ASTM E2218-02
(Test Method)Standard Test Method for Determining Forming Limit Curves
Standard Test Method for Determining Forming Limit Curves
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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Designation:E2218–02
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 (e) 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-
1.1 This method gives the procedure for constructing a 1 2
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—The graduated scales on the FLD shall
tension test to quantitatively simulate biaxial stretch and deep
be 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. 1
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.
curve showing the biaxial strain levels beyond which localized
1.5 This standard does not purport to address all of the
through-thickness thinning (necking) and subsequent failure
safety concerns, if any, associated with its use. It is the
occur during the forming of a metallic sheet. See Fig. 2.
responsibility of the user of this standard to establish appro-
3.3.1 Discussion—The curve of Fig. 2 is considered the
priate safety and health practices and determine the applica-
forming limit for the material when the metal is subjected to a
bility of regulatory limitations prior to use.
stampingpressoperation.Itwasobtainedforadrawingquality
2. Referenced Documents
aluminumkilledsteelsheet.ThecurveofFig.2correlateswith
the upper curve of Fig. 1, a generic curve representing a
2.1 ASTM Standards:
metallic sheet material with a FLD of 40%.
A568/A568M Specification for Steel, Sheet, Carbon, and o
3.3.2 Discussion—The strains are given in terms of percent
High-Strength, Low-Alloy, Hot-Rolled and Cold-Rolled,
major and minor strain measured after forming a series of test
General Requirements for,
specimen blanks by using a grid pattern. The gage lengths
E6 Terminology Relating to Methods of Mechanical Test-
before and after forming the part are measured to obtain the
ing
percentstrain.Thecurvefornegative(e )strainswillgenerally
E8M Test Methods for Tension Testing of Metallic Mate- 2
follow a constant surface area relationship to the associated
rials [Metric]
(e ) strain.
E517 Test Method for Plastic Strain Ratio r for Sheet 1
3.3.3 Discussion—Therangeofpossiblemajorstrain(e)is
Metal 1
from 0% to over 200%. The range of possible minor strain
E646 Test Method for Tensile Strain-Hardening Exponents
(e )isfrom−40%toover+60%,orevengreaterstrainlevels.
(n-Values) of Metallic Sheet Materials 2
3.3.4 Discussion—Forconvenience,theforminglimitcurve
3. Terminology
(FLC) can be plotted on a reduced range of the forming limit
diagram (FLD), for example, from +20% to +80% major (e )
3.1 Terminology E6 shall apply as well as the following 1
strains and from −20% to +30% minor (e ) strain. If the
special terms used in this method. 2
lowest(e )strainincrementoftheFLDisnot0%e ,thatvalue
1 1
shall be noted in the report.
This method is under the jurisdiction ofASTM Committee E28 on Mechanical
3.4 grid pattern—a pattern applied to the surface of a metal
Testing and is the direct responsibility of Subcommittee E28.02 on Ductility and
Flexure Testing. sheet to provide an array of precisely spaced gage points prior
Current edition approved June 10, 2002. Published August 2002.
to forming the metal into a final shape by the application of a
Annual Book of ASTM Standards, Vol 01.03.
force.
Annual Book of ASTM Standards, Vol 03.01.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
E2218–02
NOTE—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
3.4.1 Discussion—Anarrayofsquares,orcircles,orboth,is or diameter of a circle pattern.After the part has been formed,
printed on the surface of the specimen. Suggested patterns are
critical areas are measured for the resulting gage length
shown in Fig. 3.The pattern shall adhere to the metal so that it
changes in the long dimension from (L)to(L) of the pattern,
o f
will not be moved on the surface or rubbed off by the forming
and in the width dimension (W)to(W) at 90° to the long
o f
operation. Refer to Specification A568/A568M, Appendix
dimension as shown in Fig. 4. The major strain (e ) and
X4–Procedures for Determining the Extent of Plastic Defor-
associated minor strain (e ) at 90° to (e ) are calculated from
2 1
mation Encountered in Forming or Drawing, for procedures to
these gage length changes. The strains can be either engineer-
applyphotographicandelectrochemicallyprintedgridpatterns
ing strain based on the original gage length, or true strain.
and a review of strain analysis.
