1、Designation: E2218 14Standard Test Method forDetermining Forming Limit Curves1This standard is issued under the fixed designation E2218; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parenth
2、eses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.1. Scope1.1 This method gives the procedure for constructing aforming limit curve (FLC) for a metallic sheet material byusing a hemispherical deformation punch test
3、 and a uniaxialtension test to quantitatively simulate biaxial stretch and deepdrawing processes.1.2 FLCs are useful in evaluating press performance bymetal 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 u
4、nits are to be regarded as thestandard. The inch-pound equivalents are approximate.1.5 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and
5、determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2A568/A568M Specification for Steel, Sheet, Carbon,Structural, and High-Strength, Low-Alloy, Hot-Rolled andCold-Rolled, General Requirements forE6 Terminology Relating to Methods of Mechanic
6、al TestingE8/E8M Test Methods for Tension Testing of Metallic Ma-terialsE517 Test Method for Plastic Strain Ratio r for Sheet MetalE646 Test Method for Tensile Strain-Hardening Exponents(n -Values) of Metallic Sheet Materials3. Terminology3.1 Terminology E6 shall apply including the special termsuse
7、d in this method shown in 3.2.3.2 Definitions:3.2.1 biaxial stretchinga mode of metal sheet forming inwhich positive strains are observed in all directions at a givenlocation.3.2.1.1 DiscussionSee Fig. 1.3.2.2 deep drawinga metal sheet forming operation inwhich strains on the sheet surface are posit
8、ive in the directionof the punch travel (e1) and negative at 90 to that direction.3.2.2.1 DiscussionDeep drawing, see Fig. 1, occurs in thewalls of a drawn cylinder or the corner walls of a deep drawnpart when the flange clamping force is sufficient to restrainmetal movement and wrinkling, while per
9、mitting the punch topush the center area of the blank into the cavity of the die.Strain conditions that can cause wrinkling or thickening areshown in Fig. 2.3.2.2.2 DiscussionIn forming a square pan shape, metalfrom an area of the flange under a reduced clamping force ispulled into the die to form t
10、he side wall of the part.3.2.3 forming limit diagram (FLD)a graph on which themeasured major (e1) and associated minor (e2) strain combi-nations are plotted to develop a forming limit curve.3.2.3.1 DiscussionSee Fig. 2.3.2.4 forming limit curve (FLC)an empirically derivedcurve showing the biaxial st
11、rain levels beyond which localizedthrough-thickness thinning (necking) and subsequent failureoccur during the forming of a metallic sheet. See Fig. 3.3.2.4.1 DiscussionThe curve of Fig. 3 is considered theforming limit for the material when the metal is subjected to astamping press operation. It was
12、 obtained for a drawing qualityaluminum killed steel sheet. The curve of Fig. 3 correlates withthe upper curve of Fig. 2, a generic curve representing ametallic sheet material with a FLDoof 40 %.3.2.4.2 DiscussionThe strains are given in terms of per-cent major and minor strain measured after formin
13、g a series oftest specimen blanks by using a grid pattern. The gauge lengthsbefore and after forming the part are measured to obtain thepercent strain. The curve for negative (e2) strains will generallyfollow a constant surface area relationship to the associated(e1) strain.3.2.4.3 DiscussionThe ran
14、ge of possible major strain (e1)is from 0 % to over 200 %. The range of possible minor strain(e2) is from 40 % to over +60 %.1This method is under the jurisdiction of ASTM Committee E28 on MechanicalTesting and is the direct responsibility of Subcommittee E28.02 on Ductility andFormability.Current e
15、dition approved April 1, 2014. Published June 2014. Originallypublished in 2002. Last previous edition approved in 2008 as E221802(2008).DOI: 10.1520/E2218-14.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of
16、ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States13.2.5 limiting dome height (LDH) testan evaluative testfor metal sheet deformation capab
17、ility employing a hemi-spherical punch and a circumferential clamping force sufficientto prevent metal from the surrounding flange being pulled intothe die cavity.3.2.6 major strainthe largest strain (e1) developed at agiven location in the sheet specimen surface.3.2.6.1 DiscussionThe major strain (
18、e1) is measured alongthe stretched line of a square pattern, or along the major axis ofthe ellipse resulting from deformation of a circular grid pattern.3.2.7 minor strainthe strain (e2) in the sheet surface in adirection perpendicular to the major strain.3.2.7.1 DiscussionThe minor strain (e2) is m
