ASTM E112-12 Standard Test Methods For Determining Average Grain Size

 

 

Designation: E112 − 12

Standard Test Methods for

Determining Average Grain Size1 This standard is issued under the fixed designation E112; the number immediately following the designation indicates the year of  original origin al adoption or, in the case of revis revision, ion, the year of last revision. revision. A number in paren parenthese thesess indicates the year of last reappr reapproval. oval. A superscript epsilon (´) indicates an editorial change since the last revision or reapproval. This standard has been approved for use by agencies of the Department of Defense.

INTRODUCTION

These test methods These methods of det determ ermina ination tion of ave averag ragee gra grain in size in meta metallic llic mat materia erials ls are pri primar marily ily measuring procedures and, because of their purely geometric basis, are independent of the metal or alloy concerned. In fact, the basic procedures may also be used for the estimation of average grain, crystal, or cell size in nonmetallic materials. The comparison method may be used if the structure of  the material approaches the appearance of one of the standard comparison charts. The intercept and planim pla nimetr etric ic meth methods ods are alw always ays app applica licable ble for dete determi rminin ning g ave averag ragee gra grain in siz size. e. How Howeve ever, r, the comparison charts cannot be used for measurement of individual grains. 1. Sco Scope pe 1.1 These test methods cover cover the measur measurement ement of average grain size and include the comparison procedure, the planimetricc (or Jef etri Jeffri fries) es) pro proced cedure ure,, and the int interce ercept pt pro proced cedure ures. s. Thes Th esee te test st me meth thod odss ma may y al also so be ap appl plie ied d to no nonm nmeta etalli llicc materials with structures having appearances similar to those of  the metallic structures shown in the comparison charts. These test methods apply chiefly to single phase grain structures but they can be applied to determine the average size of a particular typee of gra typ grain in str struct ucture ure in a mul multip tiphas hasee or mul multico ticonst nstitu ituent ent specimen. 1.2 The These se test methods methods are use used d to det determ ermine ine the ave averag ragee grain size of specimens with a unimodal distribution of grain areas, diameters, or intercept lengths. These distributions are approximately log normal. These test methods do not cover methods meth ods to cha charact racteri erize ze the nat nature ure of the these se dis distrib tributi utions ons.. Characterization of grain size in specimens with duplex grain size distributions is described in Test Methods   E1181. E1181.   Measurement of individual, very coarse grains in a fine grained matrix is described in Test Methods  E930  E930..

1.4 These These tes testt met metho hods ds de descr scribe ibe tec techn hniq iques ues pe perf rfor ormed med manually using either a standard series of graded chart images for the comparison method or simple templates for the manual countin cou nting g meth methods ods.. Util Utilizat ization ion of sem semi-a i-auto utomat matic ic dig digitiz itizing ing tablets or automatic image analyzers to measure grain size is described in Test Methods E1382 Methods  E1382.. 1.5 These test methods methods deal only with the recommended recommended test methods and nothing in them should be construed as defining or establishing limits of acceptability or fitness of purpose of  the materials tested. 1.6 The measured measured values values are sta stated ted in SI units, units, whi which ch are regarded regard ed as sta standa ndard. rd. Equ Equiva ivalen lentt inc inch-p h-poun ound d val values ues,, whe when n listed, are in parentheses and may be approximate. 1.7   This standar standard d doe doess not purport purport to add addre ress ss all of the safet sa fetyy co conc ncern erns, s, if an anyy, as asso socia ciated ted wit with h its us use. e. It is th thee responsibility of the user of this standard to establish appro priate safety and health practices and determine the applicability of regulatory limitations prior to use. 1.8 The paragraphs paragraphs appear in the following following order:

These test methods are under the jurisdiction of ASTM Committee   E04   on Metallography and are the direct responsibility of Subcommittee  E04.08  E04.08 on  on Grain Size. Current Curre nt editio edition n appro approved ved Nov Nov.. 15, 2012. Published Published Janua January ry 2013. Originally Originally approv app roved ed in 195 1955. 5. Las Lastt pre previo vious us edi editio tion n app approv roved ed 201 2010 0 as E1 E112 12 – 10. DOI DOI::

Section Scope   Referenced Documents Terminology   Significance Signifi cance and Use Generalities of Application Sampling   Test Specimens   Calibration   Preparation of Photomicrographs Comparison Procedure Planimetric (Jeffries) Procedure General Intercept Procedures Heyn Linear Intercept Procedure Circular Intercept Procedures

10.1520/E0112-12.

