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

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In summary, The person is having trouble with getting different answers when using two different equations for calculating the Modulus of Resilience. The values used are Yield Stress = 1880 MPa, Yield Strain = 0.0068, and E = 401 GPa. The first equation, [U(r) = (Yield Stress x Yield Strain) / 2], gives an answer of 6.39 MJ/m^3 while the second equation, [U(r) = Yield Stress^2 / (2 x E)], gives an answer of 4.4 MJ/m^3. The person is wondering if there is additional information needed to resolve the discrepancy and suggests that the linear relationship between E, yield stress
  • #1
Nick Goodson
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TL;DR Summary
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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  • #2
Both of those formulas assume linear elastic behavior up to yield. Is there additional information for the problem?
 
  • #3
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.
 
  • #4
For linear elastic 1D stress, E=σ/e=276GPa so there is a discrepancy.
 
  • #5
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
 

1. What is the modulus of resilience?

The modulus of resilience is a measure of a material's ability to absorb and store energy when it is deformed elastically. It represents the maximum amount of energy that a material can absorb without undergoing permanent deformation.

2. How is yield stress related to modulus of resilience?

Yield stress is the amount of stress required to cause a material to start deforming plastically. The higher the yield stress, the more energy a material can absorb before reaching its yield point, and therefore the higher its modulus of resilience.

3. What is the significance of yield strain in calculating modulus of resilience?

Yield strain is the amount of strain a material experiences at its yield point. It is an important factor in calculating modulus of resilience because it indicates how much a material can deform before reaching its yield point and undergoing permanent deformation.

4. How is the modulus of resilience calculated?

The modulus of resilience is calculated by taking the area under the stress-strain curve up to the yield point. This can be done by using the formula E = σ^2/2ε, where E is the modulus of resilience, σ is the yield stress, and ε is the yield strain.

5. What is the unit of measurement for modulus of resilience?

The unit of measurement for modulus of resilience is joules per cubic meter (J/m^3). This unit represents the amount of energy that can be absorbed per unit volume of material before reaching its yield point.

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