19、easured at90 to the major strain, along the shorter dimension of the finalrectangular shape of a part formed using a square pattern, orthe shorter axis of the ellipse resulting from deformation of acircular grid pattern. f a square pattern becomes skewed into aparallelogram shape, it shall not be us
20、ed to measure strain.3.2.8 plane strainthe condition in metal sheet formingthat maintains a near zero (0 to +5 %) minor strain (e2) whilethe major strain (e1) is positive (in tension). It is sometimesreferred to as FLDo. See Fig. 2 and Fig. 1.3.3 Definitions of Terms Specific to This Standard:3.3.1
21、grid patterna pattern applied to the surface of ametal sheet to provide an array of precisely spaced gaugepoints prior to forming the metal into a final shape by theapplication of a force.3.3.2 major strainthe largest strain (e1)developed at agiven location in the sheet specimen surface.3.3.2.1 Disc
22、ussionThe major strain (e1) is measured alongthe stretched line of a square pattern, or along the major axis ofthe ellipse resulting from deformation of a circular grid pattern.3.3.3 minor strainthe strain (e2) in the sheet surface in adirection perpendicular to the major strain.3.3.3.1 DiscussionTh
23、e minor strain (e2) is measured at90 to the major strain, along the shorter dimension of the finalrectangular shape of a part formed using a square pattern, orthe shorter axis of the ellipse resulting from deformation of acircular grid pattern.3.3.4 plane strain, FLDothe condition in metal sheetform
24、ing that maintains a near zero (0 to +5 %) minor strain (e2)while the major strain (e1) is positive (in tension)3.3.4.1 DiscussionPlane strain is the most severe defor-mation mode and causes a low point in the forming limit curve(FLC). For convenience, many FLCs are shown with the lowpoint at0%(e2),
25、 however, such an abrupt reversal of (e1) straindoes not occur. See Fig. 3 and Figs. X2.1-X2.3.4. Summary of Test Method4.1 The procedure for determining a forming limit curve(FLC) involves the following:4.1.1 Using a hemispherical punch testing machine (LDHtester). Sometimes called a bulge tester.
26、The LDH test employsa 100 mm (4 in.) diameter machined surface punch.4.1.1.1 A universal testing machine for tension load appli-cation and a sub-press for against the metal sheet surfaceloading with a ball punch of 75 mm (3 in.), 100 mm (4 in.), orlarger diameter can be used in place of the LDH test
27、 equip-ment.4.1.2 Preparing a series of grid pattern blanks with differentwidths and a common length suitable for being securelygripped in the test apparatus.4.1.2.1 All specimens for a series shall have their longdimension in the same orientation, relative to the originalprocess rolling direction o
28、f the sample and that direction notedin the report.4.1.3 Lubricating the contact surfaces of the blank andpunch for the hemispherical punch test.FIG. 1 Possible Changes in Shape of the Grid Pattern Caused by Forming Operations on Metallic Sheet ProductsE2218 1424.1.4 Securely clamping the flanges of
29、 a blank in theserrated, or lock bead, blank-holder dies of the hemisphericalpunch test.4.1.5 Stretching the central area of the blank biaxially overthe nose of the hemispherical punch, or pulling in the tensiontest, without interrupting the force.4.1.5.1 Negative (e2) strains may be obtained using
30、shearednarrow strips stretched over the punch of the LDH tester.4.1.6 Stopping the punch advance or the force when alocalized through thickness neck (localized necking) isobserved, if possible, or as soon as the specimen fractures.4.1.7 Removing the specimen from the testing machinegrips and then pr
31、oceeding with another, different width, blankin the test series of the same material.4.1.8 Measuring and recording the (e1) and the (e2) strainsof the grid pattern on the surface area near the neck of all thetest specimens for the series.4.1.8.1 These measurements may include good (no local-ized nec
32、king), marginal (localized necking), and fracture areas.4.1.8.2 If other than good (no localized necking) locationsare included, each measured point shall be visually evaluatedand noted as illustrated in Fig. 3.4.1.9 Plotting the measured strain combinations on a FLD.See Fig. 3.4.1.10 Establishing t
33、he forming limit curve (FLC) be con-necting the uppermost good (no localized necking) (e1) strainsover the associated (e2) strain range used in the study.NOTE 1The upper curve is representative of the forming limit. Strains below the lower curve do not occur during forming metallic sheet productsin
34、the most stamping press operations. Curves to the left of % e2= 0 are for constant area of the sheet surface.FIG. 2 Forming Limit DiagramE2218 1434.1.10.1 For practical purposes, the specimens that havebeen strained to a localized neck-down, or through thicknessfracture, condition may be measured at