Hilliard Single-Circle Procedure

1.3 These These tes testt met method hodss dea deall onl only y wit with h det determ ermina ination tion of  plana pla narr gr grain ain siz size, e, th that at is, cha chara racte cteriz rizati ation on of the two two-dimensional grain sections revealed by the sectioning plane. Determination Determi nation of spatial grain size, that is, measurement measurement of the size of the three-dimensional grains in the specimen volume, is beyond the scope of these test methods. 1

Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States

Copyright by ASTM Int'l (all rights reserved); reserved); Tue Sep 3 16:40:18 EDT 2013 1 Downloaded/printed by Center For Library Initiatives pursuant to License Agreement. No further reproductions authorized.

     

             

Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 14.2

 

 

E112 − 12

Abrams Three-Circle Procedure   Statistical Analysis   Specimens with Non-equiaxed Grain Shapes   Specimens Specim ens Containing Two or More Phases or Consti Constituents tuents Report   Precision Precis ion and Bias   Keywords   Annexes: Basis of ASTM Grain Size Numbers  

 

14.3 15 16 17 18 19 20

Annex A1 Equations for Conversions Among Various Grain Size Measurements   Annex A2 Austenite Grain Size, Ferritic and Austenitic Steels Fracture Fractu re Grain Size Method

 

 

Requirements for Wrought Copper and Copper-Base Alloys Application to Special Situations

 

Appendixes: Results of Interlaboratory Grain Size Determinations Referenced Adjuncts

 

 

 

Annex A3 Annex A4 Annex A5 Annex A6 Appendix X1 Appendix X2

ing twin boundaries, the twin boundaries are ignored, that is, the structure on either side of a twin boundary belongs to the grain. 3.2.3  grain boundary intersection count— determination determination of  the number of times a test line cuts across, or is tangent to, grain boundaries (triple point intersections are considered as 1-1 ⁄ 2  intersections). 3.2.4  grain intercept count— determination determination of the number of  times a test line cuts through individual grains on the plane of  polish (tangent hits are considered as one half an interception; test lines that end within a grain are considered as one half an interception). 3.2.5   intercept length— the the distance between two opposed, adjacen adj acentt gra grain in bou bounda ndary ry inte interse rsectio ction n poi points nts on a tes testt line segment that crosses the grain at any location due to random placement of the test line. 3.3   Symbols: α

 

 A ¯   A  AI ℓ 

   

d  ¯  ¯   D  f  G ¯  ℓ  ¯  ℓ 

       

α

 

¯  ℓ  ℓ 

 

¯  ℓ  t 

 

¯  ℓ   p

 

ℓ 0

 

 L  M   M b n  N α

   

2. Referenc Referenced ed Documents Documents 2.1   ASTM Standards:2 E3 Guide E3  Guide for Preparation of Metallographic Specimens E7   Terminology Relating to Metallography E7 E407 Practice E407  Practice for Microetching Metals and Alloys E562   Test Met E562 Method hod for Det Determ ermini ining ng Volu olume me Fra Fractio ction n by Systematic Manual Point Count E691   Practic E691 Practicee for Conducting an Interl Interlaborat aboratory ory Study to Determine the Precision of a Test Method E883   Guide for Reflected–Light Photomicrography E883 E930   Test E930 Test Meth Methods ods for Est Estimat imating ing the Lar Larges gestt Gra Grain in Observed in a Metallographic Section (ALA Grain Size) E1181 Test E1181  Test Methods for Characterizing Duplex Grain Sizes E1382  Test Metho E1382 Methods ds for Determ Determining ining Average Average Grain Size Using Semiautomatic Semiautomatic and Automatic Image Analy Analysis sis 2.2   ASTM Adjuncts: 2.2.1 For a complete adjunct adjunct list, see  see   Appendix X2 3. Terminology 3.1   Definitions—  For definitions For of terms used in these test methods, see Terminology  Terminology   E7 E7.. 3.2  Definitions of Terms Specific to This Standard: 3.2.1   AST ASTM M gr grai ain n siz sizee nu numb mber er—  — the t he AS ASTM TM gr grai ain n si size ze number,   G, was originally defined as:  N  AE    5 2 G 2 1

