A portion of the stress-strain curve for a stainless steel alloy is shown in Figure P3.9. A 350-mm-long bar is loaded in tension until it elongates 2.0 mm and then the load is removed.
(a) What is the permanent set in the bar?
(b) What is the length of the unloaded bar?
(c) If the bar is reloaded, what will be the proportional limit?
Question 3.9: A portion of the stress-strain curve for a stainless steel a...
(a) The normal strain in the specimen is
\varepsilon=\frac{\delta}{L}=\frac{2.0 mm }{350 mm }=0.005714 mm / mmConstruct a line parallel to the elastic modulus line that passes through the data curve at a strain of ε = 0.005714 mm/mm. The strain value at which this modulus line intersects the strain axis is the permanent set:
permanent set = 0.0035 mm/mm
(b) The length of the unloaded bar is therefore:
\begin{aligned}&\delta=\varepsilon L=(0.0035 mm / mm )(350 mm )=1.225 mm \\&L_{f}=350 mm +1.225 mm =351.225 mm\end{aligned}
(c) From the stress-strain curve, the reload proportional limit is 444 MPa .
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