Young's Modulus: Is it a constant? 2

[bklauba]

In general, the speed of sound c is given by

c = ( C / ? ) exp 1/2

where C is a coefficient of stiffness and ? is the density.


In a solid, this stiffness is expressed as the Young's modulus.

In a solid rod (with thickness much smaller than the wavelength) the speed of sound is given by:

c (solid) = ( E / ? ) exp 1/2

where E is Young's modulus and ? (rho) is density

A not often noted phenomenon is the augmentation of the speed of sound, as a result of the presence of stress. The use of an ultrasonic signal to measure the speed of sound in a torqued bolt as compared with a non-torqued control sample is one area where this concept is applied. See:

http://www.surebolt.com/surebolt.htm

The timing of shock waves in the earth's crust (seismology) to measure the stress energy in the crust appears to be another example.

Since the density would be only effected marginally (likely undetectably) by the presence of stress, does this not mean that the Young's modulus, normally considered a constant, is the parameter undergoing similar augmentation by the presence of stress? Have I misinterpretted something?

I welcome any comments or guidance. Perhaps there is a better way of stating this.

BK

 

[metengr]

BK;
Modulus is unaffected by stress, it is affected by temperature.

 

[rconner]

While I cannot verify the correlation to sound velocity, but I believe the answer to the subject line question could to some extent depend on the specific material/stress etc. involved. For some materials there could be at leat a slight arcuate shape to the stress-strain curve. [To see what I am referring to, you could possibly do a search with th ekeywords "secant modulus".

 

[MintJulep]

Ultrasonic extensiometers do not measure a change in the speed of sound. They measure the a change in time for an echo return, the time being in proportion to a change in length.

 

[RPstress]

Elastic Young's modulus does indeed change a little bit with stress; see Professor Gordon's book "Why You Don't Fall Through the Floor, or The New Science of Strong Materials." In that he reproduces a stress-strain curve for a sapphire whisker which clearly shows the modulus falling off a bit as the whisker extends. However, you need a massive elastic range to see this, and all normal materials yield or break before it becomes noticeable.

I'm not aware of any other effect on Young's modulus of the presence of stress.

However, that doesn't mean that the speed of sound in a solid is unaffected by stress. I suspect that for ordinary compression waves (are they the P-waves in earthquakes? I forget) it doesn't, or there'd be easier ways of finding residual stresses in parts. However, for earthquakes there are the other modes of crustal vibration. These would certainly be affected by the presence of stress, like a guitar string.

 

[Compositepro]

Modulus is the slope of the stress-strain curve. This slope is not constant. Some materials are more non-linear than others. There are differing definitions on how the slope is defined (e.g., secant, tanget, cord). Polymers will increase modulus as strain increases molecular alignment. Carbon fiber can increase in modulus by 25% from zero strain to ultimate strain. Composite materials can change modulus as fiber alignment changes due to strain.

 

[EdStainless]

Even for common engineering metals you can change the tensile modulus a slight but measurable amount through cold work. This is an issue in high strength spring wire. When you cold work steel the modulus increases. There is a residual stress effect on top of this also.


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Plymouth Tube

 

[bklauba]

EdStainless,

Can elaborate on the effects on residual stress upon E? How does it change it (my suspicion is res strs would cause increased stiffness)? Can you site any references or work that further describes this effect?

Thanks!

BK

 

[EdStainless]

Yes, in wire the higher the residual stress the higher the E. In very high strength steel wire (Rocket wire) there is often a specification limit on E. They want the springs to have the design stiffness. We would test samples before and after stress relief. I am sorry but I don't recall the numbers.

= = = = = = = = = = = = = = = = = = = =
Plymouth Tube

 

[Maui]

bklauba, the two main factors that influence the value of the elastic modulus are the interatomic bonds and the atomic microstructure. For a detailed explanation, I recommend that you review the following FAQ

faq330-1441

As MintJulep stated, the ultrasonic transducers that are used to detect the incident and reflected ultrasonic waves do not measure sound velocity. The velocity is a derived quantity that is calculated based on the distance the wave travels divided by the elapsed time. When the bolts are stressed, the resulting strain changes their lengths. If this change in length is not accounted for in the velocity calculation, then errors will result that appear to cause a change in sound velocity.

For elastic deformations, the volume (and therefore the density) will be unchanged only if the Poisson ratio of the bolt material is equal to 1/2. For any other value of the Poisson ratio, the volume is not conserved during elastic deformation.

Maui