Materials Science and Engineering: An Introduction

$T_{f} = 41.34 °C (106.41°F)$
Given: steel wire with stress of 70 MPa (10,000psi) at $T_{0}= 20°C (68°F)$ Required: temperature $T_{f}$ if length is held constant and the stress is to be reduced to 17 MPa (2500 psi) Solution: Using Equation 19.8: $σ = Eα_{l}(T_{0} - T_{f})$ Since the stress is to be reduced from 70 MPa to 17 MPa, the resulting stress will be compressive, so: $σ = -53 MPa$ Substituting values for steel from Table 6.1, it follows: $(-53 MPa) = {(207 \times 10^{3} MPa) (12.0 \times 10^{-6} (°C)^{-1}) (20 °C} - T_{f})$ $T_{f} = 41.34 °C$