AbarTech
When a small piercing punch fails, it is often not because the press lacked tonnage. More often the punch was too long and too slender for the load it carried. This guide explains how the calculator works out piercing force, checks the punch as a column, finds the longest unsupported length that still meets your factor of safety, and estimates stripping force. It also covers the assumptions behind each number and where they stop applying.
The calculator checks one punch at a time. If a tool has several separate punches, check each one with the load it carries itself. Work through the four input panels:
Results update as you type. The verdict at the top of the results panel reads MEETS MODEL TARGET, BELOW TARGET or COMPRESSION LIMIT. The chart plots buckling capacity against unsupported length, with your design load and target load drawn across it. Where the capacity curve crosses the target line is the maximum allowable length. The second tab estimates stripping force for sizing the stripper.
The force to pierce a hole is the area of material sheared (cutting perimeter × thickness) multiplied by the shear strength of the stock:
The calculator then applies a load multiplier to give the design load used in every check:
The multiplier is a planning allowance for edge wear, clearance variation and lubrication. It does not model impact, stress waves or press dynamics. No reduction is taken for shear angle or step-punching. If your punch has a shear angle on its face, the real peak force will be lower and the result here is conservative.
Force is reported in kN, metric tonne-force (÷ 9 806.65 N) and US short tons (÷ 8 896.44 N), because press and punch-maker charts use all three.
Shear strength is the input most often guessed, and the force scales directly with it. Use the grade, temper and hardness actually being pierced. Work-hardened or high-strength stock can be far stronger than the textbook value for the base alloy.
Many people know the stock's tensile strength (UTS) from its certificate but not its shear strength. The Estimate from UTS option multiplies UTS by a ratio typical of the material family:
| Family | Shear ≈ × UTS | Default used |
|---|---|---|
| Mild steel | 0.70 – 0.80 | 0.80 |
| Stainless steel | ≈ 0.90 | 0.90 |
| Aluminium alloys | ≈ 0.50 | 0.50 |
| Copper alloys | 0.50 – 0.90 | 0.70 (check alloy) |
| Spring steel, annealed or pre-hardened | ≈ 0.80 (general steel approximation) | 0.80 |
The ratio stays editable. Setting it to 1.0 uses UTS directly. That over-estimates the cutting force, which is the safe direction when checking the punch. For reference, one published punch-maker tonnage chart takes hot-rolled mild steel at 50 000 psi (≈ 345 MPa) shear strength and ASTM A36 at 60 000 psi (≈ 414 MPa). The calculator lists these as starting values.
Spring steels. For spring steel strip to EN 10132-4, annealed (skin-passed) material such as C75S has a maximum UTS of 640 MPa, and 700 MPa for 51CrV4. Hardened-and-tempered (pre-hard) strip ranges from about 1200 to 1900 MPa or more, depending on grade and specification. Pre-hard strip therefore needs roughly two to three times the piercing force of annealed strip of the same thickness, and it is much harder on punch edges. Use the certificate UTS where you have it.
Two section properties matter: the area A, which sets compressive stress, and the least second moment of area I, which sets buckling resistance. The punch buckles about its weakest axis.
| Shape | Perimeter P | Area A | Least I |
|---|---|---|---|
| Round, dia d | π d | π d² / 4 | π d⁴ / 64 |
| Rectangle a × b | 2(a + b) | a b | min(a b³, b a³) / 12 |
| Obround l × w | 2(l − w) + π w | (l − w) w + π w² / 4 | (l − w) w³ / 12 + π w⁴ / 64 |
The rectangle assumes sharp corners. The obround (slot) has full-radius ends of radius w/2 and buckles across its width. For radiused rectangles, shaped punches or stepped punches, use Custom and take A and I from the CAD section at the weakest load-bearing point. I must be the least principal centroidal moment, not the polar moment. The calculator flags sections whose radius of gyration √(I/A) is physically impossible or unusually low for a solid section, which usually means a polar moment or a units error.
Slenderness is measured by the effective slenderness ratio:
Above the transition slenderness, the punch is treated as an ideal elastic column:
Euler's formula over-states the capacity of short columns, because it predicts loads the material cannot carry without yielding. Below the transition, the calculator uses the Johnson parabola:
The two curves meet at λT, where the critical stress equals Sy/2, so the capacity curve is continuous. The calculator marks this point on the chart as J | E and reports which model governs. The available factor of safety is Pcr / Fdesign.
