# Modulus of resilience

Labratory measurements show that when a certain material has a grain diameter of 2.33x10-2 mm it's yield strength is 107 MPa. When the material's grain diameter decreases to 1.84x10-2 mm it's yield strength increases to 117 MPa.
When the average grain diameter is increased to 3.28x10-2 mm, what is the modulus of resilience (in J/m^3) if the modulus of elasticity is known to be 182 GPa?

any idea? im stumped

Hi,

There is two questions.

1: Grain size may or may not affect in elastic modulus properties. In work hardening metals (like in some copper alloys) decreasing grain size may increase E a bit, not to mention effects of microstructure and residual stresses. How the grain size was decreased, or if the sample is different one. Not patronizing You, but make sure, and more importantly, make it real that you are looking at the right things. At first, does it matter that much. If it does, and the more it does, the more there is a need for normalizing properties of the material.

2: Elastic resilience (U) is usually far more complex issue than solving it by using just a single linear formula. The concept of "resilience modulus" has very dynamic nature.

But:

U = σ²/2E, where σ is (elastic) yield stress.

Check out: http://www.brushwellman.com/alloy/tech_lit/april01.pdf
(it's the "Area" there)

One problem in this concept is that yield displacement should be defined somehow (and quite well, actually). Then, whatever would happen in the material during deformations having different displacements and speed (non-linear damping, fatigue), one should most preferably consider a bit more extensive study in kinematic properties of materials. Again, not patronizing You at all, just flashbackin' some bitter events in the past :).

Of course, if You are doing some rebound tests just for fun or class work, forget about it. Being too open-minded may cause that notorious brain spillage :)