The Formability of sheet metals

Previous posts Materials Matters, “the known unknowns” and “Material plasticity visualized” covered the general aspects, common terminology, and formulation of the plastic properties in sheet metal forming problems. Accurate definition of flow curves, kinematic hardening and yield locus helps us to simulate the plastic flow of sheet metals during forming operation. Computer simulation uses those definitions to predict at each location in the sheet how the metal will deform and how strong the material is at each point after the deformation. Reliable prediction of the strains and resultant stresses in sheet metal allows us to simulate the springback with high accuracy. However, computing plastic deformation is not enough alone to predict the formability of a stamped component.

In the context of metal forming, formability can be defined in general sense as:

Capability of a material to be formed without failure

Failure can show itself as necking, splits, or wrinkles. A widely used method for failure prediction in industrial applications was proposed by Keeler (1965) and Goodwin (1968), namely the forming limit curve (FLC). The method has found a broad application because it is empirical, intuitive, and easy to understand and apply.

The concept is very simple: take the sheet metal you wish to characterize, deform it until necking, record the maximum achievable strains before necking and use these values as to define deformation limits.  Applying the limits to numerical simulation should predict if the deformation is safe or not.

Circle grid data collection for FLC determination

Marciniak test with optical strain measurement pattern applied

FLC determination

Experimental determination of these limits is performed by using different specimen geometries in order to obtain different deformation states. The specimens are usually stretched over spherical or cylindrical punches (Nakajima or Marciniak Tests). Traditionally, circle grid analysis was performed by technicians to samples artfully collected prior to the onset of failure, and then charted manually.

However, more recently optical strain measurement systems are utilized to capture the deformation history of the entire sheet surface. By this way the time point of localized necking and the corresponding strains can be identified with high accuracy. Obtained strain values from different specimen geometries are plotted in principal strain space.

A forming limit curve (FLC) is constructed by fitting a curve to the obtained coordinates (e_ma, e_mi) in strain-space.  The FLC is specific for the grade of material tested, with same mechanical properties, at the same thickness. In time, if enough samples are taken, it is sometimes possible to apply a consistent curve shape for a range of materials and predict the forming limit of similar materials at different thicknesses. Such was the conclusion of Keeler-Goodwin et al with the publishing of their FLD₀  (orFLC₀), for mild steels. With the FLC₀ formulation, given thickness and material n-value the location of a common shape FLC could be determined. However, for other materials a predictive shape and location of the FLC is not as widely accepted, requiring new empirical tests for each new material thickness and/or type.

Using FLCs

Later in the simulations the Forming Limit Curve defines the onset of necking. In post-processing of the finite element simulations, the strain state of each element is checked relative to the curve. If the strain state lies well below the curve, the elements are predicted to be safe. Points that lie below but are near the curve are considered to be marginally safe. A strain state over the line predicts a potential split. According to the position of the elements on the forming limit diagram other cases like thickening, excessive thinning or insufficient stretching can be defined.

By plotting the strains measured on a current panel against the FLC we can predict relative formability of that part or process

Strictly speaking, FLCs are valid for forming operations with linear strain paths. FLC determination is performed using specimen geometries and deformations with linear strain paths. If strain paths change, e.g. the part is stretched then compressed then stretched again, the standard FLC may not reliably predict failure. This is a major concern for engineering forming operations; it is possible that with appropriate knowledge an FLC can be modified to include non-linear strain path effects.

The concept of FLC does not have information about shear deformation or failure, thickness effects, or edge quality of the sheets. For the cases like, shear fracture of AHSS, bending over sharp radii and edge crack sensitivity of laser cut sheets alternative fracture criteria can be utilized. These criteria complement the information in FLCs with maximum available shear strains or edge strains.

Future trends:

Given the limitations of FLCs further academic research is ongoing and focuses currently on following points

• Time dependent evaluation of the FLD-test results in order to identify the onset of necking more accurately
• Strain path dependent FLCs including anisotropy effects
• Stress based FLCs
• Determination of temperature dependent FLCs for hot forming applications
• Continuum damage mechanics
• Fracture prediction based on crystal plasticity and surface texture
• Computation and prediction of FLCs based on constitutive equations.

See part one, two and three of this series.