Question 1.3: The tensile test was conducted on a mild steel bar. The foll...
The tensile test was conducted on a mild steel bar. The following data were obtained during the test:
Diameter at the steel bar: 16 mm
Gauge length at the bar: 80 mm
Load at proportionality limit: 72 kN
Extension at a load of 60 kN: 0.115 mm
Load at failure: 80 kN
Final gauge length of bar: 104 mm
Diameter of the rod at failure = 12 mm
Determine (a) Young’s modulus, (b) proportionality limit, (c) true breaking stress, (d) percentage elongation and (e) percentage reduction in cross-sectional area.
A typical load–deflection plot for a steel bar during tensile test is shown in Figure 1.18.
(a) Young’s modulus (E ) is the ratio of longitudinal stress to longitudinal strain within the proportional limit
E=\frac{P / A_o}{\Delta L / L_o}=\frac{60 \times 10^3 \times 80}{(\pi / 4) \times 16^2 \times 0.115} \frac{ N }{ mm ^2}
therefore E = 207593.4 MPa = 207.59 GPa.
(b) Proportional limit is ratio of load at proportional limit to original cross-sectional area
\text { Proportional limit }=\frac{72\left(10^3\right)}{(\pi / 4) \times 16^2} MPa
therefore proportional limit is 358.1 MPa.
(c) True breaking stress is the ratio of breaking point load to area at breaking point
\text { True breaking stress }=\frac{80 \times 10^3}{(\pi / 4) \times 12^2} \frac{ N }{ mm ^2}
Thus, the true breaking stress is 707.36 MPa.
(d) Percentage elongation is given by
\% \text { elongation }=\frac{L_{ \text{f} }-L_{ o }}{L_{ o }} \times 100=\frac{104-80}{80} \times 100
where L_{ o } \text { and } L_{ \text{f} } are initial and final gauge lengths. Therefore the percentage elongation is 30%.
(e) Percentage reduction in area is given by
\begin{aligned} \% \text { reduction } &=\frac{A_{ o }-A_{ \text{f} }}{A_{ o }} \times 100 \\ &=\frac{(\pi / 4) d_{ o }^2-(\pi / 4) d_{ \text{f} }^2}{(\pi / 4) d_{ o }^2} \times 100 \\ &=\left\lgroup 1-\frac{d_{ \text{f}}^2}{d_{ o }^2} \right\rgroup \times 100 \\ &=\left\lgroup 1-\frac{12^2}{16^2} \right\rgroup \times 100 \end{aligned}
where d_{ o } \text { and } d_{ \text{f} } are initial and final rod diameters. Therefore percentage reduction is 43.75%.
Note: Ductility of steel, quantitatively, is expressed by the parameters calculated in parts (d) and (e) above.
