1、Designation: E646 15E646 16Standard Test Method forTensile Strain-Hardening Exponents (n -Values) of MetallicSheet Materials1This standard is issued under the fixed designation E646; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision,
2、the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.INTRODUCTIONThis test method for determining tensile strain-hardening exponents n utilizes stress-stain dataobtained i
3、n a uniaxial tension test. Tensile data are obtained in a continuous and rate-controlledmanner via displacement or strain control. The strain-hardening exponents are determined from anempirical representation over the range of interest of the true-stress versus true-strain curve. Themathematical rep
4、resentation used in this method is a power curve (Note 1) of the form (1)2: = Knwhere: = true stress, = plastic component of true strain, but in special cases may be the total true strain. (See 10.2),K = is a constant, often called the strength coefficient having the units of stress, andn = strain-h
5、ardening exponent1. Scope Scope*1.1 This test method covers the determination of a strain-hardening exponent by tension testing of metallic sheet materials forwhich plastic-flow behavior obeys the power curve given in the Introduction.NOTE 1A single power curve may not be a satisfactory fit to the e
6、ntire stress-strain curve between yield and necking. If such is the case, more thanone value of the strain-hardening exponent may be obtained (2) by agreement using this test method.1.2 This test method is specifically for metallic sheet materials with thicknesses of at least 0.005 in. (0.13 mm) but
7、 not greaterthan 0.25 in. (6.4 mm). The method has successfully been and may be applied to other forms and thicknesses by agreement1.3 The values stated in inch-pound units are to be regarded as standard. The values given in parentheses are mathematicalconversions to SI units that are provided for i
8、nformation only and are not considered standard.NOTE 2The value of the strain-hardening exponent, n, is has no units and is independent of the units used in its determination1.4 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsib
9、ilityof the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatorylimitations prior to use.2. Referenced Documents2.1 ASTM Standards:3E4 Practices for Force Verification of Testing MachinesE6 Terminology Relating to Methods of Mechani
10、cal TestingE8/E8M Test Methods for Tension Testing of Metallic MaterialsE29 Practice for Using Significant Digits in Test Data to Determine Conformance with SpecificationsE83 Practice for Verification and Classification of Extensometer SystemsE111 Test Method for Youngs Modulus, Tangent Modulus, and
11、 Chord Modulus1 This test method is under the jurisdiction of ASTM Committee E28 on Mechanical Testing and is the direct responsibility of Subcommittee E28.02 on Ductility andFormability.Current edition approved Nov. 15, 2015Feb. 1, 2016. Published February 2016March 2016. Originally approved in 197
12、8. Last previous edition approved in 20072015 asE646 - 07E646 - 15.1. DOI: 10.1520/E0646-15.10.1520/E0646-162 The boldface numbers in parentheses refer to the list of references appended to this method.3 For referencedASTM standards, visit theASTM website, www.astm.org, or contactASTM Customer Servi
13、ce at serviceastm.org. For Annual Book of ASTM Standardsvolume information, refer to the standards Document Summary page on the ASTM website.This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous
14、 version. Becauseit may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current versionof the standard as published by ASTM is to be considered the official document.*A Summary of Changes
15、 section appears at the end of this standardCopyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1E177 Practice for Use of the Terms Precision and Bias in ASTM Test MethodsE691 Practice for Conducting an Interlaboratory Study to Determine t
16、he Precision of a Test Method2.2 ISO StandardISO 10275:2007 Metallic materials - Sheet and strip - Determination of tensile strain hardening exponent3. Terminology3.1 For definitions of other terms used in this test method, refer to E6 (Standard Terminology Relating to Methods ofMechanical Testing).