3.4.2 Discussion—Suggested dimensions for the gage
lengthsare2.5mm(0.100in.)forthesidesofasquarepattern,
E2218–02
Cold Rolled Drawing Quality Aluminum Killed Steel
Longitudinal Mechanical Properties
Yield Tensile
%El
Thickness Strength Strength
n Value r Value
in 50 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.
E2218–02
NOTE—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
3.4.3 Discussion—Larger patterns, of 6 mm (0.25 in.) up to drawn cylinder or the corner walls of a deep drawn part when
125 mm (5 in.), can be used to measure low strain levels on the flange clamping force is sufficient to restrain metal move-
formed parts, but are not used in determining the FLC. ment and wrinkling, while permitting the punch to push the
3.4.4 Discussion—Circles are suggested for deformations center area of the blank into the cavity of the die. Strain
where the major strain (e ) does not align with the lines of a conditions that can cause wrinkling or thickening are shown in
square pattern. This condition is less likely in the process of Fig. 1.
determining the FLC than in production stamping evaluations. 3.5.2 Discussion—In forming a square pan shape, metal
These circles commonly have diameters of 2.5 mm (0.100 in.) from an area of the flange under a reduced clamping force is
and can be spaced up to 2.5 mm (0.100 in.) apart. They are pulled into the die to form the side wall of the part.
measured across the diameter of the circle when the line width 3.6 major strain—the largest strain (e ) developed at a
is minimal. For wider lines, the enclosed area of the etched given location in the sheet specimen surface.
circle should be consistent from one circle to another and the 3.6.1 Discussion—The major strain (e ) is measured along
measurement made across the inside diameter. This is more thestretchedlineofasquarepattern,oralongthemajoraxisof
critical with wider line width patterns and at high e strains theellipseresultingfromdeformationofacirculargridpattern.
when the line spreads as the metal surface stretches. 3.7 minor strain—the strain (e ) in the sheet surface in a
3.4.5 Discussion—An alternate to circles is a pattern of direction perpendicular to the major strain.
solid dots of precise diameter, which are measured across the 3.7.1 Discussion—The minor strain (e ) is measured at 90°
diameter of the dot. to the major strain, along the shorter dimension of the final
3.5 deep drawing—a metal sheet forming operation in rectangular shape of a part formed using a square pattern, or
which strains on the sheet surface are positive in the direction the shorter axis of the ellipse resulting from deformation of a
of the punch travel (e ) and negative at 90° to that direction. circular grid pattern. f a square pattern becomes skewed into a
See Fig. 4. parallelogram shape, it shall not be used to measure strain.
E2218–02
3.8 plane strain—the condition in metal sheet forming that 4.1.3.3 Kerosene is not a good lubricant, as it cleans the
maintains a near zero (0 to +5%) minor strain (e ) while the surfaces under pressure and the metal sheet will not slide over
major strain (e ) is positive (in tension). It is sometimes the punch.
referred to as FLD . See Fig. 1 and Fig. 4. 4.1.4 Securely clamping the flanges of a blank in the
o
3.8.1 Discussion—Plane strain is the most severe deforma- serrated, or lock bead, blank-holder dies of the hemispherical
tion mode and causes a low point in the forming limit curve punch test.
(FLC). For convenience, many FLCs are shown with the low 4.1.4.1 For a tension test specimen, the standard procedure
pointat0%(e ),however,suchanabruptreversalof(e )strain for testing sheet type specimens, as shown in Fig. 1 of E8M,
2 1
does not occur. See Fig. 2 and Figs. X2.1-X2.3. shall be followed.
3.9 biaxial stretching—a mode of metal sheet forming in 4.1.5 Stretching the central area of the blank biaxially over
which positive strains are observed in all directions at a given the nose of the hemispherical punch, or pulling in the tension
location. See Fig. 4. test, without interrupting the force.
