n-Value (Strain Hardening Exponent)

1. Definition

The n-value (strain-hardening exponent) measures how rapidly a metal’s flow stress rises with plastic strain. In the Hollomon power-law form, true stress σ = K εⁿ, where K is the strength coefficient and n is the exponent. Higher n means more strengthening per strain increment and usually better resistance to early localized necking in stretch forming.

ASTM E646 frames n as useful for estimating the strain at onset of necking in uniaxial tension and for comparing relative stretch formability of similar metallic systems.

2. Hollomon Power Law

Taking logarithms, log σ = log K + n log ε. Thus n is the slope of the log true stress vs log true strain plot in the plastic region before necking. K is the true stress at a true strain of 1 (extrapolated).

A single power curve may not fit the entire path from yield to necking. Standards allow more than one n by agreement when the slope changes with strain range.

3. How n Is Measured

n is determined from a uniaxial tensile test with true stress–true strain conversion in the plastic region prior to necking. Governing methods include ASTM E646 and ISO 10275. Typical sheet thickness coverage in E646 is on the order of 0.13–6.4 mm (with notes for other forms by agreement).

• n has no units.
• n may vary with strain rate and temperature.
• Always record the strain interval used.

4. Strain Range Choices

For many low-carbon formable steels, industry practice uses roughly 10%–20% engineering strain for n. AHSS guidelines note that dual-phase grades can show high n at low strains then settle to a terminal n near conventional HSS levels. Some OEM specs therefore require both low-strain and high-strain n reporting.

5. Link to FLC / FLD

AHSS Insights emphasizes that for most steels, n-value along with thickness strongly influences the position of the forming limit curve. When global stretch formability is the concern, analyze n—not only yield/tensile/elongation.

Plane-strain forming limits relate theoretically to n under simplifying hardening assumptions; practical FLCs also reflect thickness and strain-rate sensitivity.

6. Relevance to Roll Forming

Do not ignore n on stretch-critical programs; do not panic about n alone when the failure mode is a tight bend crack with low elongation.

7. n vs Other Properties

• n — hardening rate under power-law fit
• Elongation — total/uniform stretch capacity on a gauge length
• Yield — onset of permanent set / stand loads
• r-value — resistance to thinning (anisotropy)

8. Common Mistakes

1. Comparing n values computed on different strain intervals.
2. Assuming high UTS implies high n.
3. Using only terminal n for DP steels that need low-strain n too.
4. Expecting n to fix an impossible bend radius.

9. Boundaries

• n ≠ hardness.
• n ≠ friction coefficient.
• Certificate n ≠ guaranteed zero scrap on every die.

Buyer / Engineer FAQ

Is higher n always better for roll forming?

Higher n helps distribute stretch strains. Many roll-form features are bend-dominated, so elongation, yield window, and bend radius still decide crack risk.

What strain range is used for n?

A common interval for formable low-carbon steels is about 10%–20% engineering strain (or up to uniform elongation). AHSS may need additional ranges.

How does n relate to the FLC?

With thickness, n is a primary driver of forming-limit curve height, especially near plane strain.

Does lubrication change n on the certificate?

No. Lube changes process friction; n is a material tensile-derived property.

Can I estimate n from elongation alone?

Rough correlations exist, but specification and CAE need measured n per the test method.

Is n the same as work hardening?

n quantifies how strongly flow stress rises with strain under a power-law fit. Work hardening is the broader physical phenomenon.

Plant Practice Notes

Lead RFQ conversations with measurable acceptance criteria, not adjectives. Document whether a number comes from a mill certificate, a plant trial, or a published standard table.

When two heats of the same grade behave differently, pull certificates and process logs before rebuilding tooling. Most mystery forming issues are heat-to-heat property or lubrication shifts.

• Keep units consistent (MPa vs ksi; mm vs in).
• Record test methods when citing formability indices.
• Attach heat numbers to scrap photos and CAPA files.
• Separate design minimums from actual forming windows.
• Update SOPs when a new grade or coating family is introduced.
• Train receiving to stop on out-of-window certificates.

1. Define the decision this page supports (buy / form / inspect / redesign).
2. List the three certificate or process fields that matter most.
3. List shop symptoms that should trigger a re-read of this page.
4. Name the next specialist encyclopedia page to open.
5. File the lesson learned after each coil-related incident.

Auditors respond better to traceable certificate fields than to verbal grade nicknames. Keep EN 10204 type and heat mapping visible at receiving.

After any coil change that moves yield by a large step, expect springback and load changes even when thickness is identical.

Do not invent universal machine kW or m/min values on materials encyclopedia pages.