ASTM E2218-02(2008)
(Test Method)Standard Test Method for Determining Forming Limit Curves
Standard Test Method for Determining Forming Limit Curves
SIGNIFICANCE AND USE
A forming limit curve (FLC) defines the maximum (limiting) strain that a given sample of a metallic sheet can undergo for a range of forming conditions, such as deep drawing, stretching and bending over a radius in a press and die drawing operation, without developing a localized zone of thinning (localized necking) that would indicate incipient failure.
FLCs can be obtained empirically by using a laboratory hemispherical punch biaxial stretch test and also a tension test to strain metal sheet specimens from a material sample beyond their elastic limit, just prior to localized necking and fracture.
Since this cannot be predetermined, one or both surfaces of specimens are covered with a grid pattern of gage lengths usually as squares or small diameter circles, by a suitable method such as scribing, photo-grid, or electro-etching, and then each specimen is formed to the point of localized necking, or fracture.
Strains in the major (e1) and minor (e2) directions are measured using points on the grid pattern in the area of the localized necking or fracture.
Blanks of varied widths are used to produce a wide range of strain states in the minor (e2) direction.
The major (e1) strain is determined by the capacity of the material to be stretched in one direction as simultaneous surface forces either stretch, do not change, or compress, the metal in the (e2) direction.
In the tension test deformation process, the (e2) strains are negative and the metal is narrowed both through the thickness and across its width.
These strains are plotted on a forming limit diagram (FLD) and the forming limit curve (FLC) is drawn to connect the highest measured (e1 and e2) strain combinations that include good data points.
When there is intermixing and no clear distinction between good and necked data points, a best fit curve is established to follow the maximum good data points as the FLC.
The forming limit is established at the maximum (e1) strain attained prior to necking....
SCOPE
1.1 This method gives the procedure for constructing a forming limit curve (FLC) for a metallic sheet material by using a hemispherical deformation punch test and a uniaxial tension test to quantitatively simulate biaxial stretch and deep drawing processes.
1.2 FLCs are useful in evaluating press performance by metal fabrication strain analysis.
1.3 The method applies to metallic sheet from 0.5 mm (0.020 in.) to 3.3 mm (0.130 in.).
1.4 The values stated in SI units are to be regarded as the standard. The inch-pound equivalents are approximate.
1.5 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.
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Standards Content (Sample)
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Designation: E2218 − 02(Reapproved 2008)
Standard Test Method for
Determining Forming Limit Curves
This standard is issued under the fixed designation E2218; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope 3.2 forming limit diagram (FLD)—a graph on which the
measured major (e ) and associated minor (e ) strain combi-
1 2
1.1 This method gives the procedure for constructing a
nations are plotted to develop a forming limit curve. See Fig.
forming limit curve (FLC) for a metallic sheet material by
1.
using a hemispherical deformation punch test and a uniaxial
3.2.1 Discussion—ThegraduatedscalesontheFLDshallbe
tension test to quantitatively simulate biaxial stretch and deep
in percent strain, calculated from the initial gage length.
drawing processes.
3.2.2 Discussion—The distance between FLD percentage
1.2 FLCs are useful in evaluating press performance by
increments shall be the same for both the major strain (e )
metal fabrication strain analysis.
ordinate (parallel to the vertical y axis) and minor strain (e )
1.3 The method applies to metallic sheet from 0.5 mm
abscissa (parallel to the horizontal x axis) unless the difference
(0.020 in.) to 3.3 mm (0.130 in.).
is noted in the report.
1.4 The values stated in SI units are to be regarded as the
3.3 forming limit curve (FLC)—an empirically derived
standard. The inch-pound equivalents are approximate.
curveshowingthebiaxialstrainlevelsbeyondwhichlocalized
through-thickness thinning (necking) and subsequent failure
1.5 This standard does not purport to address all of the
occur during the forming of a metallic sheet. See Fig. 2.
safety concerns, if any, associated with its use. It is the
3.3.1 Discussion—The curve of Fig. 2 is considered the
responsibility of the user of this standard to establish appro-
priate safety and health practices and determine the applica- forming limit for the material when the metal is subjected to a
stampingpressoperation.Itwasobtainedforadrawingquality
bility of regulatory limitations prior to use.
aluminumkilledsteelsheet.ThecurveofFig.2correlateswith
2. Referenced Documents
the upper curve of Fig. 1, a generic curve representing a
metallic sheet material with a FLD of 40%.
