via friction. 

 There is an engineering parameter that characterizes this
lateral apportioning of strain - it's called Poisson's ratio - and is used 
to connect between the several Moduli: Young's, Sheer, and Bulk.

This is as far as I can presently take the matter without references- but
perhaps someone will now be emboldened to set us straight?

Sincerely,


brian whatcott <inet@intellisys.net>
Altus OK