and so the failure theory, we went all the way back to my mechanical

materials part one course today, simple tension test, and

it was easy to perform and provided very good results for a variety of materials.

So we put a tensal force, we looked at the stress strain curve,

we predicted yield, we predicted fracture, we can find Young's Modulus,

a very nice test, very useful test.

But what about when we have more complex loading conditions,

when it's not just the simple axial load?

By have bi-axial loading or tri-axial loading.

Well, in those cases, the cause of failure may be unknown and

there are several theories that can be used for predicting failure for

these various types of loading.

And I'm going to focus on just three.

The first one we will review is the Maximum Normal Stress Theory, that says,

that when the normal stress in our actual engineering element is greater

than what's defined as our failure stress, then we're going to experience failure.

And it assumes that the material is subject to a combination of loads.

And it fails, can be a combination loads and

it fails when the maximum normal stress at any point exceeds the actual

failure stress as determined by that simple tension test, and

we said this by experiences was generally good for just brittle materials.

It was not good for ductile materials like steel, aluminum, plastics, etc.

For those ductile materials we also looked at the maximum shear stress theory

which is also called Tresca's Yield Crieterion and

this said that failure occurs when the shear stress, the actual shear stress,

is greater than what we define as our failure shear stress.

And this is good for ductile material and

that's because in yield, ductile materials.

Usually the yield is caused by

a slippage of crystal planes along the maximum sheer stress surfaces.

And so here's our simple tensional test.

Here's a stress block with that tension on it.

If we draw Mohr's Circle we see that tau failure is one half of

the normal failure based on the simple tension test.