2.1 ASTM Standards:
o
A568/A568M Specification for Steel, Sheet, Carbon, 3.3.2 Discussion—The strains are given in terms of percent
major and minor strain measured after forming a series of test
Structural,andHigh-Strength,Low-Alloy,Hot-Rolledand
Cold-Rolled, General Requirements for specimen blanks by using a grid pattern. The gage lengths
before and after forming the part are measured to obtain the
E6Terminology Relating to Methods of MechanicalTesting
E8/E8MTest Methods for Tension Testing of Metallic Ma- percentstrain.Thecurvefornegative(e )strainswillgenerally
follow a constant surface area relationship to the associated
terials
E517Test Method for Plastic Strain Ratio r for Sheet Metal (e ) strain.
E646Test Method for Tensile Strain-Hardening Exponents 3.3.3 Discussion—The range of possible major strain (e)is
(n -Values) of Metallic Sheet Materials
from 0% to over 200%. The range of possible minor strain
(e )isfrom−40%toover+60%,orevengreaterstrainlevels.
3. Terminology
3.3.4 Discussion—Forconvenience,theforminglimitcurve
3.1 Terminology E6 shall apply as well as the following (FLC) can be plotted on a reduced range of the forming limit
special terms used in this method. diagram (FLD), for example, from +20% to +80% major (e )
strains and from −20% to +30% minor (e ) strain. If the
lowest(e )strainincrementoftheFLDisnot0%e ,thatvalue
1 1
This method is under the jurisdiction ofASTM Committee E28 on Mechanical
shall be noted in the report.
Testing and is the direct responsibility of Subcommittee E28.02 on Ductility and
Formability.
3.4 grid pattern—a pattern applied to the surface of a metal
Current edition approved May 1, 2008. Published October 2008. Originally
sheet to provide an array of precisely spaced gage points prior
published in 2002. Last previous edition approved in 2002 as E2218–02. DOI:
10.1520/E2218-02R08.
to forming the metal into a final shape by the application of a
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
force.
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
3.4.1 Discussion—Anarrayofsquares,orcircles,orboth,is
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website. printed on the surface of the specimen. Suggested patterns are
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E2218 − 02 (2008)
NOTE 1—The upper curve is representative of the forming limit. Strains below the lower curve do not occur during forming metallic sheet products
in the most stamping press operations. Curves to the left of % e = 0 are for constant area of the sheet surface.
FIG. 1 Forming Limit Diagram
shown in Fig. 3.The pattern shall adhere to the metal so that it these gage length changes. The strains can be either engineer-
will not be moved on the surface or rubbed off by the forming ing strain based on the original gage length, or true strain.
operation. Refer to Specification A568/A568M, Appendix 3.4.3 Discussion—Larger patterns, of 6 mm (0.25 in.) up to
X4–Procedures for Determining the Extent of Plastic Defor- 125 mm (5 in.), can be used to measure low strain levels on
mation Encountered in Forming or Drawing, for procedures to formed parts, but are not used in determining the FLC.
applyphotographicandelectrochemicallyprintedgridpatterns 3.4.4 Discussion—Circles are suggested for deformations
and a review of strain analysis. where the major strain (e ) does not align with the lines of a
3.4.2 Discussion—Suggested dimensions for the gage square pattern. This condition is less likely in the process of
lengthsare2.5mm(0.100in.)forthesidesofasquarepattern, determining the FLC than in production stamping evaluations.
or diameter of a circle pattern.After the part has been formed, These circles commonly have diameters of 2.5 mm (0.100 in.)
