Chapter 4, Problem 4.15QP

A tension test was performed on an aluminum alloy specimen to fracture. The original diameter of the specimen is 0.5 in. and the gauge length is 2.0 in. The information obtained from this experiment consists of applied tensile load (P) and increase in length (ΔL). The results are tabulated in Table P4.15. Using a spreadsheet program, complete the table by calculating engineering stress (σ) and engineering strain (ε). Determine the toughness of the material (u_t) by calculating the area under the stress–strain curve, namely,

${\text{u}}_t={\displaystyle \underset{\text{0}}{\overset{{\text{ε}}_{\text{f}}}{\int }}\text{σdε}}$

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

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