What the FLD Actually Tells You
Sheet metal necks and fractures at a specific combination of major and minor strain. The Forming Limit Diagram maps those combinations — safe on one side of the curve, failed on the other. Every stamping simulation, every circle grid analysis and every DIC measurement outputs data that lands somewhere on that diagram.
The FLD does not tell you how much force the press needs. It tells you whether the material will survive the strain path the die geometry imposes. That distinction matters because a part can fail at 30% of press capacity if the local strain state crosses the forming limit curve (FLC).
Keeler introduced the right-side (biaxial tension) FLC in 1965. Goodwin added the left-side (tension-compression) in 1968. The full diagram — often called the Keeler-Goodwin diagram — has been the standard formability benchmark for six decades.
| Material | n-value | FLC₀ at 1.5 mm (%) | Strain State Risk |
|---|---|---|---|
| DC04 | 0.21 | 44.5 | Low at plane strain |
| DP600 | 0.17 | 36.0 | Moderate at plane strain |
| DP980 | 0.09 | 19.0 | High at plane strain |
| AISI 304 (annealed) | 0.45 | 87.3 | Very low at plane strain |
Temel Cikarimlar
- The Forming Limit Curve (FLC) is defined by material properties (n-value, thickness) and separates safe from failed strain states, with plane strain (ε₂ = 0) being the highest risk zone.
- FLC₀ (minimum major strain at plane strain) is calculated via the Keeler formula and is the single most important parameter for press shop decisions.
- A minimum 10% safety margin below the FLC is required for production release to account for material scatter, lubrication variation, and press force fluctuations.
Axes, Zones and the FLC
The FLD uses two axes:
- Y-axis: Major strain ε₁ — the largest principal strain at any point on the sheet surface, always positive (tensile)
- X-axis: Minor strain ε₂ — the strain perpendicular to ε₁ in the sheet plane; can be positive (biaxial) or negative (tension-compression)
Both are engineering true strains (logarithmic): ε = ln(l_f / l_0)
The Forming Limit Curve (FLC) separates three zones:
| Zone | Location | Meaning |
|---|---|---|
| Safe zone | Below FLC | No localized necking — part is stable |
| Marginal zone | Within 10% major strain below FLC | Risk increases — within production scatter |
| Critical zone | At or above FLC | Localized necking — failure is imminent or occurring |
| Fracture zone | Well above FLC | Fracture already occurred or guaranteed |
In production, strain points should sit at least 10% major strain below the FLC at every location. Running tighter than that means scatter in material properties and press force variation will produce intermittent necks — parts that pass visual inspection at the press but fail in service or in the next forming stage.
The Five Strain States on the FLD
The horizontal position of a strain point on the FLD maps directly to the local stress state in the die:
| Strain State | ε₂ Value | Typical Location | Risk Level |
|---|---|---|---|
| Uniaxial tension | ε₂ ≈ −ε₁/2 | Free-edge flanges, slotted blanks | Low — FLC is high |
| Plane strain | ε₂ = 0 | Side walls, stretch flanging, window corners | Maximum risk — FLC minimum here |
| Biaxial tension (equal) | ε₂ = ε₁ | Dome centers, hemispherical draw | Moderate |
| Biaxial tension (unequal) | 0 < ε₂ < ε₁ | Dome off-center, punch radius contact | Moderate–High |
| Tension-compression | ε₂ < 0 | Cup drawing wall, blank holder contact | Lower than plane strain |
Plane strain is always the danger zone. The FLC reaches its minimum at ε₂ = 0. Every part geometry that creates a long straight stretch zone — B-pillar sidewall, door outer panel, structural cross-section — drives material toward plane strain. That is where unexpected splits occur.
FLC₀: The Key Number to Know
FLC₀ is the major strain value at the FLC minimum (plane strain, ε₂ = 0). It is the single most important material formability parameter for press shop decisions.
