Other considerations Factors affecting the forming limit curve

and it may be seen that local necking occurs at strains rather greater than this. In many analyses, the tensile data is extrapolated, assuming that the strain-hardening index remains the same at high strains. This may not be the case and caution should be exercised. There may also be an interaction between material properties in the way that they influence the forming limit curve. In Figure 5.23, an example is given in which increasing the strain-hardening index may not increase the forming limits in all forming paths, if the change in, n, is an accompanied by a reduction in the fracture strain. As seen here, fracture will reduce the forming limit in equal biaxial tension, even though the forming limit is increased in other regions by an increase in the strain-hardening index. In the lubricated Olsen and Erichsen tests in which sheet is stretched over a well-lubricated hemispherical punch, failure occurs nearly in biaxial tension; in comparing some materials, differences may be due to different fracture properties rather than differences in strain-hardening. Fracture e 1 e 2 High, n Lower, n high, e f low, e f low, e f Figure 5.23 Diagram showing the changes in the forming limit curve when there is a property change such that strain-hardening is increased and the fracture strain lowered.

5.6 The forming window

In summary, sheet metal forming processes can be limited by various events. In the preceding sections, failure by a process of local necking and tearing has been examined. It is also possible for ductile sheet to fracture either within a necked region or before necking is established. Other limitations include wrinkling of the sheet under compressive loading. We have seen also that, for practical reasons, sheet can only be deformed by tensile forces and therefore one of the principal stresses must be positive, or, in the limit equal to zero. Taking these factors into account, it is useful to identify a forming window in which plane stress sheet forming is possible. This is illustrated in Figure 5.24. The compressive limit where the major tension just reduces to zero is shown at the strain path of β = −2. The wrinkling limit is not solely a material property and therefore the limit is only shown as a region in the second and fourth quadrants. The diagram is a pictorial aid and it can be seen that if the strain-hardening index becomes small, the window shrinks to a narrow slit along the left-hand diagonal. As mentioned, strengthening processes usually lead to reduced strain-hardening in the sheet and one of the challenges of sheet metal forming is to devise processes for forming strong materials that will permit safe straining even though the window is small. Load instability and tearing 79 Fracture Fracture Tearing Wrinkling Compression 1 −2 e 1 e 2 Forming window Figure 5.24 The forming window for plane stress forming of sheet.