The punch material list sets E and Sy from steelmakers' published data, in order of compressive strength. Compressive yield (Rc0.2) is given at a stated hardness. The figures are the steelmakers' own "approximate" values, so use your supplier's data where it differs.
| Type (reference grade) | Hardness | Rc0.2 | E |
|---|---|---|---|
| A2 (Uddeholm Rigor) | 60 / 62 HRC | 2150 / 2200 MPa | 190 GPa |
| D2 (Uddeholm Sverker 21) | 60 / 62 HRC | 2150 / 2200 MPa | 210 GPa |
| 8% Cr cold-work (Uddeholm Sleipner) | 60 / 62 / 64 HRC | 2350 / 2500 / 2650 MPa | 205 GPa |
| M2 HSS (1.3343) | 62–65 HRC | ≈ 3250 MPa* | 219 GPa |
| PM-HSS M3:2 (Vanadis 23 / ASP 2023 type) | 64 HRC | ≈ 3750 MPa* | 230 GPa |
| PM-HSS M3:2 + Co (Vanadis 30 / ASP 2030 type) | 65–66 HRC | 4000–4300 MPa* (4000 used) | 240 GPa |
| Cemented carbide | — | σc 3000–8000 MPa | 430–690 GPa |
* High-speed steel compressive yield values are AbarTech reference figures, because the steelmakers publish these only as charts against hardness. The modulus values come from the steelmaker datasheets. For PM-HSS M3:2 + Co, the lower end of the 4000–4300 MPa range is used by default. As with all presets, check against your supplier's data at your actual hardness.
Cemented carbide has no yield plateau, so the Johnson curve does not apply. The calculator uses capacity = min(Euler, A × compressive strength). Its defaults are the lower ends of the published grade ranges, which is conservative, and should be replaced with your grade's data. Carbide's high stiffness helps a great deal with buckling, but it is very sensitive to misalignment, side load and impact, none of which this axial model covers.
L is the free column length at the moment of peak cutting load. That moment is just as the punch breaks through, not bottom dead centre. Measure L from the last point of real lateral support, which is the holder face or a genuinely guiding stripper, to the stock.
| End condition (holder → tip) | K | Typical situation |
|---|---|---|
| Fixed – free | 2.0 | Rigidly held in the retainer, with no reliable restraint at the tip. This is the calculator's default. |
| Pinned – pinned | 1.0 | Ideal reference case. |
| Fixed – pinned | ≈ 0.7 | Tip located laterally by a close-fitting, stiff guide. |
| Fixed – fixed | 0.5 | Both ends fully restrained. This is rarely justified in a press tool. |
Only count a guide or stripper plate as lateral restraint if its clearance, stiffness and engagement actually hold the punch under load. A stripper that is loose or not yet engaged at breakthrough is not a guide. In the slender (Euler) range, buckling capacity scales with 1/K², so changing K from 2 to 0.7 raises capacity about eight-fold. Claim that improvement only when the tooling earns it.
The calculator solves for the length at which the column capacity equals the design load multiplied by the target factor of safety, using whichever branch applies:
If σreq reaches Sy, no length works. The section is too small for the load even as a very short block, and the verdict is COMPRESSION LIMIT.
The results also give L/d, the unsupported length divided by the diameter or minor dimension, at both the current and the maximum length, plus the inverse d/L. There is no universal maximum L/d. The allowable ratio changes with stock thickness, cutting perimeter, shear strength, punch strength and guidance, which is why it is calculated rather than looked up.
Small piercing punches are usually stepped. A short working tip, which can be round, rectangular, obround or a custom profile, is blended into a larger round body. Treating the whole punch as if it were the tip size throughout is very conservative. Select Stepped in panel 01 and enter:
A stepped column has no single closed-form buckling formula. The calculator divides the punch into short beam finite elements, uses the real section at each point, including the curved blend profile for round tips, and solves directly for the elastic buckling load Pe. The end conditions are chosen with the same cards as the straight punch. The default for a stepped punch is fixed at the holder and pinned (guided) at the stripper.
