The Science of Forming

The series of columns will include:

Fig. 1—Schematic shows the multiple atomic force interactions (represented as lines) between the nine atoms (body-centered cube) making up an iron (steel) unit cell.

1) Elastic stresses (springback)

2) Yielding (start of permanent deformation)

3) Deformation (work hardening)

4) Failure (necking and fracture)

5) Forming limits (total elongation and forming limit curves) and

6) Surfaces (roughness and coatings). This month covers the fundamentals of elastic stresses and springback.

Understanding springback begins at the atomic level. Elastic stresses hold the atoms in place in the unit cell (Fig. 1), which is iron with a very small amount of carbon. The spheres represent iron atoms. Since the unit cell for iron has the body-centered cubic (BCC) configuration, there are eight corner iron atoms (pearl spheres) and one central iron atom (blue sphere). Each unit cell shares its six faces and corner iron atoms with six adjoining unit cells. This configuration replicates itself until a sheet of steel has length, width and depth.

The lines connecting the spheres in Fig. 1 depict the elastic stresses that bind the atoms together. Instead of lines of elastic stress, now visualize the iron atoms to be connected by tension/com-pression springs. Applying an outside force to the metal causes the spacing of the atoms to increase (tensile force) or decrease (compressive force). This creates a change in the stress between the atoms and an unstable state maintained only by the outside forces. Removal of the outside forces allows the elastic spacing between atoms to return back to their stable positions, causing the metal to springback to its original shape. The springs are still extended or compressed under load, but are back in their initial condition that balances the unit cell to its least energy state. A common concept is that the metal is attempting to return to its original shape. This is true only if no plastic (permanent) deformation or shape has been added that prevents the metal from returning to its initial state. Examples are hemispherical domes, closed end channels, deep-drawn cups, and other shapes that mechanically do not allow the return of the sheetmetal to its initial state. In this case, some elastic stresses cannot return back to their initial stable, lowest energy state. These remaining elastic stresses are called residual or trapped stresses.

In terms of our spring model, the springs remain more extended or compressed than normal. The excess energy is ready to release during some forming operation further down the line, during assembly and welding, or even during in-service operation. The part may be to print when removed from the die, but often will undergo major springback when trimming the offal releases some of these residual stresses. Even worse, springback may create different trimmed part shapes during a single shift. If a change to the residual stress pattern occurs during forming, the part will take whatever new shape it can to reach a new minimum-energy state. Change the length of one of the springs somewhere in the part and watch all springs rebalance to minimize the total energy. If a thin, narrow channel can twist itself into a pretzel shape to minimize energy, it will do just that.

The elastic stresses in the unit cell are very strong. Plotting the stress-versus-strain curve from a tensile test (Fig. 2), the elastic modulus line is very steep.

Fig. 2—The amount of springback is proportional to the yield strength of the steel.

Fig. 3—Schematic shows the multiple atomic force interactions (represented as lines) between the 14 atoms (body centered cube) making up an aluminum unit cell.

Right now our sample of metal has a perfect atomic structure without any atomic imperfections or discontinuities. This atomic structure is known as a single crystal. It would elastically stretch but without any permanent deformation. As soon as the load is removed, the sample would return to its original length. If a high enough load were applied, it would break like glass without any permanent deformation. The single crystal has special scientific uses, but cannot be used for automotive body panels, kitchen sinks or beer cans. Next month will explain methods of springback compensation using our elastic spring model. MF