Sheet Metal Press Forming Simulation
Theory: splits, wrinkles and springback
Overview
What defects is stamping simulation used to find?
Three main ones: splits, wrinkles and springback. Splits occur where sheet is stretched until it thins excessively and are judged with the forming limit diagram (FLD). Wrinkles form where sheet is compressed and buckles, controlled by blank holder force and drawbeads (ridges that restrain material flow). Springback is the elastic recovery of shape after the part leaves the die, larger for higher-strength steels. For large, complex parts such as car body panels, these are predicted before the dies are made, to decide blank shape, blank holder force, beads and die shape. The sheet is modelled with shell elements and the dies as rigid bodies, usually solved for contact and friction with an explicit method, with springback computed implicitly at the end.
Forming limit and thinning
t is thickness (mm), n the strain-hardening exponent (capped at 0.21), e₁ the engineering major strain, and ε₁, ε₃ the true major and thickness strains. In plane strain the width strain is zero, so by volume constancy thickness strain equals the major strain in magnitude.
A diagram born from circles on sheet
The forming limit diagram was developed in the 1960s by Keeler and Goodwin, who printed grids of small circles on sheet, press-formed it and read the strains just before splitting from how circles turned into ellipses. It condenses into one chart how the limit depends on the combination of stretching and contracting strains, and still underpins split judgement in simulation. Today strains are usually measured by digital image correlation, tracking random speckle patterns with cameras instead of circles.
Worked examples
The Keeler-type estimate uses n_eff = min(n, 0.21). DP590 is an assumed-input comparison, not a measured lot-specific FLC. The “10% margin” subtracts ten percentage points from engineering major strain, not a relative ten percent. Do not use the result as a universal permissible thinning limit.
Example: plane-strain limits and allowable thinning for mild steel and DP590
| Material | Thickness | n | FLC₀ | Thinning at limit | Thinning with 10% margin |
|---|---|---|---|---|---|
| Mild steel | 0.8 mm | 0.22 | 34.6% | 25.7% | 19.7% |
| DP590 | 1.2 mm | 0.14 | 26.8% | 21.2% | 14.4% |
n values are typical. DP590 gains a little from its thickness, but its lower hardening exponent makes it less formable than mild steel. The formula does not apply to aluminium alloys, which often have much lower FLC₀ at the same n.
Simulation showed 18% maximum thinning, under mild steel's 20% allowance, yet the trial split. Why?
Judging by thinning alone can miss strain path and local conditions. The thinning guide assumes plane strain, but on the FLD the limit depends on the ratio of minor to major strain, and some ratios are near the limit with modest thinning. If the strain path changes during forming (say biaxial stretch first, then plane strain), splitting comes earlier than the standard FLC predicts. Other causes include coarse elements averaging out local strain peaks, friction lower than reality, low n from material scatter, and tight die radii. Plot all element strains on the FLD to see the margin to the FLC, refine only the problem area, and check friction and material data.
Practical workflow
- Prepare stress-strain curve, r-values and FLC from data close to the actual sheet lot.
- Estimate blank shape and feasibility quickly with a one-step (inverse) method.
- With incremental analysis of the process, tune blank holder force and beads and check split margins on the FLD.
- Compute springback and compensate the die shape.
- Compare with trial thickness and strain measurements (e.g. image correlation) and tune friction and material data.
“One bead removed the split”
When a split appears, the usual fix is to lower blank holder force so material flows in more easily — but that often brings wrinkles. Changing the position and strength of drawbeads, which tune inflow locally, can solve splits and wrinkles together. Simulations usually model beads not as real geometry but as lines with a restraining force, and varying that force is an efficient way to experiment.
Common mistakes
Mistakes and fixes
| Mistake | Effect | Fix |
|---|---|---|
| Judging by thinning only | Splits at other strain ratios missed | Check all elements on the FLD |
| Steel formula for aluminium | Formability overestimated | Measure the FLC |
| Coarse elements | Strain peaks averaged out | Refine problem areas |
| Guessed friction | Wrong material inflow | Tune for lubrication |
| Ignoring springback | Dimensional errors | Compute implicitly and compensate |
I'd like to learn related topics.
Related pages include deep drawing simulation, springback analysis, rolling simulation and forging simulation.
Frequently asked questions
How are splits judged in stamping simulation?
With the forming limit diagram (FLD). Each element's pair of major and minor strains is plotted; beyond the material's forming limit curve (FLC) means a split, near it a split risk. The most severe state is plane strain, with no width contraction, and its limit FLC₀ indicates a material's formability.
What is a typical FLC₀?
For steel sheet the Keeler-Brazier formula FLC₀(%) = (23.3 + 14.13t) × n/0.21 (t thickness in mm, n strain-hardening exponent, capped at 0.21) is widely used: about 35% for 0.8 mm mild steel (n = 0.22) and about 27% for 1.2 mm DP590 (n = 0.14). The formula does not apply to aluminium alloys, whose FLC must be measured.
Can I judge by thinning instead?
It is a common rule of thumb. In plane strain thickness falls by the major strain, so mild steel with FLC₀ 35% is limited to about 26% thinning and DP590 at 27% to about 21%. With a 10% safety margin the allowable thinning is about 20% for mild steel and 14% for DP590 — higher-strength steels tolerate less thinning.
References and scope of verification
Numbers are educational reference calculations under the stated assumptions. Sources document theory and setup, not proof that these numerical values were reproduced in each package. Engineering decisions require validation for the actual conditions.
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