1、Designation: E2218 141Standard 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 parent
2、heses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.1NOTEEditorial corrections were made to 3.2 and throughout the standard in May 2015.1. Scope1.1 This method gives the procedure for constructing aforming limit cur
3、ve (FLC) for a metallic sheet material byusing a hemispherical deformation punch test 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 meta
4、llic 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 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
5、 the user of this standard to establish appro-priate safety and health practices and 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 a
6、ndCold-Rolled, General Requirements forE6 Terminology Relating to Methods of Mechanical 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
7、 Materials3. Terminology3.1 Terminology E6 shall apply including the special termsused 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
8、drawinga metal sheet forming operation inwhich strains on the sheet surface are positive 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 f
9、lange clamping force is sufficient to restrainmetal movement and wrinkling, while permitting 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
10、 an area of the flange under a reduced clamping force ispulled into the die to form the 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
11、. 2.3.2.4 forming limit curve (FLC)an empirically derivedcurve showing the biaxial strain levels beyond which localizedthrough-thickness thinning (necking) and subsequent failureoccur during the forming of a metallic sheet.3.2.4.1 Discussion See Fig. 3.3.2.4.2 DiscussionThe curve of Fig. 3 is consid
12、ered theforming limit for the material when the metal is subjected to astamping press operation. It was 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.
13、2.4.3 DiscussionThe strains are given in terms of per-cent major and minor strain measured after forming a series oftest specimen blanks by using a grid pattern. The gauge lengthsbefore and after forming the part are measured to obtain the1This method is under the jurisdiction of ASTM Committee E28
14、on MechanicalTesting and is the direct responsibility of Subcommittee E28.02 on Ductility andFormability.Current edition approved April 1, 2014. Published June 2014. Originallypublished in 2002. Last previous edition approved in 2008 as E221802(2008).DOI: 10.1520/E2218-14E012For referenced ASTM stan
15、dards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of 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, P
16、A 19428-2959. United States1FIG. 1 Possible Changes in Shape of the Grid Pattern Caused by Forming Operations on Metallic Sheet ProductsNOTE 1The upper curve is representative of the forming limit. Strains below the lower curve do not occur during forming metallic sheet productsin the most stamping
17、press operations. Curves to the left of % e2= 0 are for constant area of the sheet surface.FIG. 2 Forming Limit DiagramE2218 1412Cold Rolled Drawing Quality Aluminum Killed SteelLongitudinal Mechanical PropertiesThicknessYieldStrengthTensileStrength%Elin 50mmn Value r Valuemm (in.) MPa (ksi) MPa (ks
18、i)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 1413percent strain. The curve for negative (e2) str
19、ains will generallyfollow a constant surface area relationship to the associated(e1) strain.3.2.4.4 DiscussionThe range of possible major strain (e1)is from 0 % to over 200 %. The range of possible minor strain(e2) is from 40 % to over +60 %.3.2.5 limiting dome height (LDH) testan evaluative testfor
20、 metal sheet deformation capability employing a hemi-spherical punch and a circumferential clamping force sufficientto prevent metal in the surrounding flange from being pulledinto the die cavity.3.3 Definitions of Terms Specific to This Standard:3.3.1 grid patterna pattern applied to the surface of
21、 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 strain, (e1)the largest strain, developed at agiven location in the sheet specimen surface.3.3.2.1 DiscussionThe major strain (e1) is measured alon
22、gthe 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 strain, (e2) the strain in the sheet surface in adirection perpendicular to the major strain.3.3.3.1 DiscussionThe minor strain (e2) is measured at90 to th
23、e 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 sheetforming that maintains a near zero (0 to +5 %)
24、 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), however, such an abrupt reversal of (e1)
25、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. The LDH test employsa 100 mm (4 in.) diame
26、ter 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 equip-ment.4.1.2 Preparing a series of gr
27、id 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 of the sample and that direction notedin th
28、e report.4.1.3 Lubricating the contact surfaces of the blank andpunch for the hemispherical punch test.4.1.4 Securely clamping the flanges of 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 o
29、f the hemispherical punch, or pulling in the tensiontest, without interrupting the force.4.1.5.1 Negative (e2) strains may be obtained using 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
30、 necking) isobserved, if possible, or as soon as the specimen fractures.4.1.7 Removing the specimen from the testing machinegrips and then proceeding 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 pat
31、tern 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 necking), marginal (localized necking), and fracture areas.4.1.8.2 If other than good (no localized necking) locationsare included, each measured point shall be v
32、isually 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 the forming limit curve (FLC) by con-necting the uppermost good (no localized necking) (e1) strainsover the associated (e2) strain range used in the study.4.1.1
33、0.1 For practical purposes, the specimens that havebeen strained to a localized neck-down, or through thicknessfracture, condition may be measured at a location on theopposite side of the hemispherical bulge from the fracture, in agood (no localized necking) location, to obtain values toestablish th
34、e FLC.4.1.10.2 Another acceptable 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 t
35、here are several good (no 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. Signi
36、ficance and Use5.1 A forming 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
37、 ofthinning (localized necking) 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
38、 necking andfracture.E2218 14145.1.1.1 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 fo
39、rmed to the point oflocalized necking, 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)
40、 direction.5.1.2.2 The major (e1) strain 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 negativ
41、e and the metal is narrowed both through 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 inter
42、mixing and no clear distinctionbetween 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 informi
43、ng metallic sheet products.5.1.6 FLCs 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 inT
44、est Method E646, affects the forming 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
45、will move the minor (e2) strain into 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 s
46、teel sheet product used indetermining 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 st
47、rain 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 straining
48、 may be slowed as thespecimen approaches neck-down, or fracture.5.1.9.2 The FLC can be used for conservatively predictingthe performance of an entire class of material provided the nvalue, r value and thickness of the material used are represen-tative of that class.5.1.10 Complex forming operations,
49、 in which the strain pathchanges, or the strain is not homogeneous through the metalsheet thickness, may produce limiting strains that do not agreewith the forming limit obtained by this method.5.1.11 Characterization of a materials response to plasticdeformation can involve strain to fracture as well as to theonset of necking. These strains are above the FLC.5.1.12 The FLC is not suitable for lot-to-lot quality assur-ance testing because it is specific to that sample of a materialwhich is tested to establish the forming limit.6. Apparatus6.1 Data
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