For the inelastic range, the Johnson parabola is used in its elastic-stress form:
For a uniform punch this is exactly the Johnson–Euler model in section 05. For a stepped punch, referring the stress to the tip, which is the most highly stressed section, is a conservative approximation. It is not a textbook result for stepped columns, and the calculator says so when it applies.
You choose whether the maximum-length result and the chart are solved for the point length, with the body fixed, or for the body length, with the point fixed. The results also report an equivalent K: the effective length factor a uniform punch of the tip section would need to have the same elastic buckling load.
The element solution was checked against an exact numerical solution of the column equation. It reproduces the Euler loads for all four uniform end conditions and the classical exact equation for a two-step column (Timoshenko). Across 40 random blended stepped geometries, covering all four end conditions and round, rectangular and obround tips, it agrees with the exact solution to within 0.004%.
For a round punch, the face compressive stress is σ = 4 t τ / d. It rises steeply once the punch diameter approaches the stock thickness. Punch makers publish minimum punch-diameter-to-thickness ratios, and the calculator compares the punch's minor dimension with them:
| Stock | Non-guided tooling | Fully guided tooling |
|---|---|---|
| Aluminium | 0.75 : 1 | 0.5 : 1 |
| Mild steel | 1 : 1 | 0.75 : 1 |
| Stainless steel | 2 : 1 | 1 : 1 |
Below these ratios you are in small-hole piercing territory. That calls for specially designed punches, often a larger body with a short turned-down tip, plus close guidance. The calculator flags this case but does not model the special designs. No ratio is applied for copper alloys or unlisted materials. The d/t value is still shown for them.
No published ratio was found for spring steels. As a stated judgement rather than a published figure, the calculator advises treating both annealed and pre-hardened spring steel at least as severely as stainless (2 : 1 non-guided, 1 : 1 fully guided). In practice pre-hardened strip is the more demanding of the two.
On the return stroke, the stock grips the punch and has to be stripped off. This puts the punch in tension, a separate load case from the compressive buckling check. Tab 2 estimates it as a percentage of the nominal piercing force:
Use the upper end of the range for tight clearance, thicker stock, galling materials or poor lubrication. Size the springs or gas springs so the stripper still delivers this force at the start of stripping, when the springs are at their least compression on the return stroke. The tab also reports the tensile stress at the minimum section. Hardened tool steels are weaker and more notch-sensitive in tension than in compression, so check necks and relief radii. The punch retention (head, ball-lock or clamp) must also carry this load. Retention strength is not calculated here.
Take a 3 mm round punch piercing 1 mm stock with a shear strength of 400 MPa. The punch has E = 210 GPa and Sy = 2 000 MPa, with 30 mm unsupported, fixed–free (K = 2). The load multiplier is 1.2 and the target FOS is 2. These are the calculator's default values.
| Perimeter P = π × 3 | 9.425 mm |
| Piercing force F = 9.425 × 1 × 400 | 3 770 N (3.77 kN) |
| Design load = 3 770 × 1.2 | 4 524 N |
| A = 7.069 mm² · I = 3.976 mm⁴ · r = 0.75 mm | σ = 640 MPa |
| λ = 2 × 30 / 0.75 | 80 (λT = 45.5 → Euler) |
| Pcr = π² × 210 000 × 3.976 / 60² | 2 289 N |
| Available FOS = 2 289 / 4 524 | 0.51 |
| σreq = 2 × 4 524 / 7.069 = 1 280 MPa (> Sy/2 → Johnson) | Lmax = 14.49 mm |
| Max L/d | 4.83 |
The verdict is BELOW TARGET. At 30 mm, this punch would be expected to buckle before it pierced. It needs an unsupported length of 14.5 mm or less, a genuine guide near the tip (try K = 0.7 in the calculator), or a larger section. Note that the governing model changes between the two lengths. At 30 mm the punch is slender (Euler), but at the 14.5 mm limit it is in the intermediate (Johnson) range.
A MEETS MODEL TARGET verdict means only that this idealised axial column model meets the factor of safety you entered. Treat it as one input to tool design, alongside punch-maker data, guidance design and trial.
Sources accessed October 2026. The calculator's results have been checked against an independent reference implementation across several thousand random input sets.