Fatigue Failure in Piano Wire

[Dan Squire]

      Since there has been some discussion on fatigue I would like to give a
brief overview of fatigue failure; what it is, what causes it, and how it
applies to piano wire.  This overview might seem extremely simplistic to
some but it is intended to be of benefit to those who are not familiar with
fatigue failure.  Hopefully it will provide some insight on what causes wire
to break.
      In a piano that is properly tuned that is not being played the wire is only
in tension (axial load), this tension produces a stress on the wire
(force/area) but this stress is not enough in itself to cause the wire to
fail. When the piano is being played something else is happening within the
wire.  This "something else" is fluctuating stresses.  I'll try and explain
it this way.  Imagine a segment of piano wire, now bend the wire, one side
will be in tension due to elongation and the other side will obviously be in
compression.  Now bend the wire the other way.  The side that was in
compression is now in tension and the side that was in tension is now in
compression.  Mentally keep on bending the wire at a frequency equivalent to
that in the treble section.  To this wire segment that is experiencing this
high frequency bending add in the tension of the wire.  Now the wire segment
has an axial component of stress superimposed on the bending component.  Now
just for fun, think of an entire vibrating wire that is under tension and
add in the contact stress caused by the capo bar on the wire.  Anyway, these
loads produce fluctuating stresses in the piano wire.
      Keeping this in context,  after a period of time playing the piano the wire
has been undergoing the action of repeated or fluctuating stress and the
wire fails.  This type of failure is called fatigue failure.  The
distinguishing aspect of this failures is that it occurs when the stresses
have been repeated a large number of times.
      Fatigue failures begin with a small crack in the material, internal or
external, even with irregularities caused by machining.  The crack can be so
small that it cannot be detected with the naked eye.  The crack can develop
at any discontinuity in the material, such as a nick in the wire caused by
string spacing or roughness in the surface finish of the wire.  Once the
crack in the wire has been initiated, the effect of the stress concentration
in that area increases and the size of the crack increases more rapidly.  As
the size of the crack increases the area in which the stress concentration
occurs decreases.  The crack keeps growing and the stress keeps increasing
until the remaining area of the wire around the crack fails suddenly,
without warning.  Therefore, fatigue failure has two distinct regions.  The
first region is where the crack occurred.  The second region is where the
sudden fracture occurred and is very similar in appearance to a brittle
fracture such as cast iron that failed in tension.

Dan Squire