Fundamentals of Forming Limit Curves (FLC) Testing

Sheet Formability refers to the ability of a sheet metal to be formed into the desired shape without cracking or rupturing. For the simplest explanation, the tension test will be taken as an example.

In this test, a dogbone-shaped test sample undergoes a tensile load along its axis until rupture; from force and elongation measurements, the well-known “stress/strain” curve can be constructed. The x-axis here is strain, and it represents the change in length with respect to the original length of the dogbone sample (e=∆L/L0).

Formability in this case is equivalent to the “ductility” of the material; the latter can be arbitrarily taken at the point of necking (uniform ductility) or at point of rupture (total ductility), or somewhere in between.

When moving from the simple tension test to actual sheet metal forming operations (such as the stamping of a door), the deformation of the material becomes more complicated, simply because the material is deformed in two directions at the same time.

Nevertheless, the definition of formability is similar yet scalable to this more complex case; i.e., sheet formability is a measure of the ductility of the material when deformed in two directions. If we take any particular small region within a stamped door, we will notice that the material is stretched/compressed in two directions by different amounts to generate the features and complex details of the door. If we were to measure the amount of stretching in the two directions, then the ratio between the smaller amount (minor strain) and the larger amount (major strain) is known as the “biaxial ratio”; determining the ductility limits of the material for various biaxial strain ratios is accomplished by “sheet formability testing”.

There are three main critical strain ratios (or loading paths) that are relevant to sheet formability testing: Uniaxial Tension (UT), Plane-Strain Tension (PST), and Balanced Biaxial Tension (BBT). Each one is characterized by different strain ratios.
Uniaxial Tension (UT) describes a situation where stress is applied entirely along the major axis with no loading in the transverse direction. However, the since the material is stretching along the major axis, it must also contract along the minor axis to maintain a constant volume. This leads to a typical UT strain ratio of -0.5 (the strain ratio is negative because the minor strain is compressive).
Plane-Strain Tension (PST) describes a situation where there is stretching in just the longitudinal direction without any change in the width, thus producing a strain ratio close to 0.
Balanced Biaxial Tension (BBT) describes an extreme situation where there is an even stretching in both the longitudinal and transverse directions, thus implying a strain ratio close to 1.

Based on the principles described before, formability testing requires two fundamental forces: a clamping force to hold the test sample in place, and a punch force that is responsible for deforming the test sample to failure. Any test machine capable of producing these two forces independently can be used. There are several ways available to achieve this, but typically a dual-acting hydraulic press with custom tooling is the most appropriate means.

There are even specialized hydraulically-powered machines, known as “Universal Formability Testers” (UFT), that have been built for this purpose, and they are simply compact self-contained presses designed specifically for formability testing.

In terms of sensors, the most important type needed for FLC testing is a biaxial strain sensor. As the test sample stretches, the strain sensor measures the major and minor strain accumulations across the sample. With the latest developments in FLC testing, and the need for complex algorithms to determine FLC points, optical metrology sensors using digital image correlation (DIC) are now the only practical means for satisfying the requirements of FLC testing.

The FLC is one of the most important tools used in sheet metal forming operations to provide guidance on how to design components, and select the appropriate materials with sufficient “formability limits” to accommodate the complex details of the component. As mentioned earlier, the exact algorithm by which an FLC point is determined is practically “arbitrary”, and in essence, it describes a particular state somewhere between necking and fracture. The ISO international standard on FLC testing dictates a particular approach for determining FLCs, and it is known as the Section-Based Method. Nevertheless, several manufacturers choose alternative methods to replace or to supplement the section-based method; that's why it is not unusual to see two different FLCs extracted by two methods for the same material, as shown in the example below.