1、Designation: E 646 00Standard Test Method forTensile Strain-Hardening Exponents (n -Values) of MetallicSheet Materials1This standard is issued under the fixed designation E 646; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the y
2、ear of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (e) indicates an editorial change since the last revision or reapproval.INTRODUCTIONThis test method for determining tensile strain-hardening exponents n utilizes stress-stain dataobtained in a
3、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 represe
4、ntation used in this method is a power curve (Note 1) of the form (1)2:s5Kenwhere:s = true stress,e = true plastic strain,K = strength coefficient, andn = strain-hardening exponent1. Scope1.1 This test method covers the determination of a strain-hardening exponent by tension testing of metallic shee
5、t 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 thestrain-hardening exponent can be obtained (2).1.2 This test metho
6、d 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 approximate.1.4 This standard does not purport to address all of thesaf
7、ety 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. Referenced Documents2.1 ASTM Standards:E 4 Practices for Force Verifica
8、tion of Testing Machines3E 6 Terminology Relating to Methods of Mechanical Test-ing3E 8 Test Methods for Tension Testing of Metallic Materials3E 29 Practice for Using Significant Digits in Test Data toDetermine Conformance with Specifications4E 83 Practice for Verification and Classification of Exte
9、n-someters3E 177 Practice for Use of the Terms Precision and Bias inASTM Test Methods43. Terminology3.1 Definitions:3.1.1 The definitions of terms given in Terminology E 6shall apply, with the addition of the following special termsused in this method.3.1.2 engineering strain (e)a dimensionless valu
10、e that isthe change in length (DL) per unit length of original lineardimension (L0) along the loading axis of the specimen; that is,e=(DL)/L0.3.1.3 engineering stress (S) FL2the normal stress, ex-pressed in units of applied force, F, per unit of originalcross-sectional area, A0; that is, S = F/A0.3.
11、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.1This test method is under the jurisdiction of ASTM Committee E-28 onMechanical T
12、esting, and is the direct responsibility of Subcommittee E28.02 onDuctility and Flexure.Current edition approved May 10, 2000. Published August 2000. Originallypublished as E 646 - 78. Last previous edition E 646 - 98.2The boldface numbers in parentheses refer to the list of references appended toth
13、is method.3Annual Book of ASTM Standards, Vol 03.01.4Annual Book of ASTM Standards, Vol 14.02.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.3.1.6 strength coeffcient (K) FL2an experimental con-stant, computed from the fit of the da
14、ta to the assumed powercurve, that is numerically equal to the extrapolated value oftrue stress at a true strain of 1.00.3.1.7 true strain (e)the natural logarithm of the ratio ofinstantaneous gage length, L, to the original gage length, L0;that is, e =1n(L/L0)ore = 1n (1+e).3.1.8 true stress (s) FL
15、2the instantaneous normalstress, calculated on the basis of the instantaneous cross-sectional area, A; that is, s = F/A; if no necking has occurred,s = S(1+e).4. Summary of Test Method4.1 This test method applies to materials exhibiting acontinuous stress-strain curve in the plastic region. The dis-
16、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 are presented that permit thecalculati
17、on of the true stress, s, true strain, e, 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 use only in the plasticrange for meta
18、llic 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 parameter for appraising the relati
19、vestretch 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 any portion(s) of thestress-strain
20、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 curve that exhibits discon-tinuous beha
21、vior; 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 discontinuously.NOTE 5Caution should
22、 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 vary with the displacement rate or
23、strain rate used, depending on the metal and test temperature.6. Apparatus6.1 Testing MachinesMachines used for tension testingshall conform to the requirements of Practices E 4. The loadsused to determine stress shall be within the loading range of thetesting machine as defined in Practices E 4.6.2
24、 Strain-Measurement EquipmentEquipment for mea-surement of extension shall conform to the requirements ofClass C or better as defined in Practice E 83.7. Sampling7.1 Samples shall be taken from the material as specified inthe applicable product specification.8. Test Specimens8.1 Selection and Prepar
25、ation 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 residual stresses.8.2 DimensionsO
26、ne 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 nearest0.001 in. (0.025 mm).NOTE 6The round
27、ing-off method given in Practice E 29 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 E 8 and attach the extensometer.NOTE 7The order of this step may be reversed if required by thedesign of t
28、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 andstrains are accurately indicated.9.3.2 The test speed, defined in terms of rate of separation ofheads during tests, free running crosshead speed, or rate ofstraining shall b
29、e between 0.05 and 0.50 in./in. (m/m) of thelength of the reduced section per minute (see Test MethodsE 8). 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 valuesobtained.9.3.3 If the yield p
30、oint, 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 byMethods E 8 or any other specific value. After exceeding thestrain necessary f
31、or 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 in the productspecification. Usually
32、, 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 strainE646002(for continuous-yielding material) or the end of yield-pointextension (for discontinuous-yielding material). See Fig. 2.NOTE 9T
33、here 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 if less than five data pairs
34、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.9.4.2 Other parameters may be recorded in place of loadsand strains provided that they can ultimately be transformedinto true stress and
35、 true strain at least as accurately as thosemeasured using the techniques already described in this testmethod.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(N
36、ote 12):DimensionsRequired Dimensions for Reduced Section of SpecimenDimensionsin. mmG Gage length 2.000 6 0.005 50.0 6 0.10W Width (Note 1) 0.500 6 0.010 12.5 6 0.25T Thickness (Note 2) thickness of materialR Radius of fillet, min12 13L Overall length, min 8 200A Length of reduced section, min 214
37、60B Length of grip section, min 2 50Suggested Dimensions for Ends of Specimen“Plain-End” SpecimensC Width of grip section (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-proxima
38、te112 38F Distance of edge of hole from fillet, min12 13NOTE 1The width of the reduced section shall be parallel to within 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 3
39、It 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 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,bu
40、t the requirement for dimensional tolerance in the central 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
41、reduced section within 0.01 in. (0.25 mm).NOTE 6Holes shall be on the centerline of the reduced section, within 60.002 in. (60.05 mm).FIG. 1 Specimen for Determining n -ValuesE646003log s5log K 1 n log eCalculate values of true stress and true strain from thefollowing:True stress s5S11e!True strain
42、e5ln 11e!where:(s, e ) = 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 13For convenie
43、nce 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 the same manne
44、r.10.2 Obtain the logarithms of the true-stress versus true-strain pairs calculated in 10.1. From these paired sets of (log s,log e), calculate, via linear regression analysis of log s versuslog e, the slope, n, and the standard error of the slope (3, 4).10.3 The equation for calculating the linear
45、regression is asfollows:n 5N(i 5 1Nlog eilog si! 2 (i 5 1Nlog ei (i 5 1Nlog si!N log ei!22 (i 5 1Nlog ei!2(a) Material with initial discontinuous-yielding region(b) Material with no discontinuous yieldingFIG. 2 Examples Showing Load-Strain Data PairsE646004where N = the number of data pairs.10.4 The
46、 equations for calculating the slope, the intercept,and the standard deviation of the slope are made convenient bysymbolic representations as follows:y = log s N = number of data pairsx = log e SD = standard deviation of the n-valueb = log Kn = n-value10.5 The equation for the slope of the linear re
47、gression 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 exp b#10.7 The calculation of the sta
48、ndard deviation 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 calculatingthes
49、e 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 standardshall be so indicated.11.1.2 The strain interval(s) over which the n-value(s) weredetermined.11.1.2.1 The n-value and its associated standard error, asreported, shall be considered applicable only over the straininterval for which it was determined.11.1.2.2 The number of data pairs selected for computingthe n-value.11.1.3 The direction
