Stainless Steel Strength Grade Selection: Quantitative Criteria for Annealed, Temper-Rolled, Work-Hardened and Duplex Grades

When a drawing says only 304, the delivered material may be annealed or full hard, and the proof stress differs by a factor of 4.71 between the two. In a single cold-formed square tube the flat faces yield at 205 MPa while the four corners may already sit at 515 MPa: work hardening hands you that strength for free, but most engineers neither calculate it nor notice that it eats half the ductility.

The more expensive mistake sits at the other end of the same logic. To save weight, 304 is swapped for duplex 2205, proof stress rises from 205 to 450 MPa, and the plate is thinned by 32.5 percent on an equal-strength basis. Strength checks out, then deflection grows 3.25 times and the width-to-thickness ratio overshoots by 2.19 times. Strength passes; stiffness and stability fail first.

This page splits strength-based selection into four calculable routes - the annealed baseline, the temper ladder, work-hardening back-calculation and the duplex option - and states for each one what actually governs and when thinning is not allowed.

1. 304 Is Not 205 MPa, It Is a Band from 205 to 965 MPa

The commonly quoted 205 MPa is only the ASTM A240 / ASTM A666 minimum for the annealed condition. Cold rolling pushes the same grade up to 965 MPa at full hard. ASTM A666 standardises that route into five steps:

A 4.71 times gain in proof stress costs a drop from 40 percent to 3 percent elongation - only 7.5 percent retained, a division by 13.3. Two practical consequences follow. First, a purchase order that names the grade but not the temper hands the strength decision to the mill. Second, temper-rolled material cannot simply be bent again: with 3 percent elongation, essentially any plastic forming will crack.

One caveat on scope: ASTM A666 grades elongation by thickness, with wider values below 0.38 mm (quarter hard is 10 percent at t 0.76 mm or below and 12 percent above 0.76 mm). The table uses representative values for the t at least 0.38 mm band, which is the conservative end.

2. The Work-Hardening Power Law, and Why K and n Can Be Back-Solved

Work hardening in austenitic stainless is described by the Hollomon equation: true stress sigma equals the strength coefficient K times true strain eps raised to n.

The exponent n is also, physically, the true strain at which necking begins. The higher n is, the more uniform deformation the material absorbs before it localises. 304 sits at n = 0.45, carbon steel around 0.18, ferritic 430 around 0.20 - which is the quantitative reason austenitic grades form so much better than carbon or ferritic steel.

The same law back-solves the engineering tensile strength. At necking the true strain equals n; engineering stress is true stress divided by (1 + e); and (1 + e) equals e raised to n. Hence:

For 304: 0.45 / 2.718 = 0.1656; 0.1656 to the power 0.45 = 0.4451; 1275 x 0.4451 = 567.5 MPa.

That 567.5 MPa matches the ASTM A240 minimum of 515 MPa and the measured band of 520 to 620 MPa, landing near its midpoint. Why this matters: every work-hardening figure below rests on this one law, and the law has just been validated against tensile data before being used.

Why hardness conversion fails for stainless

Hardness testing is convenient on site, so the carbon-steel rule of thumb gets applied. For austenitic stainless this fails systematically, because an indentation represents roughly 8 percent plastic strain while tensile strength corresponds to the necking strain eps = n.

Running both flow stresses through the same law:

• 304: flow stress at 8 percent = 1275 x 0.3209 = 409.1 MPa; Rm / sigma(8%) = 567.5 / 409.1 = 1.387
• Carbon steel (K = 900, n = 0.18): Rm = 900 x 0.6135 = 552.2 MPa; flow stress at 8 percent = 900 x 0.6347 = 571.2 MPa; ratio = 552.2 / 571.2 = 0.967

For the same indentation resistance, 304 carries 43.5 percent more tensile strength than carbon steel (1.387 / 0.967 = 1.435). Multiplying the usual carbon-steel coefficient of 3.45 MPa/HB by that 1.435 gives 4.95 MPa/HB.

