Calculating Modulus of Resilience: Yield Stress, Yield Strain, E

[Nick Goodson]

TL;DR

Differing answers for modulus of resilience

Hi,
I have a problem, using the 2 different equations for calculating the Modulus of Resilience, I get 2 different answers. It seems simple, but I’m a little perplexed.
For the following values:

• Yield Stress = 1880 MPa
• Yield Strain = 0.0068
• E = 401 GPa
  [U(r) = (Yield Stress x Yield Strain) / 2] - answer = 6.39 MJ/m^3
  [U(r) = Yield Stress^2 / (2 x E)] - answer = 4.4 MJ/m^3

Many thanks

 

[Frabjous]

Both of those formulas assume linear elastic behavior up to yield. Is there additional information for the problem?

 

[Nick Goodson]

Both of those formulas assume linear elastic behavior up to yield. Is there additional information for the problem?

That's all the info I have.
I guess the assumption is that the value for E would need to be defined using yield stress and yield strain to resolve, but is defined by a linear relationship.

 

[Frabjous]

For linear elastic 1D stress, E=σ/e=276GPa so there is a discrepancy.

 

[Nick Goodson]

For linear elastic 1D stress, E=σ/e=276GPa so there is a discrepancy.

Yes, that's why I was a bit perplexed