Self-tighteningTJ-15
Universal Parallel Wedge Grips
Self-tightening parallel wedges hold a flat sheet coupon square without crushing the tab, which is what keeps the plastic region clean enough to fit.
SpecificationsTesting standard
ASTM E646
Standard Test Method for Tensile Strain-Hardening Exponents (n-Values) of Metallic Sheet Materials
Written and technically reviewed by Dak System Inc. engineeringLast reviewed
ASTM E646 determines the strain-hardening exponent n of metallic sheet from an ordinary tension test. The plastic part of the curve is converted to true stress and true plastic strain, fitted to a power curve, and n is the exponent of that fit — the slope of the line on logarithmic axes. It estimates the strain at which necking begins and ranks the stretch formability of similar metallic systems.
At a glance
- Test type
- Tensile — the specimen is pulled apart
- Published by
- ASTM
- Edition
- E646-16(2024)
- Material
- Metals, alloys & welds
- Runs on
- Series 7200 and Series 9000
What the test does
An ordinary tension test on a sheet coupon, analysed differently. Instead of reading off a single strength figure, the plastic part of the curve is converted to true stress and true plastic strain and fitted to a power curve. The exponent of that fit is n; the coefficient in front of it is the strength coefficient. Plotted as the logarithm of true stress against the logarithm of true plastic strain, the fit becomes a straight line and n its slope, which is why the calculation is done by linear regression over a stated strain range rather than from two points.
What it measures, and why it matters
How fast a metal gets stronger as it deforms, and therefore how far it can be stretched before deformation localises. ASTM E646 states its own use precisely: it is useful for estimating the strain at the onset of necking in a uniaxial tension test, it gives an empirical parameter for appraising the relative stretch formability of similar metallic systems, and it measures the increase in strength produced by plastic deformation. A high n spreads strain out along the specimen; a low n lets it collect in one place, and in a press that place becomes a split.
That makes n the stretch-forming number, where the plastic strain ratio r of ASTM E517 is the deep-drawing one. Real panels need both: a shape stretched over a punch in one region and drawn in from the flange in another fails on whichever is short.
Specimen and scope
The coupon is a conventional sheet tension specimen. What is specific to this method is the thickness band it claims and the kind of curve it can be applied to.
- Material
- Metallic sheet whose plastic flow obeys a power curveThat qualification is in the scope. A material whose curve does not fit one power law can still be handled, with more than one n reported by agreement.
- Thickness range
- 0.005 in. (0.13 mm) to 0.25 in. (6.4 mm)The method has been and may be applied to other forms and thicknesses by agreement, but that is outside the stated scope.
- Geometry
- Rectangular coupon with a reduced parallel section
- Orientation
- Recorded relative to the rolling directionPracticen varies with orientation on anisotropic sheet, so the direction is part of the result rather than a detail of sampling.
- Units
- Inch-pound units are standard; n itself is dimensionlessThe standard notes explicitly that n has no units and is independent of the units used to determine it.
The thickness band is the scope of the method, not a suggestion. Testing plate or heavy strip to E646 and citing it without recording the agreement is a finding waiting to happen.
Strain range and rate
Two choices decide the number: which part of the curve is fitted, and how fast the specimen was pulled while it was being fitted.
- Range fitted
- The entire plastic curve, or any portion named in a product specification
- Common interval for low-carbon steel
- 10 % to 20 % engineering strainThe standard records this as commonly used for formable low-carbon steel products. It is a note, not a requirement.
- Upper limit
- Before the onset of neckingThe method is suitable for the plastic region prior to necking. Past maximum force the true-stress conversion no longer describes a uniformly deforming specimen.
- Rate sensitivity
- n may vary with displacement rate or strain rateIt depends on the metal and the test temperature, so the rate must be held steady through the fitted range and reported with the result.
- Data density
- Enough points across the range to support a regressionDakn is a slope. A logging rate chosen for a peak-force test can leave too few pairs across a 10 % window to fit one reliably.
Two laboratories fitting different intervals on the same coil will report different n-values, both correctly. The interval belongs in the specification and on the certificate.
Calculations
One power curve, fitted twice over — once as it is written, and once in logarithms, which is the form a least-squares fit actually uses.
Power curveσ
σ = K · εpⁿ
- σ
- true stress
- K
- strength coefficient, the stress at unit true plastic strain
- εp
- true plastic strain
- n
- strain-hardening exponent, dimensionless
The relationship the scope requires the material to obey. Where a single curve does not fit between yield and necking, more than one n may be obtained by agreement.