The Keeler empirical formula — confirmed against thousands of steel grades — calculates FLC₀ directly:
FLC₀ = (23.3 + 14.13 × t) × (n / 0.21)t= sheet thickness (mm)n= strain hardening exponent (dimensionless)- Result: FLC₀ in percent engineering strain
Worked Example
DC04 deep drawing steel, 1.0 mm thickness:
- n = 0.21 (typical value)
- t = 1.0 mm
FLC₀ = (23.3 + 14.13 × 1.0) × (0.21 / 0.21)
FLC₀ = (23.3 + 14.13) × 1.0
FLC₀ = 37.4%DP600 dual-phase steel, 1.5 mm thickness:
- n = 0.17
- t = 1.5 mm
FLC₀ = (23.3 + 14.13 × 1.5) × (0.17 / 0.21)
FLC₀ = (23.3 + 21.2) × 0.810
FLC₀ = 44.5 × 0.810
FLC₀ = 36.0%DC04 and DP600 produce nearly identical FLC₀ despite very different microstructures, because higher n in DC04 compensates for lower thickness. The practical formability difference between these two grades shows up in shape of the FLC, not just its minimum.
Material Parameters That Shift the FLC
Strain Hardening Exponent (n-value)
The most direct FLC driver. Higher n → higher, wider FLC → more forming room.
| Material | n-value | FLC₀ at 1.5 mm | Notes |
|---|---|---|---|
| DC01 | 0.17–0.19 | 30–34% | Commercial deep drawing quality |
| DC04 | 0.20–0.22 | 36–42% | Preferred for complex draw operations |
| HSLA 340 | 0.14–0.17 | 25–32% | FLC drops, formability tightens |
| DP600 | 0.15–0.18 | 26–35% | AHSS — lower n, higher strength |
| DP980 | 0.08–0.11 | 14–21% | Very narrow safe zone |
| AISI 304 (annealed) | 0.40–0.50 | 75–90% | Excellent formability before martensite transformation |
| Al 5182-O | 0.25–0.30 | 35–45% | Aluminum FLC uses different standard |
Normal Anisotropy (r-value / Lankford Coefficient)
r-value affects FLC shape more than FLC₀. High r-value (> 1.5) suppresses thinning, pushing the FLC upward — particularly in the biaxial tension region. Deep drawing steels (r = 1.6–2.2) benefit significantly here. AHSS grades (r = 0.7–0.9) lose this benefit.
For single-value r, use:
r̄ = (r_0 + 2r_45 + r_90) / 4Higher r̄ → less thinning strain → higher FLC on the right side (biaxial).
Sheet Thickness
FLC₀ scales directly with thickness per the Keeler formula. This is physically intuitive: thicker sheet delays the onset of through-thickness localized necking. Implications:
- Never substitute a thinner blank without re-checking the FLC. A 10% thickness reduction reduces FLC₀ by ~1.4 percentage points — typically enough to push marginal parts into the critical zone.
- Thinning from the previous draw stage enters the next stage with reduced local formability. Measure actual thickness distribution, not nominal.
How to Generate an FLD: Test Methods
Nakajima Test (ISO 12004-2)
The standard method for steel and aluminum. A hemispherical punch (100 mm diameter) forms blanks of varying widths against a lock bead. Narrow blanks → plane strain. Wide blanks → biaxial tension. In-between widths → intermediate strain states.
Test matrix minimum: 5 blank widths × 3 replicates = 15 specimens per material/thickness combination.
Strain measurement: either
- Circle grid analysis (2.5 mm electroetched grid, optical measurement post-fracture), or
- Digital Image Correlation (DIC) — random speckle pattern, full-field strain measurement at high frame rate
The FLC is fitted through the necking-onset strain points, not through fracture points. This is critical — DIC systems with high-speed cameras can detect the onset of localized necking before visible fracture. Fitting to fracture points overestimates the safe zone.
Marciniak Test
Alternative to Nakajima for aluminum and low-friction materials. Uses a flat punch with a carrier blank to prevent friction bias. Produces more uniform strain paths but requires careful blank/carrier blank sizing.
