Carl Fogel writes:
>>> Where can I find the abundant laboratory testing of spokes,
>>> particularly of the stress relief theory popular here on
>>> rec.bicycles.tech?
>> A bent spoke with wiggly curves stretched it in a tensile tester
>> while monitoring tension will show a straightening and steepening
>> of the tension versus strain curve. When the yield point is
>> reached the test should be ended and the spoke removed.
>> The spoke will then be as perfectly straight as one could wish. That
>> indicates that all bending stresses are gone. It doesn't take
>> "abundant" spokes samples to discover this. It takes only one.
>> Designing the experiment is often more important than carefully
>> collecting abundant data. This is one of those instances.
>> Understanding what occurred enables seeing how over-stressing a
>> spoke with residual stresses constitutes stress relief when it is
>> relaxed.
>> This is easily done in a tensile testing lab. I observed this
>> while recording stress-strain curves for the book. Of course these
>> results must be noticed to draw proper conclusions.
> Could you elaborate on this? I'm pretty sure that I'm missing your
> point.
> I gather that this test involved taking a spoke that had been bent
> enough to take a wiggly set (past its elastic limit, if that's the
> right term) and then straining it by stretching it until it took a
> set again and straightened out (again past its elastic limit).
Yes.
If a new straight spoke is bent, it will spring back to its original
straight shape unless it is bent beyond its yield stress and then it
will spring back only partially... but it does spring back partially.
The cause is that only the surface fibers on the inside and outside of
the bend exceeded yield (in tension and compression) and found a new
rest position while the remainder, the fibers closer to the center of
the spoke, did not exceed yield and these want to return to the
original straight alignment when the bending force is removed. That a
stratification of stress through the cross section of a bend is
residual stress. This gradation can be visualized by bending a
magazine while pinching the edges of the covers together so that its
pages don't slide. They will buckle and show the differences in
length change (strain) a metal would experience, or conversely, if
allowed to slide, will by their motion make this apparent.
The partial spring-back shows that the bent spoke has residual stress
and if built into a wheel where it would receive enough tension to
pull it straight, would have even more residual stress. Typically, a
spoke elbow is bet to an obtuse angle in manufacture (with
spring-back), that for outbound spokes of a flange, is bent to an
acute angle and then tensioned. That is residual shaping stress
overlayed on manufacturing stress to which tensioning stress is added.
Stretching the spoke will exceed yield, there where stress is so high
that it would result in early fatigue failure.
> Are the two sets different?
I missed the "set" or was it your serve?
> And how does this stretching until the test bend is removed compare
> to stretching a spoke by squeezing it, when neither the bent spoke
> elbow nor the threaded end of the spoke straighten?
Regardless of shape, when the entire cross section is taken to yield
and relaxed, it will have uniform stress. This goes for a wire bent
back on itself through a U-bolt or a spoke elbow supported by a hub
flange. The point is that a spoke in whatever shape, taken to yield
and relaxed, will have no residual stress from prior bending or
forming and will support tension with uniform stress.
Manual stress relieving cannot fully stress relieve because that much
force would exceed the strength of the rim and hub, and possibly the
nipples. The ideal is to impart enough of an overload to relax the
highest points of residual stress, which is as much as can be done in
practical terms.
For control wires that must bend in use, "braided" (helically wound
strands) are used so that all fibers pass though the inside and
outside of bends. This is also how these cables remain constant
length when bending because all fibers pass through the inside and
outside of the bend. The strands are thin enough to not approach
yield in the operating range of bends encountered.
Jobst Brandt
[email protected]
