Chapter 3, Problem 3.44QP

An engineering technician performed a tension test on an A36 mild steel specimen to fracture. The original cross-sectional area of the specimen is 0.25 in² and the gauge length is 4.0 in. The information obtained from this experiment consists of applied tensile load (P) and increase in length (∆L) The results are tabulated in Table P3.44. Using a spreadsheet program, complete the table by calculating the engineering stress (σ) and the engineering strain (ε). Determine the toughness of the material (u_t) by calculating the area under the stress-strain curve, namely,

$u_t={\displaystyle \underset{0}{\overset{{\epsilon }_f}{\int }}\sigma d\epsilon }$

where ε_f is the strain at fracture. The preceding integral can be approximated numerically using a trapezoidal integration technique:

$u_t={\displaystyle \underset{i=1}{\overset{n}{\sum }}{u}_i}={\displaystyle \underset{i=1}{\overset{n}{\sum }}\frac{1}{2}}\left({\sigma }_i+{\sigma }_{i-1}\right)\left({\epsilon }_i-{\epsilon }_{i-1}\right)$

TABLE P3.44