Young's Modulus: Is it a constant?
Young's Modulus: Is it a constant?
(OP)
In general, the speed of sound c is given by
c = ( C / ρ ) exp 1/2
where C is a coefficient of stiffness and ρ 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 / ρ ) exp 1/2
where E is Young's modulus and ρ (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
c = ( C / ρ ) exp 1/2
where C is a coefficient of stiffness and ρ 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 / ρ ) exp 1/2
where E is Young's modulus and ρ (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





RE: Young's Modulus: Is it a constant?
Modulus is unaffected by stress, it is affected by temperature.
RE: Young's Modulus: Is it a constant?
RE: Young's Modulus: Is it a constant?
RE: Young's Modulus: Is it a constant?
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.
RE: Young's Modulus: Is it a constant?
RE: Young's Modulus: Is it a constant?
= = = = = = = = = = = = = = = = = = = =
Plymouth Tube
RE: Young's Modulus: Is it a constant?
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
RE: Young's Modulus: Is it a constant?
= = = = = = = = = = = = = = = = = = = =
Plymouth Tube
RE: Young's Modulus: Is it a constant?
FAQ330-1441: Why is the elastic modulus relatively insensitive to changes in chemistry/temper/coldwork?
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