This direction agrees with independent handbook guidance: 3.45 for carbon and low-alloy steel, but 4.5 to 5.0 MPa/HB for austenitic stainless, explicitly stating do not use 3.45. Chinese testing laboratories publish a different band - about 3.2 x HV for carbon steel and 3.0 to 3.5 x HV for stainless.

The two conventions differ by roughly 50 percent, and this page deliberately offers no conversion factor. Use the ASTM A666 temper table, or run a tensile test. The reason is that the power law only fixes the ratio of flow stresses; the absolute ratio between hardness and flow stress (the Tabor constraint factor) also varies with n, so multiplying the two compounds the error. Everything below therefore uses tabulated standard values only.

3. How Much Strength a Cold-Bent Corner Carries: eps = t / (2Ri + t)

In a roll-formed or press-braked tube the four corners undergo plastic bending. The outer fibre is stretched, dislocation density rises, and the proof stress goes up with it. The outer-surface true strain is purely geometric:

The derivation is short: the neutral axis radius is Ri plus t/2, the outer surface radius is Ri plus t, and their ratio minus one is t / (2Ri + t). Writing Ri as r times t simplifies it further to 1 / (2r + 1).

Feeding that strain through the power law and converting true stress to engineering proof stress (true stress divided by 1 + eps) gives the corner strength at each bend radius:

Worked check (Ri/t = 2, t = 2.0 mm): eps = 2.0 / (2 x 4.0 + 2.0) = 0.200; true flow stress = 1275 x 0.4847 = 618.0 MPa; engineering proof stress = 618.0 / 1.20 = 515.0 MPa.

A very clean cross-check: at Ri/t = 2 the corner engineering proof stress is exactly 515 MPa, identical to the ASTM A666 minimum for quarter hard. That is not a coincidence - 20 percent bending strain is equivalent to rolling the material to quarter hard. The four corners of an ordinary roll-formed tube are, metallurgically, already quarter hard.

The ductility column matters just as much. The engineering uniform elongation of 304 equals e^n minus 1, i.e. 1.568 - 1 = 0.568, or 56.8 percent - consistent with the ASTM A240 minimum of 40 percent and measured values of 40 to 60 percent. At Ri/t = 0.5 the corner true strain reaches 0.50, past n = 0.45, so the uniform deformation capacity is exhausted and the corner will neck or micro-crack. That is the mechanics behind the shop-floor rule that the inner radius should not be less than 1.5 to 2 times thickness: at Ri/t = 2 some 56 percent of the uniform margin remains, at Ri/t = 1 only 26 percent, and at Ri/t = 0.5 it is gone.

4. What the Whole Section Actually Gains: a Weighted 24.8 Percent

Strong corners do not make a strong section. Take a 50 x 50 x 2.0 tube with Ri = 2t = 4 mm. The corners occupy only part of the perimeter:

• Neutral-axis perimeter = 4 x (50 - 2.0) = 192.0 mm
• Four corner arcs = 4 x (3.1416 / 2 x 5.0) = 31.4 mm (neutral radius = 4.0 + 1.0 = 5.0 mm)
• Corner share = 31.4 / 192.0 = 16.4%

Broken down: the corner contributes 0.164 × 515.0 = 84.5 MPa and the flat faces 0.836 × 205 = 171.4 MPa.

Only 24.8 percent above the 205 MPa annealed baseline. Work hardening is a local effect; designing the whole member on the corner value overestimates capacity by a factor of four. It does help exactly where it is needed: corners are where stress concentration and local denting start, so extra hardness there resists dents and wear - but it is not an allowable stress for the section.

This also explains why a longitudinal coupon cut from a cold-formed tube tests at only 230 to 270 MPa rather than the corner's 515 MPa: the coupon comes from the flat face, and the weakest region yields first.

5. Switching to 2205: 32.5 Percent Thinner, Then 3.25 Times the Deflection

Duplex 2205 carries a minimum proof stress of 450 MPa, 2.20 times that of 304 (450 / 205 = 2.195). Five independent published sources give the same number, making it the best-corroborated figure on this page. Equal strength in bending means equal section modulus times strength; for unit width W = t^2 / 6, so:

Add the density difference (2205 about 7.80, 304 about 8.00 g/cm3): 0.6749 x 7.80 = 5.264; 5.264 / 8.00 = 0.6580, 34.2 percent lighter. That is the entire benefit of the swap.

