1、Designation: E646 071E646 15Standard 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.1 NOTEThe equation in 10.3 was editorially corrected in January 2014.INTRODUCTIONThis test method for determining ten
3、sile strain-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 int
4、erest of 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, = plastic component of true strain, but in special cases may be the total true strain. (See 10.2),K = str
5、ength coefficient, andK = is a constant, often called the strength coefficient having the units of stress, andn = strain-hardening exponent1. Scope1.1 This test method covers the determination of a strain-hardening exponent by tension testing of metallic sheet materials forwhich plastic-flow behavio
6、r obeys the power curve given in the Introduction.NOTE 1A single power curve may not fit be a satisfactory fit to the entire stress-strain curve between yield and necking. If such is the case, morethan one value of the strain-hardening exponent canmay be obtained (2).) by agreement using this test m
7、ethod.1.2 This test method is specifically for metallic sheet materials with thicknesses of at least 0.005 in. (0.13 mm) but 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
8、 to be regarded as the standard. The SI equivalents shown may beapproximate.standard. The values given in parentheses are mathematical conversions to SI units that are provided for informationonly and are not considered standard.NOTE 2The value of the strain-hardening exponent, n, is has no units an
9、d 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 responsibilityof the user of this standard to establish appropriate safety and health practices and determine the applicability
10、of regulatorylimitations prior to use.2. Referenced Documents2.1 ASTM Standards:3E4 Practices for Force Verification of Testing MachinesE6 Terminology Relating to Methods of Mechanical Testing1 This test method is under the jurisdiction of ASTM Committee E28 on Mechanical Testing and is the direct r
11、esponsibility of Subcommittee E28.02 on Ductility andFormability.Current edition approved Nov. 15, 2015. Published December 2007February 2016. Originally approved in 1978. Last previous edition approved in 20002007 asE646 - 00.E646 - 071. DOI: 10.1520/E0646-07E01.10.1520/E0646-15.2 The boldface numb
12、ers 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 Service at serviceastm.org. For Annual Book of ASTM Standardsvolume information, refer to the standards Document Summary page on the
13、 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 version. Becauseit may not be technically possible to adequately depict all changes accurately, ASTM recommends that users con
14、sult prior editions as appropriate. In all cases only the current versionof the standard as published by ASTM is to be considered the official document.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1E8E8/E8M Test Methods for Tension
15、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 Chord ModulusE177 Practice for Use of the
16、Terms Precision and Bias in ASTM Test MethodsE691 Practice for Conducting an Interlaboratory Study to Determine the 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 o
17、ther terms used in this test method, refer to E6 (Standard Terminology Relating to Methods ofMechanical Testing).3.2 Definitions:3.1.1 The definitions of terms given in Terminology E6 shall apply, with the addition of the following special terms used in thismethod.3.2.1 elastic true strain, e, nelas
18、tic component of the true strain.3.2.2 engineering strain (e)strain, e, na dimensionless value that is the change in length (LL) per unit length of originallinear dimension (L0) along the loading axis of the specimen; that is, e = e = (L)L/LL0.3.2.3 engineering stress (S)stress, S FLFL2-2 , nthe nor
19、mal stress, expressed in units of applied force, F,F per unit oforiginal cross-sectional area, A0; that is, S = FS = AF/A0.3.2.4 neckingnecking, nthe onset of nonuniform or localized plastic deformation, resulting in a localized reduction ofcross-sectional area.3.2.5 plastic true strain, p, nthe ine
20、lastic component of true strain.3.2.6 strain-hardening (n)strain hardening, nan increase in hardness and strength caused by plastic deformation.3.1.6 strength coeffcient (K) FL2an experimental constant, computed from the fit of the data to the assumed power curve,that is numerically equal to the ext
21、rapolated value of true stress at a true strain of 1.00.3.2.7 true strain ()strain, , nthe natural logarithm of the ratio of instantaneous gagegauge length, L, to the originalgagegauge length, L00; that is, = 1n = ln (L L/L L0) or = 1n = ln (1+e).3.2.8 true stress ()stress, FLFL2-2 , nthe instantane
22、ous normal stress, calculated on the basis of the instantaneouscross-sectional area, A; that is, = = F/A; if no necking has occurred, = occurred , = S( S(1+e).1+e).3.3 Definitions of Terms Specific to This Standard:3.3.1 strain-hardening exponent (n), nan experimental constant, computed from the lea
23、st 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 the data to the a
24、ssumed 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 a continuous an
25、d 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 strain, , strain-
26、hardening exponent, n, and strengthcoefficient, K, for that continuous portion of the true-stress versus true-strain curve which follows the empirical relationshipsdescribed.NOTE 3TheThis test method is recommended for use only in the plastic range for metallic sheet material for which the true-stre