Logarithmic formln σ
ln σ = ln K + n · ln εp
- ln σ
- natural logarithm of true stress
- ln K
- intercept, giving the strength coefficient
- n
- slope of the fitted line — the strain-hardening exponent
n is obtained by least-squares linear regression of the paired logarithms over the chosen range, which is why the range fitted has to be stated with the value.
True stress and true plastic strainσ, εp
σ = R (1 + e); ε = ln (1 + e)
- R
- engineering stress, force divided by the original area
- e
- engineering strain over the extensometer gauge length
- ε
- true strain, from which the elastic part is subtracted to give εp
Valid only while deformation is uniform, which is another way of saying only up to maximum force.
How the test runs
- 01Cut the coupon, record its orientation to the rolling direction, and measure the cross-section.
- 02Mark the gauge length and fit an extensometer conforming to ASTM E83.
- 03Set the strain range to be fitted, from the product specification where one applies.
- 04Zero force with the specimen in the grips and unloaded.
- 05Pull at a rate held constant across the range that will be fitted.
- 06Log force and extension densely enough that the range carries a usable number of pairs.
- 07Convert to true stress and true plastic strain, subtracting the elastic part of the strain.
- 08Exclude any discontinuous region — yield-point and Lüders elongation, twinning, serrated flow.
- 09Fit ln σ against ln εp by linear regression over the chosen range.
- 10Report n as the slope, with the strength coefficient, the standard error and the range fitted.
Where curve smoothing is used to make a discontinuous region tractable, it must be agreed and recorded. The standard cautions in as many words that smoothing techniques can affect the n-value they were applied to.
Watch the test
Grips and fixtures for this method
Axial & transverse
Clip-On Extensometers
A cross-flexure clip-on gives the strain resolution the regression needs across a 10 % window, with an activation force low enough to leave thin sheet alone.
Specifications
Non-contact
Advanced Video Extensometer
Non-contact strain over the full gauge length, useful where the sheet is too thin or too soft to carry knife edges to the strains this method fits.
SpecificationsWhat the report has to contain
- Full designation and edition
- Material identification — alloy or grade, temper or condition, lot, and nominal thickness
- Orientation of the coupon relative to the rolling direction
- Cross-sectional dimensions and the area used in the stress calculation
- Extensometer gauge length and classification
- Test rate, and confirmation that it was held constant across the fitted range
- The strain range or ranges over which n was determined, and where they came from
- The regression used to obtain the slope, and the number of data pairs it was fitted through
- n and the strength coefficient, with the range of the fit they were taken over
- Any curve smoothing applied, and the agreement under which it was applied
- Where more than one n is reported, the range each belongs to
What the machine must be capable of
A tension frame with clean data through the plastic range, rather than a large one. Sheet coupons in this thickness range rarely demand more than a few kilonewtons. What the test does demand is strain measured on the specimen with an extensometer conforming to ASTM E83 and sampled densely enough to fit a regression: n comes from the shape of a curve, not from its peak, so a data rate adequate for reporting tensile strength can be inadequate here.
Rate control matters more than it appears to. The standard warns that the n-value may vary with the displacement rate or strain rate used, depending on the metal and the test temperature, so the rate has to be held steady through the evaluation range and reported with the result.
The strain range itself is a decision, not a default. The exponent may be determined over the entire plastic stress-strain curve or over any portion of it named in a product specification, and the standard records that the engineering strain interval from 10 % to 20 % is commonly used for formable low-carbon steel products. Two laboratories fitting different intervals on the same material will both be right and will not agree.
What goes wrong in practice
Fitting through a region the method excludes. E646 does not apply to any portion of the true-stress curve that behaves discontinuously, and the standard names the cases: yield-point and Lüders band elongation in mild steel, twinning, and the serrated flow of the Portevin-Le Chatelier effect in some aluminium alloys. Curve smoothing is permitted by agreement, with an explicit caution that smoothing can change the n-value it was applied to. Beyond that, the recurring errors are fitting past maximum force into the necked region, quoting n without the strain interval or the orientation, and assuming a single power curve fits everything between yield and necking — the standard says outright that it may not, and that more than one n-value may be reported by agreement where it does not.
How it differs from the standards nearest to it
The same tensile curve can yield all four of these. They are not alternatives to one another.
| ASTM E646 | ASTM E517 | ISO 10275 | ASTM E8/E8M | |
|---|---|---|---|---|
| Reports | Strain-hardening exponent n | Plastic strain ratio r | Strain-hardening exponent n | Strength and ductility |
| Forming question | Stretch forming | Deep drawing | Stretch forming | None — general tension |
| Scope | Sheet 0.13 to 6.4 mm | Sheet for deep drawing | Sheet and strip | All metallic materials |
| Rate requirement | Rate held steady and reported; n is rate-sensitive | Test must run past yield-point elongation | Strain rate not above 0,008 s⁻¹ | Two-stage rate pattern |
| Fit range | Whole curve or a named portion | A single strain or a range | Whole uniform range or a named portion | Not applicable |
ISO 10275 is the closest counterpart and is not interchangeable on paper: it caps the strain rate numerically, requires machine and extensometer classes by ISO designation, and subtracts the elastic strain explicitly. A certificate should name which of the two produced the number.