17、3.2 Definitions:3.2.1 elastic true strain, e, nelastic component of the true strain.3.2.2 engineering strain, e, na dimensionless value that is the change in length (L) per unit length of original lineardimension (L0) along the loading axis of the specimen; that is, e = L/L0.3.2.3 engineering stress
18、, S FL-2 , nthe normal stress, expressed in units of applied force, F per unit of originalcross-sectional area, A0; that is, S = F/A03.2.4 necking, nthe onset of nonuniform or localized plastic deformation, resulting in a localized reduction of cross-sectionalarea.3.2.5 plastic true strain, p, nthe
19、inelastic component of true strain.3.2.6 strain hardening, nan increase in hardness and strength caused by plastic deformation.3.2.7 true strain, , nthe natural logarithm of the ratio of instantaneous gauge length, L, to the original gauge length, L0; thatis, = ln (L/L0) or = ln (1+e).3.2.8 true str
20、ess, FL-2 , nthe instantaneous normal stress, calculated on the basis of the instantaneous cross-sectional area,A; that is, = F/A; if no necking has occurred , occurred, = S(1+e).3.3 Definitions of Terms Specific to This Standard:3.3.1 strain-hardening exponent (n), nan experimental constant, comput
21、ed from the least squares best fit, linear slope of log versus log or data over a specific strain range where is the plastic component of true strain, but in special cases may be thetotal true strain (see 10.2).3.3.2 strength coeffcient (K) FL2, nan experimental constant, computed from the fit of th
22、e data to the assumed powercurve, that is numerically equal to the extrapolated value of true stress at a true strain of 1.00.4. Summary of Test Method4.1 This test method applies to materials exhibiting a continuous stress-strain curve in the plastic region. The displacement orstrain is applied in
23、a continuous and rate-controlled manner while the normal tensile load and strain are monitored. Theinstantaneous cross-sectional area may be monitored or calculated by assuming constancy of volume in the plastic region.Equations are presented that permit the calculation of the true stress, , true st
24、rain, , strain-hardening exponent, n, and strengthcoefficient, K, for that continuous portion of the true-stress versus true-strain curve which follows the empirical relationshipsdescribed.NOTE 3This test method is recommended for use only in the plastic range for metallic sheet material for which t
25、he true-stress true-strain data followthe stated relationship.5. Significance and Use5.1 This test method is useful for estimating the strain at the onset of necking in a uniaxial tension test (1). Practically, itprovides an empirical parameter for appraising the relative stretch formability of simi
26、lar metallic systems. The strain-hardeningexponent is also a measure of the increase in strength of a material due to plastic deformation.5.2 The strain-hardening exponent may be determined over the entire plastic stress-strain curve or any portion(s) of thestress-strain curve specified in a product
27、 specification.NOTE 4The engineering strain interval 1020% is commonly used for determining the strain-hardening exponent, n, of formable low-carbon steelproducts5.3 This test method is not intended to apply to any portion of the true -stressstress versus true -strainstrain curve that exhibitsdiscon
28、tinuous behavior; however, the method may be applied by curve-smoothing techniques as agreed upon.NOTE 5For example, those portions of the stress-strain curves for mild steel, aluminum, or other alloys that exhibit yield point and Lders bandelongation, twinning, or PortevinLe Chatelier effect (PLC)
29、may be characterized as behaving discontinuously.NOTE 6Caution should be observed in the use of curve-smoothing techniques as they may affect the n-value.5.4 This test method is suitable for determining the tensile stress-strain response of metallic sheet materials in the plastic regionprior to the
30、onset of necking.E646 1625.5 The n-value may vary with the displacement rate or strain rate used, depending on the metal and test temperature.6. Apparatus6.1 Testing MachinesMachines used for tension testing shall conform to the requirements of Practices E4. The loadsforcesused to determine stress s
31、hall be within the loadingforce range of the testing machine as defined in Practices E4.6.2 Strain-Measurement EquipmentEquipment for measurement of extension shall conform to the requirements of Class C orbetter as defined in Practice E83.7. Sampling7.1 Samples shall be taken from the material as s
32、pecified in the applicable product specification.8. Test Specimens8.1 Selection and Preparation of Specimens:8.1.1 In the selection of specimen blanks, special care shall be taken to assure obtaining representative material that is flat anduniform in thickness.8.1.2 In the preparation of specimens,
33、special care shall be taken to prevent the introduction of residual stresses.8.2 DimensionsRecommended metallic sheet specimen configurations are shown in Fig. 1. Specimen configurations shallhave sides parallel to 0.001 in. and dimensions shall be reported as stated in 11.1.6.E646 163Intentionally