3.10 limiting dome height (LDH)—an evaluative test for 4.1.5.1 Negative (e ) strains can be obtained using sheared
metalsheetdeformationcapabilityemployinga200mm(4in.) narrow strips stretched over the punch of the LDH tester.
hemispherical punch and a circumferential clamping force 4.1.6 Stopping the punch advance or the force when a
sufficient to prevent metal from the surrounding flange being localized through thickness neck (localized necking) is ob-
pulled into the die cavity. served, if possible, or as soon as the specimen fractures.
3.10.1 Discussion—The LDH test was designed to give a 4.1.7 Removing the specimen from the testing machine
repeatable measure of punch movement among specimens of a grips and then proceeding with another, different width, blank
specific metal sheet sample, thus the only measured value in the test series of the same material.
would be the punch height at incipient fracture. Problems with 4.1.8 Measuring and recording the (e ) and the (e ) strains
1 2
maintaining a secure clamp result in variation of the measured of the grid pattern on the surface area near the neck of all the
LDH value.Amodification of the LDH test using a strip in the test specimens for the series.
range of 200 mm (4 in.) wide was found to give (e ) values 4.1.8.1 These measurements can include good (no localized
near 0% (e ), when the surface strains were measured using a necking), marginal (localized necking), and fracture areas.
grid pattern. On this basis, a test was developed to use a 4.1.8.2 If other than good (no localized necking) locations
sheared strip of metal sheet 200 mm (4 in.) wide and are included, each measured point shall be visually evaluated
sufficientlylongtobesecurelyclampedintheLDHtestfixture. and noted as illustrated in Fig. 2.
The height at incipient fracture was to correlate with FLD . 4.1.9 Plotting the measured strain combinations on a FLD.
o
The test was not sufficiently repeatable to be employed for See Fig. 2.
evaluation of metal sheet samples. The equipment is used to 4.1.10 Establishing the forming limit curve (FLC) be con-
stretchspecimens,withgridpatterns,thathavebeenshearedto necting the uppermost good (no localized necking) (e ) strains
various widths and is one method to obtain a range of (e ) and over the associated (e ) strain range used in the study.
2 2
associated (e ) values for plotting a FLC on a FLD. 4.1.10.1 For practical purposes, the specimens that have
been strained to a localized neck-down, or through thickness
4. Summary of Test Method
fracture, condition can be measured at a location on the
4.1 The procedure for determining a forming limit curve
oppositesideofthehemisphericalbulgefromthefracture,ina
(FLC) involves the following:
good (no localized necking) location, to obtain values to
4.1.1 Using a hemispherical punch testing machine (LDH
establish the FLC.
tester).Sometimescalledabulgetester.TheLDHtestemploys
4.1.10.2 Another acceptable procedure is to measure the
a 100 mm (4 in.) diameter machined surface punch.
grid near the necked, or fracture, location and identify these
4.1.1.1 A universal testing machine for tension load appli-
data points in determining the forming limit curve. This
cation and a sub-press for against the metal sheet surface
procedure was used in locating the FLC of Fig. 2.
loading with a ball punch of 75 mm (3 in.), 100 mm (4 in.), or
4.1.10.3 Establishing the FLC depends on judgement. Note
larger diameter can be used in place of the LDH test equip-
thatinFig.2thereareseveralgood(nolocalizednecking)data
ment.
points above the FLC and two marginal points below the FLC.
4.1.2 Preparing a series of grid pattern blanks with different
4.1.10.4 The FLC curve shall not include an area where
widths and a common length suitable for being securely
there is a preponderance of marginal data points at an (e )
gripped in the test apparatus.
strain level below the measured good (no localized necking)
4.1.2.1 All specimens for a series shall have their long
data points.
dimension in the same orientation, relative to the original
5. Significance and Use
process rolling direction of the sample and that direction noted
i
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