How materials can be broken-a conceptual understanding

[chandran]

concept problem

There is a material and it is pulled by a distance by applying a force F. Tell me whether my intuitions is correct

1.In the world around we see materials of different shapes because the inter molecular forces bonds the molecules together in such shapes.

2.If one likes to break the material he should first exceed the inter molecular force(or cut the inter molecular force)

3.My question is what is the value of that inter molecular force. If i know that it is equal to "f" i will apply a force greater than "f" and then break the material.

4.How to calculate the inter molecular force.

5.Will my understanding of the above lead to the derivation of the stress & strain.

 

[Pyrrhus]

Look for stress-strain diagram of a material. The tests specifications are given by the ASTM (American Society for Testing Materials), you might want to check that, too.

 

[Mech_Engineer]

3.My question is what is the value of that inter molecular force. If i know that it is equal to "f" i will apply a force greater than "f" and then break the material.

4.How to calculate the inter molecular force.

5.Will my understanding of the above lead to the derivation of the stress & strain.

I don't think you can just "derive" a stress-strain curve for a material. The interactions between molecules in the material are VERY complex, They don't just simply break, and that's it; the material sample will elongate with plastic deformation, crystalline grain structures can break and then re-attach to the next offset molecule (which is what causes the permanenet plastic deformation). The molecular interactions are so incredibly complex not even the biggest supercomputer can think about trying to solve it, we're talking about degrees of freedom on the order of 100 times avogadro's number!

You would also have to take into account things like interstitial molecules in the grain structure for alloys, imperfections, grain structures and orientations, grain size, pre-stressing, the list goes on forever!

While it seems like a good idea, the fact is you would need an accurate model that knew exactly how the molecules in the material were behaving, and then you would need to model EVERY MOLECULE in the sample. Prorfessors have spent their entire careers studying and trying to understand the nuances of material science, and they will be the first to tell you they have no way to model a tensile or hardness test. It is not entirely understood how the molecules interact in complex situations like the tensile test. This is why the stress-strain curve is derived experimentally, not calculated from basic material properties.

Then of course there is work hardening, and fatigue, which are even deeper subjects than this, and definitely can't be described without real-world data... They can barely be described with empirical testing!

Hope this helps some, or at least let's you know what you're in for

 

[Gokul43201]

Most everything I'd have said has been covered by Mech Eng above, but to address the specific questions...

1.In the world around we see materials of different shapes because the inter molecular forces bonds the molecules together in such shapes.

Very rarely is this true (eg: shape of a raindrop or soap bubble or snowflake). Most things are the shape they are because of external factors (eg: the glass on your window was rolled into that shape by a machine).

2.If one likes to break the material he should first exceed the inter molecular force(or cut the inter molecular force)

In general this is true.

3.My question is what is the value of that inter molecular force. If i know that it is equal to "f" i will apply a force greater than "f" and then break the material.

Only with a perfectly pure, strain-free single-crystal.

However, the term "intermolecular force" is itself a little misleading. In a metal, for instance, the glue that hold the atoms together is provided by the (delocalized) free electrons - there are no molecules involved. In a polycrystalline material there is no single value for the "intermolecular force".

4.How to calculate the inter molecular force.

Again, only for a pure single-crystal does such a calculation exist. It usually involves some form of the Tight Binding model, but even here, the more accurate calculations use hand-fed parameters. For a purely crystalline ionic solid the Madelung formulation provides solutions for simple cases.

5.Will my understanding of the above lead to the derivation of the stress & strain.

Maybe a little. That's only just the tip of the iceberg.

And now for the bombshell (after all this talk about interatomic forces): There is no net force experienced by the atoms/molecules/ions in a solid under equilibrium.

Even Newton could have told you that.