1、Designation: E 2218 02 (Reapproved 2008)Standard Test Method forDetermining Forming Limit Curves1This standard is issued under the fixed designation E 2218; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision.
2、 A number in parentheses 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 de
3、formation 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 metallic sheet from 0.5 mm(0.020 in.) to 3.3 mm (0.130 in.).1.4 The v
4、alues 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 the user of this standard to establish appro-priate safety and h
5、ealth practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2A 568/A 568M Specification for Steel, Sheet, Carbon,Structural, and High-Strength, Low-Alloy, Hot-Rolled andCold-Rolled, General Requirements forE6 Terminology Relating
6、to Methods of Mechanical Test-ingE 8/E 8M Test Methods for Tension Testing of MetallicMaterialsE 517 Test Method for Plastic Strain Ratio r for Sheet MetalE 646 Test Method for Tensile Strain-Hardening Exponents(n -Values) of Metallic Sheet Materials3. Terminology3.1 Terminology E6shall apply as wel
7、l as the followingspecial terms used in this method.3.2 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. See Fig.1.3.2.1 DiscussionThe graduated scales on the FLD shallbe in percent strain,
8、 calculated from the initial gage length.3.2.2 DiscussionThe distance between FLD percentageincrements shall be the same for both the major strain (e1)ordinate (parallel to the vertical y axis) and minor strain (e2)abscissa (parallel to the horizontal x axis) unless the differenceis noted in the rep
9、ort.3.3 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. See Fig. 2.3.3.1 DiscussionThe curve of Fig. 2 is considered theforming limit
10、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. 2 correlates withthe upper curve of Fig. 1, a generic curve representing ametallic sheet material with a FLDoof 40 %.3.3.2 DiscussionThe stra
11、ins are given in terms of percentmajor and minor strain measured after forming a series of testspecimen blanks by using a grid pattern. The gage lengthsbefore and after forming the part are measured to obtain thepercent strain. The curve for negative (e2) strains will generallyfollow a constant surf
12、ace area relationship to the associated(e1) strain.3.3.3 DiscussionThe range of possible major strain (e1)isfrom 0 % to over 200 %. The range of possible minor strain(e2) is from 40 % to over +60 %, or even greater strain levels.3.3.4 DiscussionFor convenience, the forming limit curve(FLC) can be pl
13、otted on a reduced range of the forming limitdiagram (FLD), for example, from +20 % to +80 % major (e1)strains and from 20 % to +30 % minor (e2) strain. If thelowest (e1) strain increment of the FLD is not 0 % e1, that valueshall be noted in the report.3.4 grid patterna pattern applied to the surfac
14、e of a metalsheet to provide an array of precisely spaced gage points priorto forming the metal into a final shape by the application of aforce.1This method is under the jurisdiction of ASTM Committee E28 on MechanicalTesting and is the direct responsibility of Subcommittee E28.02 on Ductility andFo
15、rmability.Current edition approved May 1, 2008. Published October 2008. Originallypublished in 2002. Last previous edition approved in 2002 as E221802.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStan
16、dards volume information, refer to the standards Document Summary page onthe ASTM website.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.3.4.1 DiscussionAn array of squares, or circles, or both, isprinted on the surface of the speci
17、men. Suggested patterns areshown in Fig. 3. The pattern shall adhere to the metal so that itwill not be moved on the surface or rubbed off by the formingoperation. Refer to Specification A 568/A 568M, AppendixX4Procedures for Determining the Extent of Plastic Defor-mation Encountered in Forming or D
18、rawing, for procedures toapply photographic and electrochemically printed grid patternsand a review of strain analysis.3.4.2 DiscussionSuggested dimensions for the gagelengths are 2.5 mm (0.100 in.) for the sides of a square pattern,or diameter of a circle pattern. After the part has been formed,cri
19、tical areas are measured for the resulting gage lengthchanges in the long dimension from (Lo)to(Lf) of the pattern,and in the width dimension (Wo)to(Wf) at 90 to the longdimension as shown in Fig. 4. The major strain (e1) andassociated minor strain (e2) at 90 to (e1) are calculated fromthese gage le
20、ngth changes. The strains can be either engineer-ing strain based on the original gage length, or true strain.NOTEThe upper curve is representative of the forming limit. Strains below the lower curve do not occur during forming metallic sheet products inthe most stamping press operations. Curves to
21、the left of % e2= 0 are for constant area of the sheet surface.FIG. 1 Forming Limit DiagramE 2218 02 (2008)2Cold Rolled Drawing Quality Aluminum Killed SteelLongitudinal Mechanical PropertiesThicknessYieldStrengthTensileStrength%Elin 50 mmn Value r Valuemm (in.) MPa (ksi) MPa (ksi)0.866 (0.034) 163.
