in Science materials, what is difference b/w E and G?

I'm studying Science Materials on Callister's Materials Science and Engineering: An Introduction. I've never studied Mechanics (except for basic Physics courses), so I was wandering:

1. when talking about stress-strain, what is the difference b/w these two? $$\sigma= E \epsilon \\ \tau= G \gamma$$ I know the 1st eq is Hook's Law, E is Young's elastic modulus (usually measured in MPa or GPa), and that $\gamma=\tan{\theta}$, but what is $\theta$?
2. What is $\sigma_y$, so-called yield strength? Where do I find it in a stress-strain curve?
3. In what conditions do I trace the parallel to the elastic portion of the $\sigma - \epsilon$ curve, passing through $\epsilon=0.002$? Is this technique valid only for certain materials? Which are they?

1. your first equation applies to tension & compression, the second to torsion.

http://en.wikipedia.org/wiki/Torsion_(mechanics) the link also shows what theta is.

1. The point where plastic (permanent) deformation occurs. Where it is on the stress strain curve depends on how you define it, wiki shows the various methods:

http://en.wikipedia.org/wiki/Yield_(engineering)

1. In the condition that you are looking for proof stress. I was taught this method but told it was not commonly used (outside of the USA IIRC) . from the link: ""High strength steel and aluminum alloys do not exhibit a yield point, so this offset yield point is used on these materials.[5]""

If you are able to make the switch from the conventional scalar representation of material properties to tensor representations, you will be better off. It will open up an entirely new way of looking at things, if you can handle the math.

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