1、Designation: E646 071Standard 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, the ye
2、ar 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.1NOTEThe equation in 10.3 was editorially corrected in January 2014.INTRODUCTIONThis test method for determining tensile str
3、ain-hardening exponents n utilizes stress-stain dataobtained in 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
4、 the true-stress versus true-strain curve. Themathematical representation used in this method is a power curve (Note 1) of the form (1)2: = Knwhere: = true stress, = true plastic strain,K = strength coefficient, andn = strain-hardening exponent1. Scope1.1 This test method covers the determination of
5、 a strain-hardening exponent by tension testing of metallic sheet mate-rials for which plastic-flow behavior obeys the power curvegiven in the Introduction.NOTE 1A single power curve may not fit the entire stress-strain curvebetween yield and necking. If such is the case, more than one value of thes
6、train-hardening exponent can be obtained (2).1.2 This test method is for metallic sheet materials withthicknesses of at least 0.005 in. (0.13 mm) but not greater than0.25 in. (6.4 mm).1.3 The values stated in inch-pound units are to be regardedas the standard. The SI equivalents shown may be approxi
7、mate.1.4 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 determine the applica-bility of regulatory limitations prior to use.2. Referen
8、ced Documents2.1 ASTM Standards:3E4 Practices for Force Verification of Testing MachinesE6 Terminology Relating to Methods of Mechanical TestingE8 Test Methods for Tension Testing of Metallic MaterialsE29 Practice for Using Significant Digits in Test Data toDetermine Conformance with SpecificationsE
9、83 Practice for Verification and Classification of Exten-someter SystemsE177 Practice for Use of the Terms Precision and Bias inASTM Test MethodsE691 Practice for Conducting an Interlaboratory Study toDetermine the Precision of a Test Method3. Terminology3.1 Definitions:3.1.1 The definitions of term
10、s given in Terminology E6 shallapply, with the addition of the following special terms used inthis method.3.1.2 engineering strain (e)a dimensionless value that isthe change in length (L) per unit length of original lineardimension (L0) along the loading axis of the specimen; that is,e=(L)/L0.1This
11、test method is under the jurisdiction of ASTM Committee E28 onMechanical Testing and is the direct responsibility of Subcommittee E28.02 onDuctility and Formability.Current edition approved Dec. 1, 2007. Published December 2007. Originallyapproved in 1978. Last previous edition approved in 2000 as E
12、646 - 00. DOI:10.1520/E0646-07E01.2The boldface numbers in parentheses refer to the list of references appended tothis method.3For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information,
13、 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 States13.1.3 engineering stress (S) FL2the normal stress, ex-pressed in units of applied force, F, per unit of originalcross-sec
14、tional area, A0; that is, S = F/A0.3.1.4 neckingthe onset of nonuniform or localized plasticdeformation, resulting in a localized reduction of cross-sectional area.3.1.5 strain-hardening (n)an increase in hardness andstrength caused by plastic deformation.3.1.6 strength coeffcient (K) FL2an experime
15、ntalconstant, computed from the fit of the data to the assumedpower curve, that is numerically equal to the extrapolated valueof true stress at a true strain of 1.00.3.1.7 true strain ()the natural logarithm of the ratio ofinstantaneous gage length, L, to the original gage length, L0;that is, =1n(L/
16、L0)or = 1n (1+e).3.1.8 true stress () FL2the instantaneous normalstress, calculated on the basis of the instantaneous cross-sectional area, A; that is, = F/A; if no necking has occurred, = S(1+e).4. Summary of Test Method4.1 This test method applies to materials exhibiting acontinuous stress-strain
17、curve in the plastic region. The dis-placement or strain is applied in a continuous and rate-controlled manner while the normal tensile load and strain aremonitored. The instantaneous cross-sectional area may bemonitored or calculated by assuming constancy of volume inthe plastic region. Equations a
18、re presented that permit thecalculation of the true stress, , true strain, , strain-hardeningexponent, n, and strength coefficient, K, for that continuousportion of the true-stress versus true-strain curve which followsthe empirical relationships described.NOTE 2The test method is recommended for us
19、e only in the plasticrange for metallic sheet material for which the true-stress true-strain datafollow the stated relationship.5. Significance and Use5.1 This test method is useful for estimating the strain at theonset of necking in a uniaxial tension test (1). Practically, itprovides an empirical