critical areas are measured for the resulting gage length and can be spaced up to 2.5 mm (0.100 in.) apart. They are
changes in the long dimension from (L)to(L) of the pattern, measured across the diameter of the circle when the line width
o f
and in the width dimension (W)to(W) at 90° to the long is minimal. For wider lines, the enclosed area of the etched
o f
dimension as shown in Fig. 4. The major strain (e ) and circle should be consistent from one circle to another and the
associated minor strain (e ) at 90° to (e ) are calculated from measurement made across the inside diameter. This is more
2 1
E2218 − 02 (2008)
Cold Rolled Drawing Quality Aluminum Killed Steel
Longitudinal Mechanical Properties
Yield Tensile
%El
Thickness Strength Strength
in 50 n Value r Value
mm
mm (in.) MPa (ksi) MPa (ksi)
0.866 (0.034) 163.4 (23.7) 304.7 (44.2) 43.5 0.230 1.71
Chemical Composition
Element C S N Mn Al P Si
Percent 0.035 0.006 0.006 0.19 0.29 0.006 0.004
FIG. 2 Forming Limit Curve (FLC) for a Cold Rolled Drawing Quality Aluminum Killed Steel Sheet.
critical with wider line width patterns and at high e strains 3.5 deep drawing—a metal sheet forming operation in
when the line spreads as the metal surface stretches.
which strains on the sheet surface are positive in the direction
3.4.5 Discussion—Analternatetocirclesisapatternofsolid
of the punch travel (e ) and negative at 90° to that direction.
dots of precise diameter, which are measured across the
See Fig. 4.
diameter of the dot.
E2218 − 02 (2008)
NOTE 1—The basic pattern is reapeated over the area of the part to be studied on a flat specimen blank.
FIG. 3 Examples of patterns for Gage Length measurement units used in Determining Forming Limit Curves (FLC)
FIG. 4 Possible Changes in Shape of the Grid Pattern Caused by Forming Operations on Metallic Sheet Products
3.5.1 Discussion—Deep drawing occurs in the walls of a 3.8 plane strain—the condition in metal sheet forming that
drawn cylinder or the corner walls of a deep drawn part when maintains a near zero (0 to +5%) minor strain (e ) while the
the flange clamping force is sufficient to restrain metal move- major strain (e ) is positive (in tension). It is sometimes
ment and wrinkling, while permitting the punch to push the referred to as FLD . See Fig. 1 and Fig. 4.
o
center area of the blank into the cavity of the die. Strain 3.8.1 Discussion—Plane strain is the most severe deforma-
conditions that can cause wrinkling or thickening are shown in tion mode and causes a low point in the forming limit curve
Fig. 1. (FLC). For convenience, many FLCs are shown with the low
3.5.2 Discussion—In forming a square pan shape, metal pointat0%(e ),however,suchanabruptreversalof(e )strain
2 1
from an area of the flange under a reduced clamping force is does not occur. See Fig. 2 and Figs. X2.1-X2.3.
pulled into the die to form the side wall of the part.
3.9 biaxial stretching—a mode of metal sheet forming in
3.6 majorstrain—thelargeststrain(e )developedatagiven which positive strains are observed in all directions at a given
location in the sheet specimen surface. location. See Fig. 4.
3.6.1 Discussion—The major strain (e ) is measured along
3.10 limiting dome height (LDH)—an evaluative test for
thestretchedlineofasquarepattern,oralongthemajoraxisof
metalsheetdeformationcapabilityemployinga200mm(4in.)
theellipseresultingfromdeformationofacirculargridpattern.
hemispherical punch and a circumferential clamping force
3.7 minor strain—the strain (e ) in the sheet surface in a sufficient to prevent metal from the surrounding flange being
direction perpendicular to the major strain. pulled into the die cavity.
