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quite correct to go deeper google "Young's modulus of elasticity", every elastic material even plastic materials have some value of Y or Young's modulus, since speakers have a larger diameter they need more "stress" or work to be done on them for the fibers in the material to be re-aligned in the best possible pattern to reduce strain on them.
Burn in is a repetitive process but the first one has maximum effect.
What?!? That's a fabulous non sequitur. Stress /= work.
Since stress is force per unit area, yes, a larger
force is needed to reach a given amount of stress for a larger diaphragm of equivalent design - but the actual level of stress is also dependent on the diaphragm design, shape, materials, and more... Thus the stress experienced by any given part of the driver cannot in any way be directly correlated to the work done to it when we're talking about different designs.
And the fibers being re-aligned in the best possible pattern to reduce strain on them? What's the exact cause of this so-called "re-alignment"? The only transducer material containing fibers of any sort are paper or fiber-reinforced cones and domes - and the paper is never part of the suspension - it never plastically deforms (not even small parts of the cone/dome), which would indeed cause some changes.
Now the suspension, which is of course an isotropic polymer in almost every case - whether it's a separate rubber or foam suspension for a cone or a molded part of a dome - certainly undergoes higher levels of stress/strain (its job is to flex, after all...). There are going to be residual stresses from the molding process that are "fighting" to return to a different shape, but if some parts of the suspension were actually be pretty close to yielding (plastically deforming) as a result, those parts of the suspension would stretch out, reducing the residual stresses.
However, if that were the case, I would have expected to get far more failures due to fatigue, because there would still be many points within the suspension that don't quite reach yielding with each cycle. But... When's the last time you saw a driver suspension that wasn't overworked to the point of ridiculousness fail of fatigue? The truth is, other things break drivers first almost all of the time. For the suspension itself, material deterioration unrelated to fatigue is the primary problem - foam rot, rubber cracking, and domes getting brittle with age. Those problems are independent of fatigue.
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Who said burn in makes the SQ magically increase. It has little effect on the sound, rather it is a natural process that occurs again and again, the only thing that changes is the weave pattern of the cone and diaphragm to handle more stress with lesser strain.
So you're saying that the cones and diaphragms get stiffer when breaking in? And as a result of changes
in the weave pattern? Don't tell that to my polypropelyne woofers, they might go on strike!
Seriously, there's no work hardening going on unless there's plastic deformation. And there isn't in the cones or the non-suspension parts of diaphragms. And like I said before, there may be minute plastic deformations in the surround, but until we see some tests or the testimonial of a real materials engineer, we don't know. And yet again, like I said before, that plastic deformation would also be causing serious fatigue problems if it's continuously happening every time you cycle the driver. And we know there's few fatigue failures of speaker transducers.
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Theory
Youngs modulus = Stress / strain , elastic fatigue is 0 for perfect materials but incase of headphone diaphrams they DO have some value which changes strain or impact on them.
thus changing sound
Oooh, another non sequitur! Again, if fatigue were a significant factor in the response of transducer suspensions, we would see far more failures as a result of it. Rather than virtually none.
Your argument wouldn't be so bad if you explained it a bit more - for example: "Headphone diaphragms suffer from fatigue cracking as a result of the elastic deformation of the diaphragm during normal use. Those cracks, which enlarge over time, increase the strain (deformation) of the diaphragm at a given signal level - thus changing sound."
But again, we see little to no failures due to fatigue cracking.
Honestly, we won't know the truth until someone does an independent investigation into the matter. It's actually pretty close to my thesis topic - fatigue failure of bicycle spokes - but I'm already pretty much set on that.