34、tapered specimens shall not be used.DimensionsRequired Dimensions for Reduced Section of SpecimenDimensionsin. mmG Gage length 2.000 0.005 50.0 0.10W Width(Note 1) 0.500 0.010 12.5 0.25W WidthA 0.500 0.010 12.5 0.25T Thickness(Note 2) thickness of materialT ThicknessB thickness of materialR Radius o
35、f fillet, min 12 13L Overall length, min 8 200A Length of reduced section, min 214 60B Length of grip section, min 2 50Suggested Dimensions for Ends of Specimen“Plain-End” SpecimensC Width of grip section(Note 3andNote 4) 34 20C Width of grip sectionCand D 34 20“Pin-End” SpecimensC Width of grip sec
36、tion, approxi-mate(Note 5)2 50C Width of grip section, approximateE 2 50D Diameter of hole for pin(Note 6) 12 13D Diameter of hole for pinF 12 13E Distance of center of pin from end, ap-proximate112 38F Distance of edge of hole from fillet, min 12 13A The width of the reduced section shall be parall
37、el to within 0.001 in. (0.025 mm).NOTE 1The width of the reduced section shall be parallel to within 60.001 in. (60.025 mm).B The thickness of the reduced section shall not vary by more than 0.0005 in. (0.013 mm) or 1 %, whichever is larger, within the gage length, G.C It is desirable, if possible,
38、that the grip sections be long enough to extend into the grips a distance equal to two-thirds or more the length of the grips.NOTE 2The thickness of the reduced section shall not vary by more than 60.0005 in. (0.013 mm) or 1 %, whichever is larger, within the gage length,G.D Narrower grip sections m
39、ay be used. If desired, the width may be 0.500 0.010 in. (12.5 0.25 mm) throughout the length of the specimen, but the requirement fordimensional tolerance in the central reduced section stated in footnote A shall apply. The ends of the specimen shall be symmetrical with the center line of the reduc
40、edsection within 0.01 in. (0.25 mm).E The ends of the specimen shall be symmetrical with the center line of the reduced section within 0.01 in. (0.25 mm).NOTE 3It is desirable, if possible, that the grip sections be long enough to extend into the grips a distance equal to two-thirds or more the leng
41、th ofthe grips.F Holes shall be on the centerline of the reduced section, within 0.002 in. (0.05 mm).NOTE 4Narrower grip sections may be used. If desired, the width may be 0.5006 0.010 in. (12.5 6 0.25 mm) throughout the length of the specimen,but the requirement for dimensional tolerance in the cen
42、tral reduced section stated in Note 1 shall apply. The ends of the specimen shall be symmetricalwith the center line of the reduced section within 0.01 in. (0.25 mm).NOTE 5The ends of the specimen shall be symmetrical with the center line of the reduced section within 0.01 in. (0.25 mm).NOTE 6Holes
43、shall be on the centerline of the reduced section, within 60.002 in. (60.05 mm).FIG. 1 Specimen for Determining n -ValuesE646 164NOTE 7While this test method standard is specifically for metallic sheet materials, it has been successfully applied to many tensile specimens havinga uniform cross-sectio
44、nal area, that is,for example, round bars and flats where parallel sides have been maintained.maintained to within 0.001 in. asrequired by 8.2. Since other test results may be desired to be obtained, specimens may be intentionally tapered with sides parallel to within the sametolerance of 0.001 in.9
45、. Procedure9.1 Measure and record the original thickness T, of the reduced section of the specimen to at least the nearest 0.0005 in. (0.013mm) and the width, W, of the reduced section to at least the nearest 0.001 in. (0.025 mm).9.1.1 The rounding-off method given in method to record observed value
46、s, given in 7.2 of Practice E29, shall be used for allmeasurements.9.2 Grip the specimen in the testing machine in a manner to ensure axial alignment of the specimen as noted in Test MethodsE8/E8M and attach the extensometer.9.2.1 The order of this step may be reversed if required by the design of t
47、he extensometer or the specimen grips, or both.9.3 Speed of Testing:9.3.1 The speed of testing shall be such that the loads and strains are accurately indicated.9.3.2 In the absence of any specified limitations on the speed of testing (by, for example, the appropriate product specification),the test
48、 speed, defined in terms of rate of separation of heads during tests, free running crosshead speed, or rate of straining shallbe between 0.05 in./in. (m/m) and 0.50 in./in. (m/m) of the length of the reduced section per minute (in accord with Test MethodE8/E8M, Standard Test Methods for Tension Test
49、ing Metallic Materials, 7.6.4 Speed of Testing When Determining TensileStrength) The speed setting shall not be changed during the strain interval over which the strain hardening exponent, n, is to bedeterminedNOTE 8The mode of control and the rate used may affect the values obtained.9.3.3 If the yield point, yield-point elongation, yield strength, or any combination of these is to be determined also, the rate ofstress or strain application or crosshead separation during this portio