22、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. 2 Forming Limit Curve (FLC) for a Cold Rolled Drawing Quality Aluminum Killed Steel Sheet.E 2218 02 (2008)33.4.3 DiscussionLarger patterns, of 6 mm (0.25 in.) up to125
23、 mm (5 in.), can be used to measure low strain levels onformed parts, but are not used in determining the FLC.3.4.4 DiscussionCircles are suggested for deformationswhere the major strain (e1) does not align with the lines of asquare pattern. This condition is less likely in the process ofdetermining
24、 the FLC than in production stamping evaluations.These circles commonly have diameters of 2.5 mm (0.100 in.)and can be spaced up to 2.5 mm (0.100 in.) apart. They aremeasured across the diameter of the circle when the line widthis minimal. For wider lines, the enclosed area of the etchedcircle shoul
25、d be consistent from one circle to another and themeasurement made across the inside diameter. This is morecritical with wider line width patterns and at high e1strainswhen the line spreads as the metal surface stretches.3.4.5 DiscussionAn alternate to circles is a pattern ofsolid dots of precise di
26、ameter, which are measured across thediameter of the dot.3.5 deep 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.See Fig. 4.3.5.1 DiscussionDeep drawing occurs in the walls of adra
27、wn cylinder or the corner walls of a deep drawn part whenthe flange clamping force is sufficient to restrain metal move-ment and wrinkling, while permitting the punch to push thecenter area of the blank into the cavity of the die. Strainconditions that can cause wrinkling or thickening are shown inF
28、ig. 1.3.5.2 DiscussionIn forming a square pan shape, metalfrom an area of the flange under a reduced clamping force ispulled into the die to form the side wall of the part.3.6 major strainthe largest strain (e1) developed at agiven location in the sheet specimen surface.3.6.1 DiscussionThe major str
29、ain (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.3.7 minor strainthe strain (e2) in the sheet surface in adirection perpendicular to the major strain.3.7.1 DiscussionThe minor strain (e2) is
30、measured at 90to 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 u
31、sed to measure strain.NOTEThe 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
32、 Operations on Metallic Sheet ProductsE 2218 02 (2008)43.8 plane strainthe condition in metal sheet forming thatmaintains a near zero (0 to +5 %) minor strain (e2) while themajor strain (e1) is positive (in tension). It is sometimesreferred to as FLDo. See Fig. 1 and Fig. 4.3.8.1 DiscussionPlane str
33、ain is the most severe deforma-tion mode and causes a low point in the forming limit curve(FLC). For convenience, many FLCs are shown with the lowpoint at 0 % (e2), however, such an abrupt reversal of (e1) straindoes not occur. See Fig. 2 and Figs. X2.1-X2.3.3.9 biaxial stretchinga mode of metal she
34、et forming inwhich positive strains are observed in all directions at a givenlocation. See Fig. 4.3.10 limiting dome height (LDH)an evaluative test formetal sheet deformation capability employing a 200 mm (4 in.)hemispherical punch and a circumferential clamping forcesufficient to prevent metal from
35、 the surrounding flange beingpulled into the die cavity.3.10.1 DiscussionThe LDH test was designed to give arepeatable measure of punch movement among specimens of aspecific metal sheet sample, thus the only measured valuewould be the punch height at incipient fracture. Problems withmaintaining a se
36、cure clamp result in variation of the measuredLDH value.Amodification of the LDH test using a strip in therange of 200 mm (4 in.) wide was found to give (e1) valuesnear 0 % (e2), when the surface strains were measured using agrid pattern. On this basis, a test was developed to use asheared strip of
37、metal sheet 200 mm (4 in.) wide andsufficiently long to be securely clamped in the LDH test fixture.The height at incipient fracture was to correlate with FLDo.The test was not sufficiently repeatable to be employed forevaluation of metal sheet samples. The equipment is used tostretch specimens, wit
38、h grid patterns, that have been sheared tovarious widths and is one method to obtain a range of (e2) andassociated (e1) values for plotting a FLC on a FLD.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 te
39、sting machine (LDHtester). Sometimes called a bulge tester. 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
40、in.), orlarger diameter can be used in place of the LDH test 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 orie
41、ntation, relative to the originalprocess rolling direction of the sample and that direction notedin the report.4.1.3 Lubricating the contact surfaces of the blank andpunch for the hemispherical punch test.4.1.3.1 Mineral oil and a thin polyethylene sheet is anexcellent lubricant.4.1.3.2 Drawing lubr
42、icants, or greases containing graphite,are acceptable.4.1.3.3 Kerosene is not a good lubricant, as it cleans thesurfaces under pressure and the metal sheet will not slide overthe punch.4.1.4 Securely clamping the flanges of a blank in theserrated, or lock bead, blank-holder dies of the hemispherical
43、punch test.4.1.4.1 For a tension test specimen, the standard procedurefor testing sheet type specimens, as shown in Fig. 1 ofE 8/E 8M, shall be followed.4.1.5 Stretching the central area of the blank biaxially overthe nose of the hemispherical punch, or pulling in the tensiontest, without interrupti
44、ng the force.4.1.5.1 Negative (e2) strains can 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 necking) is ob-served, if possible, or as soon as the specimen fractures.4.
45、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 pattern on the surface area near the neck of all thetest specimens for the se
46、ries.4.1.8.1 These measurements can include good (no localizednecking), 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. 2.4.1.9 Plotting the measu
47、red strain combinations on a FLD.See Fig. 2.4.1.10 Establishing the forming limit curve (FLC) be con-necting the uppermost good (no localized necking) (e1) strainsover the associated (e2) strain range used in the study.4.1.10.1 For practical purposes, the specimens that havebeen strained to a locali
48、zed neck-down, or through thicknessfracture, condition can 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 the FLC.4.1.10.2 Another acceptable procedure is to measure thegrid near the n
49、ecked, or fracture, location and identify thesedata points in determining the forming limit curve. Thisprocedure was used in locating the FLC of Fig. 2.4.1.10.3 Establishing the FLC depends on judgement. Notethat in Fig. 2 there 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. Significance and Use5.1 A formin
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