35、 a location on theopposite side of the hemispherical bulge from the fracture, in agood (no localized necking) location, to obtain values toestablish the FLC.Cold Rolled Drawing Quality Aluminum Killed SteelLongitudinal Mechanical PropertiesThicknessYieldStrengthTensileStrength%Elin 50mmn Value r Val
36、uemm (in.) MPa (ksi) MPa (ksi)0.866 (0.034) 163.4 (23.7) 304.7 (44.2) 43.5 0.230 1.71Chemical CompositionElement C S N Mn Al P SiPercent 0.035 0.006 0.006 0.19 0.29 0.006 0.004FIG. 3 Forming Limit Curve (FLC) for a Cold Rolled Drawing Quality Aluminum Killed Steel Sheet.E2218 1444.1.10.2 Another acc
37、eptable procedure is to measure thegrid near the necked, or fracture, location and identify thesedata points in determining the forming limit curve. Thisprocedure was used in locating the FLC of Fig. 3.4.1.10.3 Establishing the FLC depends on judgement. Notethat in Fig. 3 there are several good (no
38、localized necking) datapoints above the FLC and two marginal points below the FLC.4.1.10.4 The FLC curve shall not include an area wherethere is a preponderance of marginal data points at an (e1)strain level below the measured good (no localized necking)data points.5. Significance and Use5.1 A formi
39、ng limit curve (FLC) defines the maximum(limiting) strain that a given sample of a metallic sheet canundergo for a range of forming conditions, such as deepdrawing, stretching and bending over a radius in a press and diedrawing operation, without developing a localized zone ofthinning (localized nec
40、king) that would indicate incipientfailure.5.1.1 FLCs may be obtained empirically by using a labora-tory hemispherical punch biaxial stretch test and also a tensiontest to strain metal sheet specimens from a material samplebeyond their elastic limit, just prior to localized necking andfracture.5.1.1
41、.1 Since this cannot be predetermined, one or bothsurfaces of specimens are covered with a grid pattern of gaugelengths usually as squares or small diameter circles, by asuitable method such as scribing, photo-grid, or electro-etching, and then each specimen is formed to the point oflocalized neckin
42、g, or fracture.5.1.2 Strains in the major (e1) and minor (e2) directions aremeasured using points on the grid pattern in the area of thelocalized necking or fracture.5.1.2.1 Blanks of varied widths are used to produce a widerange of strain states in the minor (e2) direction.5.1.2.2 The major (e1) st
43、rain is determined by the capacityof the material to be stretched in one direction as simultaneoussurface forces either stretch, do not change, or compress, themetal in the (e2) direction.5.1.2.3 In the tension test deformation process, the (e2)strains are negative and the metal is narrowed both thr
44、ough thethickness and across its width.5.1.3 These strains are plotted on a forming limit diagram(FLD) and the forming limit curve (FLC) is drawn to connectthe highest measured (e1and e2) strain combinations thatinclude good data points.5.1.3.1 When there is intermixing and no clear distinctionbetwe
45、en good and necked data points, a best fit curve isestablished to follow the maximum good data points as theFLC.5.1.4 The forming limit is established at the maximum (e1)strain attained prior to necking.5.1.5 The FLC defines the limit of useful deformation informing metallic sheet products.5.1.6 FLC
46、s are known to change with material (specificallywith the mechanical or formability properties developed duringthe processing operations used in making the material), and thethickness of the sheet sample.5.1.6.1 The strain hardening exponent (n value), defined inTest Method E646, affects the forming
47、 limit. A high n valuewill raise the limiting major strain (e1), allowing more stretchunder positive (+e2) strain conditions.5.1.6.2 The plastic strain ratio (r value), defined in TestMethod E517, affects the capacity of a material to be deepdrawn. A high r value will move the minor (e2) strain into
48、 aless severe area to the left of the FLDo, thus permitting deeperdraws for a given major (e1) strain.5.1.6.3 The thickness of the material will affect the FLCsince a thicker specimen has more volume to respond to theforming process.5.1.6.4 The properties of the steel sheet product used indeterminin
49、g the FLC of Fig. 3 included the n value and the rvalue.5.1.7 FLCs serve as a diagnostic tool for material strainanalysis and have been used for evaluations of stampingoperations and material selection.5.1.8 The FLC provides a graphical basis for comparisonwith strain distributions on parts formed by sequential pressoperations.5.1.9 The FLC obtained by this method follows a constantproportional strain path where there is a fixed ratio of major(e1) to minor (e2) strain.5.1.9.1 There is no interrupted loading, or reversal ofstraining, but the rate of
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