Sheet can fail in forming even when no single uniaxial strain limit has been exceeded, because different regions experience different combinations of in-plane strain.

Let $\varepsilon_1$ be the larger principal in-plane strain and $\varepsilon_2$ the smaller. A forming-limit diagram (FLD) plots combinations $(\varepsilon_2,\varepsilon_1)$ and marks an empirical boundary above which localized necking is likely.

Different operations occupy different regions of this plane:

• drawing-like deformation can combine major tension with minor compression;
• plane-strain stretching has $\varepsilon_2\approx0$;
• biaxial stretching has both in-plane principal strains positive.

Suppose measurements from a stamped panel give

$$\varepsilon_1=0.24,\qquad \varepsilon_2=-0.08.$$

That point is compared with the material's forming-limit curve. If it lies safely below the curve, the strain state has margin against localized necking; if it approaches or exceeds the curve, process redesign is needed.

FLDs are not universal material constants independent of conditions. Sheet thickness, strain path, temperature, strain rate and material state can shift observed limits.

The value of the diagram is that it converts a complex sheet-forming problem into a local strain-state check. Simulation or grid measurements can identify critical regions before an actual tear occurs.