20、parameter for appraising the relativestretch formability of similar metallic systems. The strain-hardening exponent is also a measure of the increase instrength of a material due to plastic deformation.5.2 The strain-hardening exponent may be determined overthe entire plastic stress-strain curve or
21、any portion(s) of thestress-strain curve specified in a product specification.NOTE 3The strain interval 1020% is commonly utilized for deter-mining the n-value of formable low carbon steel products.5.3 This test method is not intended to apply to any portionof the true-stress versus true-strain curv
22、e that exhibits discon-tinuous behavior; however, the method may be applied bycurve-smoothing techniques as agreed upon.NOTE 4For example, those portions of the stress-strain curves formild steel or aluminum alloys which exhibit yield-point elongation orLders bands may be characterized as behaving d
23、iscontinuously.NOTE 5Caution should be observed in the use of curve-smoothingtechniques as they may affect the n-value.5.4 This test method is suitable for determining the tensilestress-strain response of metallic sheet materials in the plasticregion prior to the onset of necking.5.5 The n-value may
24、 vary with the displacement rate orstrain rate used, depending on the metal and test temperature.6. Apparatus6.1 Testing MachinesMachines used for tension testingshall conform to the requirements of Practices E4. The loadsused to determine stress shall be within the loading range of thetesting machi
25、ne as defined in Practices E4.6.2 Strain-Measurement EquipmentEquipment for mea-surement of extension shall conform to the requirements ofClass C or better as defined in Practice E83.7. Sampling7.1 Samples shall be taken from the material as specified inthe applicable product specification.8. Test S
26、pecimens8.1 Selection and Preparation of Specimens:8.1.1 In the selection of specimen blanks, special care shallbe taken to assure obtaining representative material that is flatand uniform in thickness.8.1.2 In the preparation of specimens, special care shall betaken to prevent the introduction of r
27、esidual stresses.8.2 DimensionsOne of the specimen configurationsshown in Fig. 1 shall be used.9. Procedure9.1 Measure and record the original thickness of the reducedsection of the specimen to at least the nearest 0.0005 in. (0.013mm) and the width of the reduced section to at least the nearest0.00
28、1 in. (0.025 mm).NOTE 6The rounding-off method given in Practice E29 shall be usedfor all measurements.9.2 Grip the specimen in the testing machine in a manner toensure axial alignment of the specimen as noted in TestMethods E8 and attach the extensometer.NOTE 7The order of this step may be reversed
29、 if required by thedesign of the 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 andstrains are accurately indicated.9.3.2 The test speed, defined in terms of rate of separation ofheads during tests, free running crosshead spee
30、d, or rate ofstraining shall be between 0.05 and 0.50 in./in. (m/m) of thelength of the reduced section per minute (see Test MethodsE8). The speed setting shall not be changed during the straininterval over which n is to be determined.NOTE 8The mode of control and the rate used may affect the values
31、obtained.9.3.3 If the yield point, yield-point elongation, yieldstrength, or any combination of these is to be determined also,the rate of stress application or crosshead separation during thisportion of the test shall be within the range permitted byE646 0712Methods E8 or any other specific value.
32、After exceeding thestrain necessary for this information, adjust the crossheadspeed to within the range specified prior to the next step.9.4 Record the load and corresponding strain for at least fiveapproximately equally spaced levels of strain (Note 10) en-compassing the range of interest specified
33、 in the productspecification. Usually, the greatest of these strains is at orslightly prior to the strain at which the maximum load occurs,and usually the lower bound of these strains is the yield strain(for continuous-yielding material) or the end of yield-pointextension (for discontinuous-yielding
34、 material). See Fig. 2.NOTE 9There is a statistical basis for points equally spaced in areference frame.NOTE 10The requirement that at least five load-strain data pairs berecorded is met with an autographic recording and the selection of five ormore pairs from that curve.NOTE 11The test is not valid
35、 if less than five data pairs are obtained.9.4.1 If multiple n-values are to be determined (Note 1), useat least five stress and strain values for the calculation of n ineach interval of strain.DimensionsRequired Dimensions for Reduced Section of SpecimenDimensionsin. mmG Gage length 2.000 0.005 50.
