The formula to calculate the Modulus of Resilience (Ur) is:
\[ Ur = \frac{σy^2}{2E} \]
Where:
The Modulus of Resilience is the strain energy per unit volume required to stress a material from an unloaded state up to the point of yielding.
Yield Strength can be defined as follows: a straight line is constructed parallel to the elastic portion of the stress–strain curve at a strain offset of 0.002.
Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.
Let's assume the following values:
Using the formula:
\[ Ur = \frac{35,000,000^2}{2 \cdot 15} \]
Evaluating:
\[ Ur \approx 40,833,333,333,333.3 \]
The Modulus of Resilience is approximately 40,833,333,333,333.3 Pascals.
| Yield Strength (σy) (Pa) | Young's Modulus (E) (N/m) | Modulus of Resilience (Ur) (Pa) |
|---|---|---|
| 30000000 | 10 | 45,000,000,000,000.000000000000 |
| 30000000 | 15 | 30,000,000,000,000.000000000000 |
| 30000000 | 20 | 22,500,000,000,000.000000000000 |
| 35000000 | 10 | 61,250,000,000,000.000000000000 |
| 35000000 | 15 | 40,833,333,333,333.335937500000 |
| 35000000 | 20 | 30,625,000,000,000.000000000000 |
| 40000000 | 10 | 80,000,000,000,000.000000000000 |
| 40000000 | 15 | 53,333,333,333,333.335937500000 |
| 40000000 | 20 | 40,000,000,000,000.000000000000 |