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How are stress and strain measured in a metal test?

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Diagram of a zinc-lead blast furnace system showing ore and coke entering through charge hoppers, with labeled furnace, air preheater, blower, taphole for slag and lead bullion, and a connected lead-splash condenser using rotors to separate and cool lead and zinc, with pathways for molten metals and off-gas. — metallurgy A zinc-lead blast furnace and lead-splash condenser. This technology is utilized mainly for producing zinc while managing both lead and zinc from raw materials, a technique that was highly influential in 20th-century smelting.

In metallurgy, stress and strain are typically measured during a tensile test, where a metal sample is subjected to a controlled load to evaluate its mechanical properties.1

Measuring Stress and Strain

Stress ( $σ$ ): This is defined as the force ( $F$ ) applied to the sample divided by its initial cross-sectional area ( $A$ ). It represents the internal resistance of the material to the applied load.231
Strain ( $ϵ$ ): This is the relative deformation of the material. In a tensile test, it is calculated as the change in length ( $L_{n} - L_{0}$ ) divided by the original length ( $L_{0}$ ).24

Test Observations

As the load increases, the relationship between these two values is often plotted on a stress-strain curve. Initially, the material undergoes elastic deformation, where strain is proportional to stress and the sample returns to its original shape upon unloading. If the load exceeds the yield stress, the metal undergoes permanent, or plastic, deformation. Continued loading eventually leads to the ultimate tensile stress and, ultimately, fracture. These measurements are essential for predicting how materials will perform under structural loads.5241