During a tensile test in which the starting gage length 100

During a tensile test in which the starting gage length = 100.0 mm and the cross-sectional area = 150 mm2. During testing, the following force and gage length data are collected: 17, 790 N at 100.2 mm, 23, 040 N at 103.5 mm, 27, 370 N at 110.5 mm, 28, 910 N at 122.0 mm. Yielding occurred at a load of 19, 390 N (0.2% offset value), and the maximum load (4) was 28, 960 N. Determine the strength coefficient and the strain-hardening exponent in the flow curve equation.

Solution

Since yielding occur at 19.39 KN, so values above it will be considered for flow equation.

From data 2

F = 23.04 KN, Lf = 103.5 mm

Using eq AfLf = AoLo

Af = 144.927 mm²

Therefore True stress = 23040/144.927 = 158.976 MPa

Also at this point True Strain = ln(103.5/100) = 0.0344

Therefore, S=Keⁿ .... 158.927 = K(0.0344)ⁿ ..... (1)

Similarly for load P = 27370 N, Af = 135.746 mm²

Therefore Stress S = 27370/135.746 = 201.625 MPa

Also strain at this point e = ln(110.5/100) = 0.099

the flow equation 201.625 = K(0.099)ⁿ ...... (2)

from equation 1 and 2

strain hardening exponent n = 0.225

and strength cofficient K = 339.3 MPa