The cost is stiffness. Deflection is inversely proportional to E x I; for unit width I = t^3 / 12; and both grades sit at roughly 200 GPa:

On an equal-strength reduction the strength just passes and deflection triples. For deflection-controlled parts - handrails (commonly limited to L/120), grating panels, large cladding panels - that trade is unacceptable.

Inverting the question: if only a 1.5 times deflection increase is tolerable, then t2 / t1 = cube root of (1 / 1.5) = 0.8736, so only 12.6 percent can come off, not 32.5 percent.

The correct split is therefore:

• Strength-controlled parts (tie rods, bolts, short-span connections, stub columns): the full 32.5 percent is real.
• Stiffness- or stability-controlled parts (long-span panels, handrails, grating, cladding): it is not. The duplex benefit then lies in chloride stress-corrosion resistance and incidental weight saving, not in thinning.

Local buckling: the b/t limit tightens from 59.4 to 40.1

There is a harder limit still. For a simply supported plate in uniform compression the elastic critical stress is:

Setting the critical stress equal to the yield strength and solving for the width-to-thickness limit:

• 304 (f = 205): 205 / 723047 = 0.00028353, square root = 0.016838, b / t limit = 59.4
• 2205 (f = 450): 450 / 723047 = 0.00062241, square root = 0.024948, b / t limit = 40.1

Yield goes up 2.20 times but the b/t limit only slackens to 0.675 of the original (1 / sqrt(2.195) = 0.675) - that is, it tightens from 59.4 to 40.1.

A concrete case: a compressed plate 180 mm wide needs t at least 180 / 59.4 = 3.03 mm in 304. Swapping to 2205 on equal strength gives t2 = 3.03 x 0.6749 = 2.05 mm, and then b / t = 180 / 2.05 = 87.8 against a limit of 40.1 - 2.19 times over, so the plate buckles well before it yields. To make 2.05 mm in 2205 work, a stiffener must bring b down below 40.1 x 2.05 = 82 mm, i.e. one intermediate stiffener.

This is the step most often skipped when moving to a higher-strength grade: strength and deflection are checked, stability is not.

6. Temper-Rolled Material Cannot Be Welded: 49.8 Percent Joint Efficiency

Temper strength comes from cold-work dislocations, and the weld heat-affected zone reheats that region into the annealing range. The dislocations rearrange and strength falls back to the annealed value. For half-hard 304:

• Tensile: parent 1035 MPa, HAZ back to 515 MPa, joint efficiency = 515 / 1035 = 49.8%
• Proof: parent 760 MPa, HAZ back to 205 MPa, efficiency = 205 / 760 = 27.0%

Designing to the 760 MPa parent value leaves the heat-affected zone at 205 MPa after welding - three quarters of the safety margin gone. Therefore:

• Use temper-rolled material for non-welded joints: bolting, riveting, clipping, clamping.
• For anything welded, design to annealed strength; do not pay for strength you cannot keep.
• Forming and welding first, then strengthening the whole assembly by cold work, is the only route to both, and is rarely practical on site.

7. Temperature and Magnetism Boundaries

Two negative criteria that get overlooked:

Duplex is not a high-temperature material. Continuous service for 2205 is capped at about 250 to 300 degrees Celsius (ASME Section VIII Division 1 provides design data to 315 degrees Celsius). Two embrittlement routes set the limit: sigma phase precipitating between 600 and 1000 degrees Celsius (kinetically peaking near 850), and spinodal decomposition of the ferrite near 475 degrees Celsius. As little as 1 to 2 volume percent sigma phase cuts room-temperature impact toughness by more than half, and only a full solution anneal at 1020 to 1100 degrees Celsius with rapid cooling restores it. Where temperature is present, the thinning benefit has to be re-evaluated.

