The bend radius is the inside radius of a formed bend — the distance from the bend’s neutral axis to its inner surface. Get it too tight and the material cracks at the outer fibre. Get it too loose and the part geometry changes, requiring die substitution and adding setup time. The minimum bend radius is the smallest inside radius a specific material can accept without fracture or significant surface cracking, and it is determined by the material’s tensile ductility, yield-to-tensile ratio, and thickness.
For steel, minimum bend radius is not a single number — it shifts significantly with alloy, temper, and grain orientation. A mistake in specification costs material and machine time; understanding the physics behind the limit lets you predict when standard guidelines apply and when you need to verify.
The Physics: Why Bends Crack
When sheet metal is bent, the outer surface is in tension and the inner surface is in compression. The outer fibre strain at the bend is:
ε = t / (2r + t)
Where:
- t = material thickness
- r = inside bend radius
- ε = outer fibre tensile strain
For a 3 mm steel sheet bent to a 3 mm inside radius:
ε = 3 / (2 × 3 + 3) = 3 / 9 = 0.333 (33.3% strain)
If the material’s total elongation to fracture is less than 33.3%, the outer surface will crack. A36 mild steel has approximately 20–23% elongation — meaning a 3 mm radius on 3 mm A36 steel is right at or beyond the limit, depending on grain direction.
The minimum bend radius is conventionally expressed as a multiple of material thickness. A minimum bend radius of 1t means the inside radius must be at least equal to the material thickness; 2t means twice the thickness; 0.5t means half the thickness (a tighter bend, only achievable on ductile materials).
Learn more:
Bending Radius Calculator: Predicting Material Cracking
Minimum Bend Radius Reference: Steel Grades
Mild steel (ASTM A36, 1008, 1010, 1018)
| Thickness (mm) | Minimum r (across grain) | Minimum r (with grain) |
|---|---|---|
| 0.5–1.5 | 0.5t | 1t |
| 1.5–3.0 | 0.5t–1t | 1t–1.5t |
| 3.0–6.0 | 1t | 1.5t–2t |
| 6.0–12.0 | 1.5t | 2t–2.5t |
Mild steel is the most forgiving common sheet metal. High elongation (20–25%) allows relatively tight bends. As thickness increases, the recommended minimum radius increases because absolute strain at the outer fibre for a given r/t ratio becomes harder to achieve uniformly through the thickness.
High-strength low-alloy (HSLA) steel — ASTM A572, A514, S355
| Grade | Yield strength | Minimum r (across grain) |
|---|---|---|
| A572 Gr.50 | 345 MPa | 1.5t–2t |
| A572 Gr.65 | 450 MPa | 2t–2.5t |
| S355 | 355 MPa | 1.5t–2t |
| A514 | 690 MPa | 2.5t–3t |
HSLA steels have significantly reduced ductility relative to mild steel. The higher yield-to-tensile ratio means less “stretch room” before fracture. A514 (690 MPa yield) at 2.5t–3t is a common minimum — any tighter and outer fibre cracking is likely on production material without pre-heating or process controls.
304/316 Stainless steel
| Thickness (mm) | Minimum r (across grain) | Minimum r (with grain) |
|---|---|---|
| 0.5–2.0 | 0.5t | 1t |
| 2.0–5.0 | 1t | 1.5t |
| 5.0–10.0 | 1.5t | 2t |
Austenitic stainless steel has excellent ductility (40–50% elongation for 304) but work-hardens rapidly during forming. The work hardening means that the material reaching the outer fibre can be harder and less ductile than the specification implies — particularly in heavier gauges where the bending strain accumulates through a larger cross-section. Grain direction matters considerably for stainless.
Dual-phase (DP) and advanced high-strength steels (AHSS)
| Grade | Tensile strength | Minimum r |
|---|---|---|
| DP590 | 590 MPa | 2t |
| DP780 | 780 MPa | 2.5t–3t |
| DP980 | 980 MPa | 3t–4t |
| TRIP780 | 780 MPa | 2t–2.5t |
AHSS grades are increasingly common in automotive structural fabrication. Their high strength comes at the cost of reduced formability — minimum radii at 3t–4t for DP980 limit the geometry of stamped and folded parts. For automotive press brake work, DP780 and above frequently require tooling specifically designed for these tight material constraints.
Grain Direction: The Factor Most Overlooked in Shop Practice
Steel sheet is rolled, and rolling produces a grain structure aligned with the rolling direction. Bending perpendicular to the rolling direction (across the grain) places the grain boundaries favorably in compression on the inner surface and tension on the outer surface. Bending parallel to the rolling direction (with the grain) stresses the grain boundaries at a less favorable angle, reducing the practical elongation.
The practical impact: The minimum bend radius across the grain is typically 30–50% tighter than with the grain for the same material and thickness. Where nesting orientation on a laser-cut blank is controllable — which it almost always is with CNC nesting software — specifying bends to run across the rolling direction is free manufacturing quality improvement.
