Hooke's Law and Stress Fracture

[Thomas]

Experience shows that for many materials Hooke's Law holds only over a very small range. A steel bar for instance can only be extended by about 1% by an applied force before it fractures. Translate into the microscopic picture this means that the distance between the molecules changes only by about 1% before dissociation is achieved and the molecular bond breaks. Now the potential curve of molecular bonds typically varies over a range of 1 Angstrom ( i.e. the average distance between the molecular nuclei; see http://www.chem.vt.edu/chem-ed/quantum/harmonic-oscillator.html [Broken]). This however would mean that one would roughly need to double the distance between the nuclei before dissociation is achieved, in contradiction to experience. What is the explanation for this discrepancy ? Is the potential curve in metals only 10^-2 Angstrom wide (and the dissociation energy reduced by a corresponding amount) and if yes why?

 

[Tyger]

Fracture in a crystaline allow,

of which hard steel is, occurs in the form of a notch which rips open progressivly. You might want to check on rupture of single crystal of Iron or other metals, where Hooke's Law may work over a wider range.

 

[Thomas2]

I have examined this topic now in more detail on my webpage regards Hooke's Law and it appears that electrostatic forces due to plasma polarization fields could be responsible here (rather than molecular forces).

 

[Mike2]

Experience shows that for many materials Hooke's Law holds only over a very small range. A steel bar for instance can only be extended by about 1% by an applied force before it fractures.

More generally, are there elements in the equations for the stress on a material that imply that anything that undergoes stress may also fracture? Can the force necessary to fracture be calculated from the force required to elongate by some distance?

Thanks

 

[Thomas2]

With the molecular force interpretation, the force required to fracture a material is given by the work required to break the molecular bonds i.e. the dissociation energy. This is usually of the order of a few electron Volts and as you can see from the first diagram in http://www.chem.vt.edu/chem-ed/quantum/harmonic-oscillator.html [Broken], this should happen at an atomic separation of a couple of Angstroms, i.e. you would have to extend the steel bar to more than twice its length (the normal separation of the atoms is given by the minimum of the curve which is somewhat less than 1 A). This would correspond to a force about 100 times as high as actually observed (as mentioned, a steel bar fractures already at about 1% elongation).
There is a theory that cracks in the material are responsible for this discrepancy, but as indicated on my page http://www.physicsmyths.org.uk/hooke.htm this is rather implausible and a better explanation could be made in terms of plasma physics.