A magnet proves nothing. Annealed 304 is non-magnetic, but cold bending produces deformation-induced martensite and measurable magnetism - strongest exactly at the corners calculated above. Duplex 2205 is magnetic in the annealed condition because of its ferrite phase. So the magnet test works only on annealed flat sheet, misreads tube corners, and is useless on duplex. For grade verification use a portable spectrometer: Ni at least 8 percent indicates 304, Mo at least 2.0 percent indicates 316L.

At the low end the ranking reverses: 316L austenitic goes down to -196 degrees Celsius, duplex is generally guaranteed only to about -40, and ferritic 430 has a ductile-to-brittle transition that rules it out of cryogenic or impact service. The strain-hardening exponent is the same underlying variable: 430 has n around 0.20 and only 22.1 percent engineering uniform elongation, against 56.8 percent for 304.

8. Reproducible Calculation Checklist

Every expression used on this page is listed here so it can be re-checked with a calculator.

9. Cross-Check Against Published Data

One Quarter Hard, Three Different Numbers, 35 Percent Apart

Published data carry three coexisting conventions for temper strength, and this is the main reason figures never seem to agree:

The spread is widest at quarter hard, where the 515 MPa minimum sits 35 percent above the lower end of the typical range. The three columns mean different things: A666 gives an acceptance floor, the typical range is a production distribution, and the mill value is a model input calibrated for forming simulation. State which one the order is placed against, or the same drawing will produce entirely different thinning and springback predictions.

Independent Evidence: the Harder the Temper, the Faster n Collapses

A published forming-simulation study on cold-rolled SUS304 calibrated all four tempers and reported the hardening exponent and forming limit:

These figures corroborate this page from two directions. First, n falls monotonically with temper, from 0.381 to 0.106 - about a quarter of the starting value. Because n is numerically the true strain at which necking begins, it governs elongation directly, which is the mechanical origin of the 3 percent elongation at full hard listed above, not an empirical coincidence. Second, springback grows faster than strength: proof stress rises from 470 to 1080 MPa (2.30 times) while maximum springback goes from 2.28 to 7.69 mm (3.37 times), roughly 47 percent above linear. That study attributes the excess to a rising yield ratio and a falling n, consistent with the argument here. Temper-rolled material should not be re-formed for a springback reason as well as a ductility one.

How Conservative the Back-Solved Rm Is

One source quotes typical measured values for annealed 2B sheet of 260 to 300 MPa proof stress and 600 to 650 MPa tensile. The 567.5 MPa back-solved here from K = 1275 MPa and n = 0.45 is 6 to 13 percent below that band. The cause is K: the handbook tabulated value is 1275, while fitted values run to 1500 to 1600. This page uses the conservative end, so the conclusions err on the safe side, but estimating actual delivered strength this way runs about 10 percent low. It also shows how literal the statement that 205 MPa is only a floor really is - typical deliveries sit at 260 to 300 MPa.

Apart from those three, the only remaining substantive disagreement is the hardness conversion, and this page avoids it rather than picking a side, for the reason given above: the power law fixes only the flow-stress ratio, while the hardness-to-flow-stress factor itself varies with n, so multiplying them is uncontrolled.

10. Selection Matrix

Five Common Mistakes

1. What goes wrong: the order specifies 304 with no temper.
   Consequence: anything from 205 to 965 MPa proof stress is contractually compliant, and the design does not match the delivery.
   Correct approach: state the ASTM A666 temper code (AN, 1/4H, 1/2H, 3/4H, FH) and the minimum Rp0.2.
2. What goes wrong: converting HV to tensile strength with the carbon-steel factor 3.45.
   Consequence: a systematic underestimate of about 30 percent, giving false conservatism or false rejection.
   Correct approach: do not convert; read the temper table or run a tensile test.
3. What goes wrong: thinning 32.5 percent on the strength of 2205's higher proof stress.
   Consequence: deflection up 3.25 times, b/t over the limit by 2.19 times, buckling before yielding.
   Correct approach: first decide whether strength, stiffness or stability governs; in stiffness-controlled cases the saving is at most 12.6 percent.
4. What goes wrong: designing a welded joint on the parent strength of temper-rolled material.
   Consequence: the heat-affected zone anneals and joint efficiency drops to 49.8 percent (27.0 percent on proof stress).
   Correct approach: design welded parts on annealed values, or use mechanical fastening.
5. What goes wrong: checking the grade with a magnet.
   Consequence: cold-bent corners carry deformation martensite and read as fake; duplex is magnetic anyway and cannot be checked at all.
   Correct approach: portable spectrometry - Ni at least 8 percent for 304, Mo at least 2.0 percent for 316L.

