stretching wire

[John Delacour]

At 03:24 -0400 10/4/08, Dean May wrote:

>...I havenÕt yet been able to substantiate MikeÕs claim that with 
>modern piano wire the yield strength is closer to the ultimate. I 
>have found sources that place it at 43-35%...
>
>...It is important to understand though that some plastic 
>deformation does occur before Yield Strength, though not really 
>appreciable...

As I've mentioned before in various contexts, in bass string making 
and generally otherwise in the scale I do not exceed 70% of what 
Paulello refers to as the "elasticity limit" of the wire:

[ "The elasticity limit of a string stands at about 80 % of its real 
breaking strength. Beyond that, it is irreversibly drawn out of 
shape, does not stay in tune, becomes very inharmonic and finally 
breaks." - Paulello ]

So for people who work with the UTS figures, my 70% is roughly their 
55%.  I think there is no serious disagreement on this matter, and I 
know from 25 years of string-making that strings designed to exceed 
these limits always eventually break.

I mentioned (not for the first time) the experiment quoted by A.E.H. 
Love in his classic "A Treatise of the Mathematical Theory of 
Elasticity" carried out by one of the French pioneers of suspension 
bridges, who "found that wires held stretched, with a tension equal 
to one quarter of the breaking stress, retained the length to which 
this tension brought them throughout the whole time of his 
experiments (33 months) , while similar wires stretched with a 
tension equal to half the breaking stress, exhibited a notable 
gradual increase of extension."

Love goes on to mention briefly other characteristics such as 
"recovery" from this permanent set, but unfortunately these 
observations are made in the context of more general matter and there 
is no detailed development of these interesting facts.

It should be noted that Vicat was working about 1830 and will not 
have had available the patented wire of Webster and Horsfall : "By 
1850, James Horsfall's hard drawing, heat treatments and quenching 
produced wire that had twice the tensile strength previously known. 
This so-called "patented wire" is now a term in worldwide use. " -- 
<http://www.websterandhorsfall.co.uk/history.htm>.  It is likely 
therefore that he was using wire of the type I mentioned that we use 
for early period pianofortes.

Now supposing that Vicat was taking as his "breaking strength" the 
Ultimate Tensile Strength of the wire and not the "elastic limit" 
that Paulello and I use, then since most strings on a piano are 
subjected to more than a quarter of their breaking strength and, 
according to his observations can be expected to exhibit a gradual 
increase of extension.  Indeed no factors outside the string itself, 
I suggest, can account for a piano sinking in pitch more than a full 
tone when left untuned for many years.

But note well that I have not referred to "plastic deformation", and 
it is quite clear that Vicat's wire increased in extension well below 
any point, call it what you will, that would be considered a safe 
limit.  The fact that a piano has sunk a tone below pitch over the 
years owing to this gradual extension of the wire does not mean that 
it cannot be brought safely to pitch and quickly stabilize.  I have 
such a piano at the moment, which I roughly pulled up and rough-tuned 
as soon as I bought it 8 weeks ago and which has not shifted since.

So far as I understand the phenomenon, this elongation of the wire 
when kept under tension is quite different from the permanent 
elongation that takes place when the elastic limit has been exceeded 
(plastic deformation) and which will lead eventually to failure.  I 
have had the phenomenon explained to me a very clever Swiss physicist 
of my acquaintance, who was very familiar with it.  I would have 
detained him longer to explain in detail if I were capable of 
absorbing the physical and mathematical details. One thing is certain 
: that I would not have bothered to ask the question if I had not 
over many years been puzzled by this behaviour of a supposedly 
"elastic" material.  What school physics teaches us about elasticity 
is a highly simplified generalization.  I cannot pretend to 
understand a tenth of A.E.H. Love's Treatise, but I recommend the 
book to any serious student if it is only for the historical 
introduction which traces the development of the science from Galileo 
onwards in a most interesting (to me) and understandable way.

JD