1、Designation: E2218 15Standard 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 MaterialsE2208 Guide for Evaluating Non-Contacting Optical StrainMeasurement Systems
7、3. 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 drawinga m
8、etal 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 flange clam
9、ping 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 an area o
10、f 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. 2.3.2.4
11、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 considered thefo
12、rming 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 %.3.2.4.3 Disc
13、ussionThe 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 on Mechani
14、calTesting and is the direct responsibility of Subcommittee E28.02 on Ductility andFormability.Current edition approved Oct. 1, 2015. Published December 2015. Originallypublished in 2002. Last previous edition approved in 2014 as E2218141. DOI:10.1520/E2218-152For referenced ASTM standards, visit th
15、e 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, PA 19428-2959. U
16、nited States1percent strain. The curve for negative (e2) strains 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
17、%.3.2.5 limiting dome height (LDH) testan evaluative testfor 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 St
18、andard:3.3.1 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 strain, (e1)the largest strain, developed at agiven location in the sheet specimen surf
19、ace.3.3.2.1 DiscussionThe major strain (e1) is measured eitheralong the stretched line of a square pattern, or along the majoraxis of the ellipse resulting from deformation of a circular gridpattern, or along the direction of the maximum surface strainusing a non-contacting optical strain measuremen
20、t technique.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 the major strain, either along the shorter dimension ofthe final rectangular shape of a part formed using a squarepattern,
21、or along the shorter axis of the ellipse resulting fromdeformation of a circular grid pattern, or along the direction ofthe minimum surface strain using a non-contacting opticalstrain measurement technique.3.3.4 plane strain, FLDothe condition in metal sheetforming that maintains a near zero (0 to +
22、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), however, such an abrupt reversal of (
23、e1) straindoes not occur. See Fig. 3 and Figs. X2.1-X2.3.4. Summary of Test Method4.1 Determination of a forming limit curve (FLC) involvesselecting a style of testing apparatus, deforming multiplespecimens biaxially, measuring the resulting strain (includingjudging if these strains are localized),
24、and drawing a curvethrough the measured points.4.2 Various test apparatus (see Section 6) may be used todeform specimens biaxially including a hemispherical punchtesting machine such as an LDH tester, a sub press in auniversal testing machine, or a hydraulic bulge testing ma-chine.4.2.1 Contact surf
25、aces of the blank and punch are lubricatedfor the hemispherical punch test.4.2.2 The flanges of a blank are securely clamped in serratedor lock bead, blank-holder dies for the hemispherical punchand hydraulic bulge tests.4.3 Stretching the central area of the blank biaxially orpulling in the tension
26、 test is performed without interrupting theforce.4.3.1 A series of grid pattern blanks is prepared withdifferent widths and a common length suitable for beingsecurely gripped in the test apparatus.4.3.2 Negative (e2) strains can be obtained using shearednarrow strips stretched over the punch of a he
27、misphericalpunch tester.4.3.3 If possible, the punch advance or the force is stoppedwhen a localized through-thickness neck (localized necking) isobserved, or as soon as the specimen fractures.4.4 The (e1) and the (e2) strains of the grid pattern on thesurface area are measured near the neck of all
28、the testspecimens for the series and recorded.4.4.1 The strain measurements may include good (no local-ized necking), marginal (localized necking), and fracture areas.4.4.2 The measured strain combinations are plotted on aforming limit diagram (see Fig. 3).FIG. 1 Possible Changes in Shape of the Gri
29、d Pattern Caused by Forming Operations on Metallic Sheet ProductsE2218 1524.4.3 If other than good (no localized necking) locations areincluded, then each measured point is visually evaluated andnoted as illustrated in Fig. 3.4.5 The FLC is established by drawing a curve on the FLDbased on the crite
30、ria in 13.4.5. Significance 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 develop
31、ing a localized zone 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, jus
32、t prior to localized necking andfracture.5.1.1.1 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 spec
33、imen is formed 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
34、minor (e2) direction.5.1.2.2 The major (e1) strain is determined by the capacityof the material to be stretched in one direction as simultaneousNOTE 1The upper curve is representative of the forming limit. Strains below the lower curve do not occur during forming metallic sheet productsin the most s
35、tamping press operations. Curves to the left of % e2= 0 are for constant area of the sheet surface.FIG. 2 Forming Limit DiagramE2218 153Cold Rolled Drawing Quality Aluminum Killed SteelLongitudinal Mechanical PropertiesThicknessYieldStrengthTensileStrength%Elin 50mmn Value r Valuemm (in.) MPa (ksi)
36、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 154surface forces either stretch, do not cha
37、nge, 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 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
38、 drawn to connectthe highest measured (e1and e2) strain combinations thatinclude good data points.5.1.3.1 When there is intermixing 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
39、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 FLCs are known to change with material (specificallywith the mechanical or formability properties developed duringthe processing operations us
40、ed 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 limit. A high n valuewill raise the limiting major strain (e1), allowing more stretchunder positive (+e2) strain conditions.5.1.6.2 The pl
41、astic 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 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
42、 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 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 use
43、d 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
44、of major(e1) to minor (e2) strain.5.1.9.1 There is no interrupted loading, or reversal ofstraining, but the rate of straining 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 provide
45、d the nvalue, r value and thickness of the material used are represen-tative of that class.5.1.10 Complex forming operations, 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 obtai
46、ned 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
47、 a materialwhich is tested to establish the forming limit.6. Apparatus6.1 Data points for minor strains (e2) near 0 % and forpositive strains (+e2) associated with major strains (e1) may beobtained using a hemispherical punch testing machine such asa LDH tester, a sub press in a universal testing ma
48、chine, or ahydraulic bulge testing machine.NOTE 1The LDH test was designed to give a repeatable measure ofpunch movement among specimens of a specific metal sheet sample; thusthe only measured value would be the punch height at incipient fracture.Problems with maintaining a secure clamp result in va
49、riation of themeasured LDH value. A modification of the LDH test using a strip in therange of 200 mm (8 in.) wide was found to give (e)1values near0%(e2),when the surface strains were measured using a grid pattern. On this basis,a test was developed to use a sheared strip of metal sheet 200 mm (8 in.)wide and sufficiently long to be securely clamped in the LDH test fixture.The height at incipient fracture was to correlate with FLDo. The test wasnot sufficiently repeatable to be employed for evaluation of metal sheetsamples. The equipment is used to str