Questions we are asked about this test
What is ASTM E646?
It is the ASTM test method for the tensile strain-hardening exponent, or n-value, of metallic sheet materials. The plastic part of a tension curve is converted to true stress and true plastic strain and fitted to a power curve; n is the exponent. The current edition is E646-16(2024).
What does the n-value tell you?
How fast the metal strengthens as it deforms, and therefore how far it can stretch before deformation localises. The standard states its uses directly: estimating the strain at the onset of necking in a uniaxial tension test, appraising the relative stretch formability of similar metallic systems, and measuring the increase in strength produced by plastic deformation.
What thickness of sheet does ASTM E646 cover?
At least 0.005 in. (0.13 mm) and not more than 0.25 in. (6.4 mm). The standard notes that the method has been applied to other forms and thicknesses successfully, but only by agreement — outside that band it is not covered by the scope as written.
What strain range should n be determined over?
Whatever the product specification names. The exponent may be taken over the entire plastic stress-strain curve or over any portion of it, and the standard records that the engineering strain interval from 10 % to 20 % is commonly used for formable low-carbon steel products. Whichever range is used has to be reported, because the value depends on it.
Why can ASTM E646 not be used on a discontinuous curve?
Because a power curve cannot describe one. The method is not intended for any portion of the true-stress curve that behaves discontinuously, and the standard names the cases: yield-point and Lüders band elongation in mild steel, twinning, and the serrated flow of the Portevin-Le Chatelier effect. Curve smoothing may be used by agreement, with the caution that it can change the n-value.
Does the test speed affect the n-value?
Yes. The standard says plainly that n may vary with the displacement rate or strain rate used, depending on the metal and the test temperature. The practical consequence is that the rate must be held constant through the range being fitted and reported alongside the result, or two laboratories will not reproduce one another.
What is the difference between n-value and r-value?
n is the stretch-forming parameter from ASTM E646 and describes how quickly the metal hardens as it deforms. r is the deep-drawing parameter from ASTM E517 and describes how well it resists thinning. A pressed panel usually needs both, because different regions of the same part are stretched and drawn.
How does ASTM E646 compare with ISO 10275?
They determine the same quantity by the same power-law fit, but with different conventions. ISO 10275 caps the strain rate of the parallel length at 0,008 s⁻¹, calls up machine verification to ISO 7500-1 class 1 and extensometers to ISO 9513, and subtracts the elastic strain explicitly in its current edition. Name the method the value came from rather than treating the two as one.
What machine does an n-value test need?
An ordinary tension frame, since sheet coupons in this thickness band rarely draw more than a few kilonewtons. What the test does need is contact or optical strain measurement conforming to ASTM E83, steady rate control across the fitted range, and a data rate high enough to give the regression enough points to work with.
Running ASTM E646 on the Series 7200 and Series 9000
Dak verifies against whichever standard the method names, and where a class applies our frames sit a class tighter than it asks.
| The method asks for | Dak supplies | |
|---|---|---|
| Capacity | Low — coupons between 0.13 and 6.4 mm thick rarely draw more than a few kilonewtons, so data quality through the plastic range decides the frame, not capacity. | Load cells from 1 kg to 60 ton on the Series 7200, and 0.5 to 100 kN on the Series 9000 |
| Force accuracy | unknown — the force-verification class is not stated on the ASTM catalogue record | ISO 7500-1 Class 0.5, verified to ASTM E4, DIN 51221 and BS 1610 |
| Strain measurement | An extensometer to Practice E83 — the required class was not confirmed for the current edition on an issuing-body page, gauge length unknown — a conventional reduced-section sheet coupon with a marked gauge length; the geometry comes from the product specification | Certified to ISO 9513 Class 1 and ASTM E83 — non-contact video, clip-on and high-elongation |
| Gripping | flat-faced wedge grips for the sheet coupon; no special fixture is called for | Our self-tightening serrated wedge grips, with V-jaws for round specimens, built to the specimen |
| Environment | Ambient laboratory conditions; no conditioning atmosphere is specified | 3009 series chambers, −150 °C to +400 °C — temperature only |
This page describes the method as practised. The governing text is the current edition from the issuing body. Tell us what you are testing and we will answer with the machine, the fixture and a quotation.