27、ss true-strain datafollow the 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 similar metallic
28、 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 specificati
29、on.NOTE 4The engineering strain interval 1020% is commonly utilizedused for determining the n-value strain-hardening exponent, n, of formable lowcarbon low-carbon steel products.productsE646 1525.3 This test method is not intended to apply to any portion of the true-stress versus true-strain true -s
30、tress versus true -straincurve that exhibits discontinuous 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 steel, aluminum, or aluminumother alloys which exhibit yield-pointelongati
31、on or Lders bands that exhibit yield point and Lders band elongation, twinning, or PortevinLe Chatelier effect (PLC) may be characterizedas 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 suitab
32、le for determining the tensile stress-strain response of metallic sheet materials in the plastic regionprior to the onset of necking.5.5 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
33、tension testing shall conform to the requirements of Practices E4. The loads used todetermine stress shall be within the loading 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
34、 orbetter as defined in Practice E83.7. Sampling7.1 Samples shall be taken from the material as specified 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 rep
35、resentative material that is flat anduniform in thickness.8.1.2 In the preparation of specimens, special care shall be taken to prevent the introduction of residual stresses.8.2 DimensionsOne of theRecommended metallic sheet specimen configurations are shown in Fig. 1 shall be . Specimenconfiguratio
36、ns shall have sides parallel to 0.001 in. and dimensions shall be reported as stated in 11.1.6. Intentionally taperedspecimens shall not be used.NOTE 7While this test method is specifically for metallic sheet materials, it has been successfully applied to many tensile specimens having a uniformcross
37、-sectional area, that is, round bars and flats where parallel sides have been maintained.9. 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 width, W, of the reduced section to at least the nea
38、rest 0.001 in. (0.025 mm).NOTE 6The rounding-off method given in Practice E29 shall be used for all measurements.9.1.1 The rounding-off method given in Practice E29 shall be used for all measurements.9.2 Grip the specimen in the testing machine in a manner to ensure axial alignment of the specimen a
39、s noted in Test MethodsE8E8/E8M and attach the extensometer.NOTE 7The order of this step may be reversed if required by the design of the extensometer or the specimen grips, or both.9.2.1 The order of this step may be reversed if required by the design of the extensometer or the specimen grips, or b
40、oth.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 The In the absence of any specified limitations on the speed of testing (by, for example, the appropriate productspecification), the test speed, defined in terms of rate of sep
41、aration of heads during tests, free running crosshead speed, or rate ofstraining shall be between 0.05 in./in. (m/m) and 0.50 in./in. (m/m) of the length of the reduced section per minute (see TestMethods(in accord with Test Method E8E8/E8M). , Standard Test Methods for Tension Testing Metallic Mate
42、rials, 7.6.4 Speed ofTesting When Determining Tensile Strength) The speed setting shall not be changed during the strain interval over which the strainhardening exponent, n, is to be determined.determinedNOTE 8The mode of control and the rate used may affect the values obtained.9.3.3 If the yield po
43、int, 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 portion of the test shall be within the range permitted by TestMethods E8E8/E8M or any other specificspecified value. After e
44、xceeding the strain necessary for this information, adjust thecrosshead speed to within the range specified prior to the next step.by this standard.9.4 Record the loadforce and corresponding strain for at least five approximately equally spaced levels of strain (Note 109)encompassingcovering the str
45、ain range of interest specified or required in the product specification. Usually, the greatest of theseE646 153strains is at or slightly prior to the strain at which the maximum loadforce occurs, and usually the lower bound of these strainsis the yield strain (for continuous-yielding material) or t
46、he end of yield-point extension (for discontinuous-yielding material). SeeFig. 2. The requirement that at least five force-strain data pairs be recorded is met with an autographic recording and the selectionof five or more pairs from that curve.NOTE 9There Since the slope of the curve may vary sligh
47、tly along its length, there is a statistical basis for choosing points equally spaced in areference frame.out along the strainrange.NOTE 10The requirement that at least five load-strain data pairs be recorded is met with an autographic recording and the selection of five or morepairs from that curve
48、.9.4.1 The test is not valid if fewer than five data pairs are obtained.NOTE 11The test is not valid if less than five data pairs are obtained.9.4.2 If multiple nvalues-values of the strain-hardening exponent are to be determined (Note 1), use at least five stress and strainvalues for the calculatio
49、n of nthe strain-hardening exponent in each interval of strain.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 0.25T Thickness (Note 2) thickness of materialR Radius of 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 (
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