Engineering stress-strain units are based on the starting dimensions of the tensile test sample: Engineering stress is the load divided by the starting cross-sectional area, and engineering strain is the change in length relative to the starting gauge length (2 inches, 50mm, or 80mm for ASTM [ISO I], JIS [ISO III], or DIN [ISO II] tensile test samples, respectively.)
Metals get stronger with deformation through a process known as strain hardening or work hardening. This is represented on the stress strain curve by the parabolic shaped section after yielding.
Concurrent with the strengthening as the tensile test sample elongates is the reduction in the width and thickness of the test sample. This reduction is necessary to maintain consistency of volume of the test sample.
Initially the positive influence of the strengthening from work hardening is greater than the negative influence of the reduced cross-section, so the stress-strain curve has a positive slope. As the influence of the cross-section reduction begins to overpower the strengthening increase, the stress-strain curve slope approaches zero.
When the slope is zero, the maximum is reached on the vertical axis of strength. This point is known as the ultimate tensile strength, or simply the tensile strength. The strain at which this occurs is known as uniform elongation.
Strain concentration after uniform elongation results in the formation of diffuse necks and local necks and ultimately fracture.
Figure 1: Tensile Strength is the Strength at the Apex of the Engineering Stress – Engineering Strain Curve.