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

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The discussion centers on the calculation of the Modulus of Resilience using two different equations, which yield conflicting results. The first formula, using yield stress and yield strain, gives an answer of 6.39 MJ/m^3, while the second, based on yield stress squared divided by twice the modulus of elasticity, results in 4.4 MJ/m^3. Both formulas assume linear elastic behavior up to yield, but the modulus of elasticity (E) appears to be inconsistent, calculated as 276 GPa from the yield stress and strain. This discrepancy raises questions about the assumptions made regarding the material's behavior. Clarification on the definition of E in relation to yield stress and strain is necessary to resolve the issue.
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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
 
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Both of those formulas assume linear elastic behavior up to yield. Is there additional information for the problem?
 
Frabjous said:
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.
 
For linear elastic 1D stress, E=σ/e=276GPa so there is a discrepancy.
 
Frabjous said:
For linear elastic 1D stress, E=σ/e=276GPa so there is a discrepancy.
Yes, that's why I was a bit perplexed
 
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