Daniel Schaeffler Daniel Schaeffler

Metal Properties: Tensile Strength

September 26, 2022

Note: This article continues a series on metal properties: Elastic Modulus, August 2022 issue of MetalForming; and Yield Strength, September 2022 issue of MetalForming.

Determining material strength during a tensile test requires dividing the pulling load by the cross-sectional area of the tensile bar, leading to the units of lb./in.2. Impacting the results are whether the calculation incorporates the tensile-bar width and thickness before testing begins, or whether the calculations consider the ever-changing dimensions instead.

Metal Matter graphUsing the initial dimensions of the tensile bar creates the engineering stress-strain curve. The material provider bases the material’s properties, provided on the metal certifications, on engineering units. Because the initial cross-sectional area is a constant, any changes in stress reflect changes in the load required to deform the tensile specimen. This stress-strain curve has a characteristic parabolic shape, with the maximum strength defined as the ultimate tensile strength (UTS, TS or Rm). After reaching the tensile strength, the curve shape might suggest that the metal softens. However, it does not, with other aspects of the test at play to explain the downward-sloping shape.

While using the initial dimensions of the tensile bar is convenient, it does not reflect what occurs during the test. A tensile load elongates the test sample, with both the thickness and width decreasing. Remembering that metal alloys gain strength with additional deformation from work hardening, the applied load continues to increase.  With the cross-sectional area continually decreasing as the test progresses, strength (load divided by the instantaneous cross-sectional area) continues to rise. Using the ever-changing dimensions of the tensile bar creates the true stress-strain curve. Properties incorporated into metal forming simulations are based on true units, accounting for dimensional changes occurring with deformation.

Engineering vs. True Curve-Shape Differences

During a tensile test, strength and sample dimensions continually change. The applied load required to pull the sample increases, since the sheet metal gets stronger as it deforms during the tensile test. Concurrently, the sample width and thickness decrease, but this is not factored into the engineering units that only rely on the starting dimensions. Initially, the positive influence of the strengthening from work hardening exceeds the negative influence of the reduced cross-section; this gives the stress-strain curve a positive slope. As the influence of the cross-section reduction begins to overpower that of the strengthening increase, the slope of the stress-strain curve approaches zero. When the slope reaches zero, the vertical axis (strength) reaches a maximum UTS; the corresponding strain is the uniform elongation, as necking has not yet initiated.

As shown in the accompanying figure, the true stress always exceeds the corresponding engineering stress, because the instantaneous cross-section always is smaller than the initial cross-section.

When considering the true stress-strain curve, which reflects the dimensional changes occurring on the sample, there is no stress maximum occurring during the test. The material continues to harden and deform at stresses well above the UTS. MF

Industry-Related Terms: Alloys, Forming, Tensile Strength, Thickness, Work Hardening
View Glossary of Metalforming Terms


See also: Engineering Quality Solutions, Inc., 4M Partners, LLC

Technologies: Materials


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