For mild steel, grain direction often makes little practical difference at standard thicknesses. For HSLA, AHSS, and stainless steel at thickness above 3 mm, grain direction can be the difference between a clean bend and a cracked part.
Springback and Its Relationship to Bend Radius
Minimum bend radius and springback are related but distinct issues. Springback is the elastic recovery after forming that opens the bend angle from the intended geometry. Tighter radii produce more springback because the stress gradient across the thickness is steeper.
The springback angle for a V-die air bend is approximately:
Δθ ≈ (σ_y / E) × (r/t + 0.5) × θ_formed
Where σ_y is yield strength, E is elastic modulus (200 GPa for steel), r/t is the radius-to-thickness ratio, and θ_formed is the bend angle.
For A36 steel (σ_y = 250 MPa) at r/t = 2, bending to 90°:
Δθ ≈ (250/200,000) × (2 + 0.5) × 90° = 0.00125 × 2.5 × 90° = 0.28° springback
Negligible. For A514 (σ_y = 690 MPa) at r/t = 3:
Δθ ≈ (690/200,000) × 3.5 × 90° = 1.08°
Still modest. The springback calculation confirms that for structural steel grades, the primary constraint is cracking at minimum radius — not springback, which is easily compensated by overbending.
For AHSS at DP980 yield strength (~900 MPa) at r/t = 4:
Δθ ≈ (900/200,000) × 4.5 × 90° = 1.82°
At production tolerances, this matters. AHSS press brake operations on DP980 require springback compensation in the program and often in-process angle measurement.
V-Die Opening Selection and Its Effect on Minimum Radius
The V-die opening width directly determines the inside bend radius in air bending. The rule of thumb: inside radius ≈ V-opening / 8 for mild steel. This means the V-die opening controls whether the minimum bend radius is achievable — a die too narrow will crack the material; a die too wide will produce a larger radius than intended.
V-die selection for minimum radius bends:
For a 1.5t minimum radius on 3 mm A36 (minimum r = 4.5 mm): Required V-opening ≈ r × 8 = 4.5 × 8 = 36 mm
For A514 at 2.5t minimum on 6 mm plate (minimum r = 15 mm): Required V-opening ≈ 15 × 8 = 120 mm
The press brake’s available die set constrains which minimum radii are achievable without custom tooling. When a customer specifies a bend radius tighter than what the available V-die can produce, the options are: accept the larger radius (if functionally acceptable), order a narrower V-die, or consider coining/bottom bending which directly impresses the punch tip radius into the material.
Coining vs. Air Bending at Minimum Radius
Air bending allows the inside radius to float with the V-die geometry — the punch tip radius must be smaller than the achieved radius, but the die controls the final geometry. Coining (bottoming) forces the punch tip radius directly into the material, producing a precise, consistent inside radius equal to the punch tip.
Coining requires 3–10× more press force than air bending at equivalent thickness. For minimum radius bends on HSLA or AHSS where the air-bend radius is the limit of what the die can achieve, coining allows a tighter radius by directly forming the material against the punch. This is the approach for precision tight-radius bends on high-strength material where the air-bend method leaves too much springback variation.
The punch tip must be hardened sufficiently to withstand the increased load without yielding. For D2 tool steel punch tips at HRC 60, the compressive yield strength is approximately 2,000–2,500 MPa — adequate for coining most structural steel grades.
Frequently Asked Questions
What is the minimum bend radius for 3 mm mild steel?
Approximately 0.5t to 1t (1.5–3 mm) depending on grain direction. Across the grain, 1.5 mm inside radius is achievable. With the grain, 3 mm is a more conservative minimum.
How do I calculate the minimum bend radius for a specific steel?
Use r_min ≈ (t × 50) / (% elongation − 10) as a starting approximation, or use the material’s tensile test elongation to check whether the outer fibre strain (t / (2r + t)) falls below the fracture elongation with appropriate safety margin.
Why does grain direction affect minimum bend radius?
Rolling produces elongated grains aligned with the rolling direction. Bending with the grain runs crack-initiating grain boundaries parallel to the bend line, making them easier to open under tension. Bending across the grain keeps grain boundaries more favorably oriented, improving effective ductility at the outer fibre.
References
- Oberg, E., et al., Machinery’s Handbook, 31st Edition. Industrial Press, 2020. (V-die selection, air bending force and radius, springback calculations for structural steel grades.)
- ASM Handbook, Volume 14B: Metalworking — Sheet Forming. ASM International, 2006. (Minimum bend radius data by grade and grain direction; formability limits for HSLA and AHSS.)
- Budynas, R.G., and Nisbett, J.K., Shigley’s Mechanical Engineering Design, 11th Edition. McGraw-Hill, 2020. (Outer fibre strain derivation; springback calculation methodology.)
- ASTM A36/A36M, ASTM A572/A572M, ASTM A514/A514M — current editions. (Mechanical property minimums — yield, tensile strength, elongation — underlying all minimum bend radius calculations for structural steel grades.)
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