## Materials Science and Engineering: An Introduction

For steel, $1.67 \times 10^{6} J/m^{3}$ For brass, $7.44 \times 10^{5} J/m^{3}$ For aluminum, $5.48 \times 10^{5} J/m^{3}$ For titanium, $2.22 \times 10^{6} J/m^{3}$
Given: refer to the given table (steel alloy, brass alloy, aluminum alloy, and titanium alloy) from Table 6.1, the modulus of elasticity for each alloy is as follows: Steel alloy = 207 GPa Brass alloy = 97 GPa Aluminum alloy= 69 GPa Titanium alloy = 107 GPa Required: moduli of resilience for each alloy Solution: Using Equation 6.14: $U_{r} = \frac{σ_{y}^{2}}{2E}$ For steel, $U_{r} = \frac{(830 \times 10^{6} N/m^{2})^2}{(2)(207 \times 10^{9} N/m^{2})} = 1.67 \times 10^{6} J/m^{3}$ For brass, $U_{r} = \frac{(380 \times 10^{6} N/m^{2})^2}{(2)(97 \times 10^{9} N/m^{2})} = 7.44 \times 10^{5} J/m^{3}$ For aluminum, $U_{r} = \frac{(275 \times 10^{6} N/m^{2})^2}{(2)(69 \times 10^{9} N/m^{2})} = 5.48 \times 10^{5} J/m^{3}$ For titanium, $U_{r} = \frac{(690 \times 10^{6} N/m^{2})^2}{(2)(107 \times 10^{9} N/m^{2})} = 2.22 \times 10^{6} J/m^{3}$