Determining FLC from Supplier Data
For common steel grades (DC01–DC06, HSLA 240–550, DP500–DP1000), material suppliers and steel producers (voestalpine, SSAB, ArcelorMittal, Baosteel) publish measured FLC data sheets per thickness and heat treatment. Always request:
- FLC₀ value
- FLC data points at ε₂ = −0.20, −0.10, 0, +0.10, +0.20, +0.30
- Measurement standard used (ISO 12004-2 or ASTM E2218)
- Batch/heat-specific values if running high-risk geometry
Reading the FLD: A Production Example
Consider a deep-drawn door inner panel in DC04, 0.8 mm. After circle grid analysis, three regions show these strain measurements:
| Region | ε₁ (%) | ε₂ (%) | FLC at this ε₂ (%) | Status |
|---|---|---|---|---|
| Door window corner | 28 | +2 | 34 | Safe (6% margin) |
| Rear flange stretch zone | 31 | −1 | 32 | Marginal (1% margin) |
| Punch radius contact area | 22 | +18 | 38 | Safe (16% margin) |
| Door hinge mounting tab | 33 | +1 | 33 | Critical — at FLC |
The rear flange stretch zone and hinge tab both need corrective action before production release:
- Rear flange: reduce blank holder force, add draw bead radius, or add material by shifting blank edge 5–8 mm
- Hinge tab: add pre-draw, modify punch radius, or change steel grade to DC05
The dome area has 16% margin — no risk, no action required.
Circle Grid Analysis: Step-by-Step
-
Mark the blank — electrochemical etching of a 2.5 mm circle grid (per ISO 12004-2) or photochemical transfer. Both methods are compatible; electrolytic etching depth must not exceed 0.01 mm to avoid stress concentration.
-
Form the part — standard production conditions: same lubricant, BHF, press speed, die temperature.
-
Identify suspect regions — look for visible thinning, rough surface, color change (steel). Circles in these areas are the priority.
-
Measure ellipses — circles deform into ellipses. Measure major axis (a) and minor axis (b):
ε₁ = ln(a / 2.5) [major strain] ε₂ = ln(b / 2.5) [minor strain] -
Plot on FLD — compare each measured point to the FLC for the material and thickness.
-
Apply safety margin — flag any point within 10% major strain below the FLC.
DIC (Digital Image Correlation) in Production
DIC systems (ARAMIS, ARGUS — GOM/Zeiss; ISTRA — Dantec Dynamics) replace circle grids with full-field optical measurement. Advantages:
- Full-surface strain map, not discrete point measurements — catches necking initiation between grid circles
- Higher accuracy: ±0.1–0.3% strain vs. ±1–2% from manual circle measurement
- No pre-marking required for ARGUS (structured light; works on production parts)
- Real-time measurement at 100–10,000 fps for dynamic event capture
Limitations: capital cost (€50,000–€200,000 for a full system), setup time per part geometry, and sensitivity to surface reflectivity. For production QA on high-volume drawn parts, ARGUS-type structured-light scanning on stamped parts after forming is the current practical standard.
