Question

An alloy has a yield strength of 805 MPa and an elastic modulus of 107 GPa. Calculate the modulus of resilience for this alloy (in J/m3, which is equivalent to Pa) given that it exhibits linear elastic stress-strain behavior. J/m3

Answer 1

The modulus of resilience is
`3.028* 10^(6)` joules per cubic meter.

Step-by-step explanation:

At first we assume that allow behaves elastically, then the formula for the modulus of resilience (
`U_(r)`), measured in joules per cubic meter, is:

`U_(r) = (\sigma_(y)^(2))/(2\cdot E)` (Eq. 1)

Where:

`\sigma_(y)` - Yield strength, measured in pascals.

`E` - Modulus of elasticity, measured in pascals.

If we know that
`\sigma_(y) = 805* 10^(6)\,Pa` and
`E = 107* 10^(9)\,Pa`, then the modulus of resilience is:

`U_(r) = ((805* 10^(6)\,Pa)^(2))/(2\cdot (107* 10^(9)\,Pa))`

`U_(r) = 3.028* 10^(6)\,(J)/(m^(3))`

The modulus of resilience is
`3.028* 10^(6)` joules per cubic meter.