Eren Billur
Technical Manager

# Digital Image Correlation for Creating FLCs

June 1, 2020

The forming limit curve (FLC) has been a key problem solver in the metal forming industry since the 1960s. Developed by the late Dr. Stuart Keeler, formerly the author of the Science of Forming column for MetalForming magazine, stampers use the FLC during tool development and production-problem analysis. However, most users do not understand the origin and variables that influence the shape and placement of the curve.

Unfortunately, often we see the terms FLC and FLD (forming limit diagram) incorrectly used interchangeably. Fig. 1 displays their differences.

FLC changes with material type and thickness, and with the material supplier. It also can change from coil to coil and batch to batch, and even within the same coil. In addition, different test methods can result in different FLCs.

Strain distribution depends on the material and the forming process. To measure strain distributions, we apply a grid before deforming the part. As Keeler pointed out, circle grids are easier to analyze, as their orientation simply gives the principal strains. Note: For additional information on circle-grid analysis, visit www.metalformingmagazine.com/article/?/quality-control/cmms-scanning-systems-camera-systems-others/introduction-to-strain-analysis-measuring-strains.

After stamping a part, the circles on the grid may become ellipses, or circles with different radii. By calculating the percentage elongations with respect to the original circle diameters, we can calculate strain distribution. Then, knowing the strain distributions on the stamped part and the FLC of the incoming material, we can evaluate forming severity, how close the process is to failure, and the process robustness relative to the material’s forming limits.

Determining FLC

While FLC theory originated during the 1960s, no standards existed until 2002, which saw the publication of ASTM E2218, Standard Test Method for Determining Forming Limit Curves. In 2008, ISO published ISO 12004—Metallic materials—Sheet and strip—Determination of forming-limit curves—Part 2: Determination of forming-limit curves in the laboratory.

Today, most shops determine FLCs using approximation methods, primarily based on a material’s n-value (strain-hardening exponent) and sheet thickness. As an alternative, we now can use digital image correlation (DIC) systems to determine FLC experimentally. Here, we prepare several Nakajima (shown in Fig. 1) or Marciniak test specimens for different strain paths. We paint the specimens white and apply a black speckle pattern. Each specimen then is clamped around the periphery and stretched using either a hemispherical punch (Nakajima test) or a flat-bottom punch with a carrier blank (Marciniak test) until fracture. The different punch shapes produce different strain paths and, as a result, different FLCs.

In the past, those conducting the test would try to sense necking of the specimen using their fingers. Once they sensed necking, they would manually measure the strain distribution on that section. Now, noncontact optical DIC systems can sense the onset of necking and then measure strain distribution. The operator can set the DIC system to take photographs of the test specimen at given time increments (at least 10 photos/sec., according to ISO 12004-2008) from the time the punch starts to deform the sheet metal until after a crack forms (Fig. 2A).

At test completion, the operator uses the last photo before fracture to calculate the strains at the most critical sections (Fig. 2B). A curve fit is applied to find the major and minor strains at the apex, and includes only the data points that have not already necked. Fig. 2C shows the major strain calculation of 1-mm-thick DP590, with minor strain shown in red. For the given geometry, major strain was calculated as 0.211 and minor as 0.051. This corresponds to point AB in Fig. 1.

Developing an FLC requires at least 15 experiments (according to ISO 12004-2008). Confidence in the results increases with the number of experiments. Fig. 1 shows an FLC derived from more than 30 experiments (eight geometries with three to five repetitions). The previous technique of detecting necking by touch and then manually measuring a number of ellipses was time-consuming, with accuracy depending on operator skill. Modern techniques using DIC reduce the operator’s subjectivity in sensing the neck initiation and save time in measuring and calculating strain distribution. MF

Come hear Dr. Eren Billur speak at the 3rd Metal Forming Technology Day, in Bursa, Turkey. Visit www.billur.com.tr/meftech for more information. The author would like to thank Turkay Muratoglu of Atilim University and Dr. Danny Schaeffler for their valuable help in preparing this column.

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