Daniel Schaeffler Daniel Schaeffler
President

Metal Properties: Uniform Elongation

November 30, 2022
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The elongation value found on metal certs relates to its ductility to the point of fracture. Certs show this as “elongation at fracture” or “elongation after fracture,” depending on the test method used. These values differ from the focus of this article—uniform elongation.

MM Dec 2022- Fig 1During a tensile test, the dogbone-shaped sample undergoes a reduction in the cross-sectional width and thickness as its length increases in tension. A stress-strain curve plots the material’s response to the applied load and resulting elongation. The shape of this curve shows a peak at the maximum engineering stress, called the tensile strength. This characteristic shape results from the opposing effects of the work hardening and the reduction in cross-sectional area that occurs when the sample deforms in tension. 

The beginning of the curve slopes upward due to work hardening effect outweighing that from the cross-sectional area reduction. Starting at the tensile strength, reduction in the cross-sectional area of the test sample overpowers the work hardening and the slope of the engineering stress-strain curve decreases. A diffuse neck forms at this maximum engineering stress, typically found in the middle of the sample in the reduced-width portion of the gauge length.

The elongation where the maximum stress occurs is called “uniform elongation.” In a tensile test, uniform elongation is the percent increase in gauge length occurring at peak stress relative to the initial gauge length. For example, if the gauge length at peak stress measures 59 mm and the initial gauge length was 50 mm, uniform elongation is (59-50)/50 = 18 percent.

The diagrams in Fig. 1 illustrate how the tensile bar changes shape during the test, with the gauge region highlighted in blue. Through uniform elongation, the cross-section has a rectangular shape. Necking begins at uniform elongation, and the cross-section no longer is rectangular. All subsequent deformation concentrates in the necked region, becoming the site of eventual fracture.

MM -Dec 2022- Fig 2Accurate metal forming simulation requires capturing the stress-strain relationship at all strains, but a tensile test alone provides valid data only through uniform elongation. Beyond this value, simulation engineers assume either a certain behavior, or more accurately rely on the results from bulge testing or other methods to capture the correct response.

Theory and experiments show that uniform elongation expressed in true strain units is numerically equivalent to the instantaneous n-value.

Uniform Elongation: Not That Uniform

Load increases during the tensile test, and until recently, the deformation was thought to be distributed uniformly over the gauge length prior to reaching uniform elongation. Recently, however, researchers have gathered evidence confirming that a nonuniform strain distribution exists within the gauge region prior to reaching uniform elongation. Acquiring this new knowledge required moving from traditional extensometers to the use of a refined noncontact imaging approach called digital image correlation (DIC), discussed in the Cutting Edge column in the February 2020 issue of MetalForming magazine.

Traditional extensometers calibrated for 50- or 80-mm gauge lengths determine elongation from deformation measured relative to this initial length. This approach averages results over these lengths and leads to greater peak-strain measurements over the smaller reference length.

With the aid of DIC, researchers now can use a much smaller reference length by setting a virtual gauge length generated through application of a fine, random speckle pattern on the sample before testing. A camera captures the motion of the speckle pattern during the test, calculating elongation relative to gauge lengths as small as 0.5 mm. 

While conventional wisdom held that uniform strains exist prior to strains reaching uniform elongation, researcher Thomas Stoughton, in 2021, monitored the movement of more than 200 points in the traditional 50-mm span and showed that each one experienced a unique strain evolution, with differences starting before reaching uniform elongation (Fig. 2). In addition, he showed that for DP980 steel, this approach obtains useful data at as much as 61-percent strain rather than only to the uniform elongation of 8-percent strain. This study suggests that DIC-aided measurements potentially can reduce or eliminate the need for many of the tests required for accurate metal forming simulations. MF

Industry-Related Terms: Ductility, Edge, Forming, Gauge, Point, 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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