Question

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Table 1: TENSILE TEST RESULTS OF A METAL SAMPLE with d = 7.42, lo = 40mm (4 marks) Load, KN Extension, mm Stress, MPa Strain 0 0 10 0.05 17 0.08 25 0.11 30 0.14 34 0.20 37.5 0.40 38.5 0.60 36 0.90 Cross-sectional Area (A) Modulus of Elasticity (E) Tensile Strength (ST) Percent Elongation (%EL) A = T d2 4 E = Sy Ey ST = PU A %EL = Extension at fracture Gauge Length

Answer 1

d = 7.42 mm

l_o = 40 mm

$A = \frac{\pi}{4}d^2 = \frac{\pi}{4}7.42^2 = 43.22 mm^2$

$Stress = \frac{Load}{Area} = \frac{10\times10^3}{43.22}= 231.38 MPa$

0.05 Strain ertension 1 0.0013 40

Load, kN Extension, mm Stress, MPa Strain 0 0 0 0 10 0.05 231.38 0.0013 17 0.08 393.34 0.0020 25 0.11 578.45 0.0028 30 0.14 694.13 0.0035 34 0.2 786.69 0.0050 37.5 0.4 867.67 0.0100 38.5 0.6 890.81 0.0150 36 0.9 832.96 0.0225

I. Stress- Strain Diagram

Yield Strength, S_Y = 700 MPa

1000 Ultimate Strength 800 Yield Strength 600 Stress, MPa 400 200 0 0.0 0.2 0.4 0.6 0.8 1.0 Yield Strain Strain

Yield Strain, $\epsilon_y$ = 0.14

Modulus of elasticity

$E = \frac{S_y}{\epsilon_y} =\frac{700}{0.14}=5000 MPa$

Ultimate Tensile Load

$P_U = S_T \times A = 890 \times 43.22 = 38465.8 N = 38.46 kN$

II. The stress and strain in the graph shows linear upto the material attains the yield strength (700 MPa). Within this point, if the load is removed the material returns to its original undeformed form. This region is called the elastic region. After this point, there is permanent strain occurs. The stress-strain curve beyond the elastic region is called plastic region. Strain above the 0.14 are the plastic region. The elastic region is upto the strain of 0.14.

III. Tensile test is performed on the material in order to understand the mechanical behavior of the material. Before using any material in design, it is essential to know the limiting values such as yield stress, ultimte load, strain and strain hardening, linear and non-linear mechanisms of the material.