# Various parameters for Lab 1

I hope this guide helps you in getting all the various slopes and parameters.

## 1. Young’s modulus or the slope of elastic line

Young’s modulus provides an important measure of stiffness, which is the ability of the body to resist deformation. It is a fundamental property of the material and you might have used it all the time in 104 lectures.

Draw a straight (red) line for the initial linear slope and get the slope of the red line by:

$$Young^{‘}s\ modulus = \frac{Stress\ at\ Blue - Stress\ at\ Yellow}{Strain\ at\ Blue - Strain\ at\ Yellow}$$

Rebound modulus provides an estimate of how material would behave on unloading and reloading after the plastic deformation has occurred. Observe how the complete deformation is not recovered and there is some plastic deformation. Yet, the rebound modulus line is pretty parallel to Young’s modulus line.

Draw a straight (red) line for the rebound slope and get the slope of the red line by:

$$Rebound modulus = \frac{Stress\ at\ Blue - Stress\ at\ Yellow}{Strain\ at\ Blue - Strain\ at\ Yellow}$$

## 3. Initial yield strain ( $\epsilon_0$)

The yield point is the point on a stress-strain curve that indicates the limit of elastic behavior and the beginning of plastic behavior. Prior to the yield point, a material will deform elastically and will return to its original shape when the applied stress is removed. After this point there are irrecoverable plastic deformations.

To get the $\epsilon_0$, just eye ball the point where you think the graph is starting to bend from the linear section. The strain at that eye ball point is the $\epsilon_0$.

Now eye balling is subjective and changes from person to person, so just pick a point which is inside the blue square where you think the graph starts the bend. The strain at that point is rhe $\epsilon_0$ and you will use that in the fitting.

## 4. Yield stress ($\sigma_y$)

Yield stress is how much stress needs to be applied to an object to cause it to change from elastic deformation to purely plastic deformation. After this point, the plastic material just goesssss, expanding/elongating with minimal increase in stress.

Make a line (red) parallel to the initial linear elastic section which starts at 0.002 micron strain (or, 0.2% strain). The stress at the point where this line intersects the original graph (blue circle) is the yield stress. Again, please report me your own specific values.

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