Calculation basis. All worked examples use 304 annealed Hollomon constants (K = 1275 MPa, n = 0.45, handbook tabulated), ASTM A666 minimum temper values (t at least 0.38 mm band), and a duplex 2205 minimum proof stress of 450 MPa. On that basis: back-solved tensile strength 567.5 MPa (consistent with the A240 lower bound of 515 and the measured 520 to 620 range); cold-bend corner engineering proof stress 515.0 MPa at Ri/t = 2, equal to quarter hard; equal-strength thickness ratio 0.6749 (32.5 percent thinner); deflection ratio 3.25; b/t limits 59.4 and 40.1; half-hard welded joint efficiency 49.8 percent. Included: work hardening within uniform elongation, equal-strength bending conversion, elastic buckling of a simply supported plate in uniform compression, and weld heat-affected-zone softening. Not included: the Bauschinger effect and reverse loading, anisotropy (measured K varies about 6 percent between rolling, diagonal and transverse directions), strain-rate and temperature effects on flow stress, weld metal strength mismatch, fatigue and ratcheting under cyclic load, and the residual stress distribution from cold bending. All strength figures are standard minimums; mill certificates typically run 10 to 30 percent higher, so use the certificate for design and the standard lower bound for acceptance. No hardness-to-tensile conversion factor is offered.

In one line: 304 is not 205 MPa, it is a selectable band from 205 to 965 MPa; temper rolling and cold bending buy 2.5 to 4.7 times the proof stress but cost ductility and weldability; and switching to 2205 saves 32.5 percent of thickness only if your part is genuinely strength-controlled - otherwise deflection and buckling will make the decision for you.

FAQ

What is the yield strength of 304 stainless steel, and why do different datasheets disagree?

Because the temper differs. ASTM A240 annealed minimum is 205 MPa; ASTM A666 tempers reach 965 MPa at full hard, with 515 MPa at quarter hard, 760 MPa at half hard and 930 MPa at three-quarter hard in between - a 4.71 times spread within one grade. Datasheets usually omit the temper code, so always state AN or 1/2H plus the minimum Rp0.2 on the order.

How much thickness can I save by switching from 304 to duplex 2205?

32.5 percent on paper. Equal-strength scaling gives t2/t1 = sqrt(205/450) = 0.6749, and with the density difference (7.80 versus 8.00 g/cm3) that is 34.2 percent less weight. But this holds only for strength-controlled parts. In stiffness-controlled parts the same 32.5 percent thinning raises deflection 3.25 times; if only a 1.5 times deflection increase is allowed, the saving drops to 12.6 percent. The b/t limit also tightens from 59.4 to 40.1, so an 180 mm wide plate thinned to 2.05 mm exceeds the limit by 2.19 times and needs a stiffener.

How do I calculate the corner strength of a cold-formed tube, and why is it higher than the flat sheet?

Work backwards from the outer fibre strain. Strain eps equals thickness divided by twice the inner radius plus thickness, t/(2Ri+t). For a 2.0 mm wall with Ri = 2t, eps = 0.200; feeding 304 Hollomon constants (K = 1275 MPa, n = 0.45) gives a true flow stress of 618.0 MPa, and the engineering proof stress is 618.0/1.20 = 515.0 MPa - exactly the quarter hard minimum. However the corners are only about 16.4 percent of the tube perimeter, so the weighted proof stress of the whole section is 255.9 MPa, just 24.8 percent above the annealed value.