36、0 0.10W Width (Note 1) 0.500 0.010 12.5 0.25T Thickness (Note 2) thickness of materialR Radius of fillet, min12 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
37、(Note 3 and Note 4)34 20“Pin-End” SpecimensC Width of grip section, approximate (Note5)250D Diameter of hole for pin (Note 6)12 13E Distance of center of pin from end, ap-proximate112 38F Distance of edge of hole from fillet, min12 13NOTE 1The width of the reduced section shall be parallel to within
38、 60.001 in. (60.025 mm).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.NOTE 3It is desirable, if possible, that the grip sections be long enough to extend into the grips a distance equal to two-third
39、s or more the length ofthe grips.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 central reduced section stated in Note 1 shall apply. The ends of the s
40、pecimen 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 shall be on the centerline of the reduced section, within 60.002 in.
41、 (60.05 mm).FIG. 1 Specimen for Determining n -ValuesE646 07139.4.2 Other parameters may be recorded in place of loadsand strains provided that they can ultimately be transformedinto true stress and true strain at least as accurately as thosemeasured using the techniques already described in this te
42、stmethod.10. Calculations10.1 Determine the strain-hardening exponent from thelogarithmic form of the power curve representation of thetrue-stress versus true-strain curve within the plastic range(Note 12):log 5 logK1nlogCalculate values of true stress and true strain from thefollowing:True stress 5
43、 S11e!True strain 5 ln11e!where:(, ) = a true-stress versus true-strain pair in the selectedinterval,S = engineering stress, ande = engineering strain.NOTE 12Any logarithmic base may be used in these calculationsunless otherwise noted. The use of the term “log” does not imply the useof base 10.NOTE
44、13For convenience when the elastic strain is less than 10 % ofthe total strain, it is not necessary to subtract the elastic strain. Elasticstrain may be calculated by dividing the true stress by the nominal valueof modulus of elasticity. All data pairs used to calculate an n-value mustbe treated in
45、the same manner.(a) Material with initial discontinuous-yielding region(b) Material with no discontinuous yieldingFIG. 2 Examples Showing Load-Strain Data PairsE646 071410.2 Obtain the logarithms of the true-stress versus true-strain pairs calculated in 10.1. From these paired sets of (log ,log ), c
46、alculate, via linear regression analysis of log versuslog , the slope, n, and the standard error of the slope (3, 4).10.3 The equation for calculating the linear regression is asfollows:n 5N(i51Nlog ilog i!2S(i51Nlog i(j51Nlog jDNS(i51Nlog i!2D2S(i51Nlog iD2where N = the number of data pairs.10.4 Th
47、e equations for calculating the slope, the intercept,and the standard deviation of the slope are made convenient bysymbolic representations as follows:y =log N = number of data pairsx =log SD = standard deviation of the n-valueb =logKn = n-value10.5 The equation for the slope of the linear regressio
48、n lineprovides the strain-hardening exponent as follows.n 5N(xy 2(x(yN(x22 (x!2NOTE 14Ref (5) is one source for the above equation and the basis forothers that follow.10.6 The equations for the strength coefficient (5.7) are asfollows.b 5(y 2 n(xNMK 5 expb#10.7 The calculation of the standard deviat
49、ion of the n-valueis based upon the variance of the slope of the regression line.This measure of variability contains the computed n-value(10.5) and the computed strength coefficient (10.6).SD 5H(y 2 b 2 nx!2N(x22 (x!23NN 2 2J1/210.8 An example of a worksheet for manually calculatingthese values is found in Appendix X1.11. Report11.1 The report shall include the following:11.1.1 The material represented by commercial standardnomenclature. Materials that have no commercial st
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