FLD in FEA Simulation (AutoForm, Dynaform, PAM-STAMP)
Finite element simulation of sheet metal forming requires the FLC as input data, not output. The material card must contain:
- Yield surface definition (Hill ‘48, Barlat 2000, Yld2004-18p for AHSS)
- Hardening curve (Voce, Swift, or measured stress-strain to high strain)
- FLC data points (ε₂ vs. ε₁ pairs at the forming limit)
Simulation output includes:
- FLD plot: each finite element colored by position relative to FLC
- Thinning distribution map
- Maximum thinning percentage
- Wrinkle indicator (compression flag)
Critical simulation practices:
- Use material data from the same thickness as the production blank — FLC is thickness-dependent, do not interpolate carelessly
- Validate the simulation against a physical tryout on at least the first die before trusting simulation margins blindly
- Mesh refinement in high-gradient regions: element size must be ≤ 3 mm in draw radius and corner zones — coarser mesh underestimates peak strain by 15–30%
Safety Margin Definition for Production Release
No part should enter mass production with less than the minimum margins below:
| Risk Level | Safety Margin (major strain below FLC) | Action |
|---|---|---|
| Standard parts | ≥ 10% | Acceptable for production |
| High-complexity or safety-critical | ≥ 15% | Required before die approval |
| Marginal (5–10%) | — | Engineering review; corrective action or source-level control |
| Critical (< 5%) | — | Production hold; die modification required |
These margins account for:
- Material property scatter between heats: ±0.01 in n-value
- Lubricant variation: ±15% in effective friction coefficient
- Press force variation: ±3–5% in servo-driven, ±8–12% in mechanical presses
- Blank positioning tolerance: ±0.5–2 mm depending on feed system
Common Mistakes with FLDs in Production
1. Using FLC₀ as a uniform strain limit FLC₀ applies only at plane strain (ε₂ = 0). Applying it as a universal pass/fail at all ε₂ values underestimates failure risk on the biaxial side (ε₂ > 0) and is overly conservative on the uniaxial side (ε₂ < 0). Always compare to the FLC at the correct ε₂ value.
2. Ignoring thickness change between draw stages In a multi-stage process, thinning from stage 1 reduces the local thickness entering stage 2. Reduced thickness reduces FLC₀. The simulation for stage 2 must use the actual thickness distribution from stage 1 output, not the nominal blank thickness.
3. Using generic FLC data for AHSS Advanced high-strength steels have FLCs that deviate significantly from the Keeler formula — particularly in biaxial tension where martensite and retained austenite microstructures alter strain distribution. AHSS FLCs must be measured per ISO 12004-2 for the specific grade and thickness; do not use Keeler formula predictions for DP780 and above.
4. Circle measurement after fracture instead of at onset Measuring strains at fracture overestimates the safe zone — material above the FLC has already strained past the limit. Measurement target is the last circle before visible necking begins, not the circle adjacent to the fracture.
5. Simulating springback after ignoring FLD violations A simulation that shows FLC violations and proceeds to springback analysis produces meaningless springback predictions — the material behavior post-necking is no longer governed by the constitutive model. Fix the FLC violation first.
Practical Reference: FLC₀ Table by Grade and Thickness
| Material Grade | Thickness (mm) | n-value (typical) | FLC₀ (%) |
|---|---|---|---|
| DC01 | 0.8 | 0.18 | 29.7 |
| DC01 | 1.5 | 0.18 | 37.0 |
| DC04 | 0.8 | 0.21 | 34.6 |
| DC04 | 1.5 | 0.21 | 44.5 |
| DC04 | 2.0 | 0.21 | 51.7 |
| HSLA 340 | 1.0 | 0.15 | 28.0 |
| HSLA 340 | 2.0 | 0.15 | 35.5 |
| DP600 | 1.5 | 0.17 | 36.0 |
| DP800 | 1.5 | 0.12 | 25.4 |
| DP980 | 1.5 | 0.09 | 19.0 |
| AISI 304 (annealed) | 1.0 | 0.45 | 87.3 |
| Al 5182-O | 1.0 | 0.27 | 44.3 |
FLC₀ calculated via Keeler formula. Verify against measured data for production decisions.
Summary
The FLD and FLC are not outputs from simulation — they are inputs. The decision to release a die for production cannot be made without knowing where every critical strain point sits relative to the FLC, measured with a defined safety margin.
Three rules apply:
- Know your FLC₀ before die design starts. It defines the upper strain limit and eliminates impossible part geometries before tool steel is cut.
- Measure during tryout. Simulation predicts; circle grid or DIC measurement confirms. Production release requires measured data, not simulation data alone.
- Maintain the 10% margin. Margin erosion during die spotting and tryout is the most common path to intermittent production failures. If the margin is below 10% after corrections, the die geometry or material specification needs changing — not the acceptance criteria.
Emrah Demirezen — Metal Forming Expert, Press Design Engineer
info@demirezenengineering.com