3.7.1 Discussion—The minor strain (e ) is measured at 90° 3.10.1 Discussion—The LDH test was designed to give a
to the major strain, along the shorter dimension of the final repeatablemeasureofpunchmovementamongspecimensofa
rectangular shape of a part formed using a square pattern, or specific metal sheet sample, thus the only measured value
the shorter axis of the ellipse resulting from deformation of a would be the punch height at incipient fracture. Problems with
circular grid pattern. f a square pattern becomes skewed into a maintaining a secure clamp result in variation of the measured
parallelogram shape, it shall not be used to measure strain. LDH value.Amodification of the LDH test using a strip in the
E2218 − 02 (2008)
range of 200 mm (4 in.) wide was found to give (e ) values 4.1.8 Measuring and recording the (e ) and the (e ) strains
1 1 2
near 0% (e ), when the surface strains were measured using a of the grid pattern on the surface area near the neck of all the
grid pattern. On this basis, a test was developed to use a test specimens for the series.
sheared strip of metal sheet 200 mm (4 in.) wide and
4.1.8.1 These measurements can include good (no localized
sufficientlylongtobesecurelyclampedintheLDHtestfixture.
necking), marginal (localized necking), and fracture areas.
The height at incipient fracture was to correlate with FLD .
o 4.1.8.2 If other than good (no localized necking) locations
The test was not sufficiently repeatable to be employed for
are included, each measured point shall be visually evaluated
evaluation of metal sheet samples. The equipment is used to
and noted as illustrated in Fig. 2.
stretchspecimens,withgridpatterns,thathavebeenshearedto
4.1.9 Plotting the measured strain combinations on a FLD.
various widths and is one method to obtain a range of (e ) and
See Fig. 2.
associated (e ) values for plotting a FLC on a FLD.
4.1.10 Establishing the forming limit curve (FLC) be con-
necting the uppermost good (no localized necking) (e ) strains
4. Summary of Test Method
over the associated (e ) strain range used in the study.
4.1.10.1 For practical purposes, the specimens that have
4.1 The procedure for determining a forming limit curve
(FLC) involves the following: been strained to a localized neck-down, or through thickness
fracture, condition can be measured at a location on the
4.1.1 Using a hemispherical punch testing machine (LDH
oppositesideofthehemisphericalbulgefromthefracture,ina
tester).Sometimescalledabulgetester.TheLDHtestemploys
good (no localized necking) location, to obtain values to
a 100 mm (4 in.) diameter machined surface punch.
establish the FLC.
4.1.1.1 A universal testing machine for tension load appli-
4.1.10.2 Another acceptable procedure is to measure the
cation and a sub-press for against the metal sheet surface
grid near the necked, or fracture, location and identify these
loading with a ball punch of 75 mm (3 in.), 100 mm (4 in.), or
data points in determining the forming limit curve. This
larger diameter can be used in place of the LDH test equip-
procedure was used in locating the FLC of Fig. 2.
ment.
4.1.10.3 Establishing the FLC depends on judgement. Note
4.1.2 Preparing a series of grid pattern blanks with different
thatinFig.2thereareseveralgood(nolocalizednecking)data
widths and a common length suitable for being securely
points above the FLC and two marginal points below the FLC.
gripped in the test apparatus.
4.1.10.4 The FLC curve shall not include an area where
4.1.2.1 All specimens for a series shall have their long
there is a preponderance of marginal data points at an (e )
dimension in the same orientation, relative to the original
strain level below the measured good (no localized necking)
process rolling direction of the sample and that direction noted
data points.
in the report.
4.1.3 Lubricating the contact surfaces of the blank and
5. Significance and Use
punch for the hemispherical punch test.
5.1 A forming limit curve (FLC) defines the maximum
4.1.3.1 Mineral oil and a thin polyethylene sheet is an
(limiting) strain that a given sample of a metallic sheet can
excellent lubricant.
undergo for a range of forming conditions, such as deep
4.1.3.2 Drawing lubricants, or greases containing graphite,
drawing,stretchingandbendingoveraradiusinapressanddie
are acceptable.
drawing operation, without developing a localized zone of
4.1.3.3 Kerosene is not a good lubricant, as it cleans the
thinning (localized necking) that would indicate incipient
surfaces under pressure and the metal sheet will not slide over
failure.
the pu
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