(1 )

where  N  AE  is the number of grains per square inch at 100X magnification. To obtain the number per square millimetre at 1X, multiply by 15.50. 3.2.2   grain— that that area within within the confines confines of the original original (primary) boundary observed on the two-dimensional planeof-pol ofpolish ish or tha thatt vol volume ume enc enclos losed ed by the ori origin ginal al (pr (prima imary) ry) boundary in the three-dimensional object. In materials contain-

2

For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at [email protected]. For  Annual Book of ASTM  Standards volume information, refer to the standard’s Document Summary page on the ASTM website.

 N  A  N  Aα

 

         

 N  AE 

 

 N  Aℓ 

 

 N  At 

 

Copyright by ASTM Int'l (all rights reserved); reserved); Tue Sep 3 16:40:18 EDT 2013 2 Downloaded/printed by Center For Library Initiatives pursuant to License Agreement. No further reproductions authorized.

= matr matrix ix gr grain ainss in a tw two o ph phase ase (c (con onsti stitu tuen ent) t) microstructure. = tes testt ar area ea.. = mean grain cross section sectional al area. = grain elong elongation ation ratio or anisot anisotropy ropy index for a longitudinally oriented plane. = mean planar grain diamete diameterr (Plate III). = mean mean spatial (volu (volumetric) metric) grain diamete diameterr. = Jef Jeffries fries multip multiplier lier for planim planimetric etric method method.. = ASTM grain size numb number er.. = mean lineal lineal intercept intercept length. length. = mean mean lin lineal eal int interce ercept pt len length gth of the   α   matrix phase in a two phase (constituent) microstructure. = mean mean lin lineal eal int interc ercept ept leng length th on a lon longitu gitudidinally na lly or orien iented ted su surf rfac acee fo forr a no nonn-eq equi uiax axed ed grain structure. = mean lineal interce intercept pt length on a transv transversely ersely orien or iented ted su surf rface ace fo forr a no nonn-eq equi uiax axed ed gr grai ain n structure. = mean lin lineal eal int interc ercept ept len length gth on a pla planar nar ori ori-ented surface for a non-equiaxed grain structure. = base interc intercept ept length of 32.00 mm for definin defining g the relationship between  G  and  ℓ  (and  N  L) for macroscopi macro scopically cally or micros microscopica copically lly deter deter-mined grain size by the intercept method. = len length gth of a test lin line. e. = magnifi magnification cation used. = magnification used by a chart pictur picturee series series.. = numbe numberr of fields measur measured. ed. = num number ber of  α  α  grains intercepted by the test line in a two phase (constituent) microstructure. = numbe numberr of gra grains ins per mm2 at 1X. = nu numb mber er of   α   grains per mm2 at 1X in a two phase (constituent) microstructure. = number number of gra grains ins per inc inch h2 at 100X. =   N  A   on a longitudinally oriented surface for a non-equiaxed grain structure. =   N  A   on a tran transve sverse rsely ly ori orient ented ed sur surface face for a non-equiaxed grain structure.

 

 

E112 − 12

=   N  A   on a pl plan anar ar or orie ient nted ed su surf rface ace fo forr a no nonnequiaxed grain structure.  N  I    = num number ber of int interc ercept eptss with a tes testt line line..  N Inside   = number number of of grai grains ns comp comple letel tely y with within in a test test circle.  N   Intercepted   = numb number er of grain grainss intercepted intercepted by the the test circle.   = number number of inte interce rcepts pts per uni unitt len length gth of test  N  L line.  N  Lℓ    =   N  L   on a longitudinally oriented surface for a non-equiaxed grain structure.  N  Lt    =   N  L   on a tra transv nsvers ersely ely ori orient ented ed sur surfac facee for a non-equiaxed grain structure.  N  Lp   =   N  L   on a pl plan anar ar or orien iented ted surface surface fo forr a no nonnequiaxed grain structure. P I    = numb number er of grain boun boundary dary inters intersections ections with a test line. P L   = numbe numberr of gra grain in bou bounda ndary ry inte interse rsectio ctions ns per unit length of test line. P Lℓ    =   P L   on a longitudinally oriented surface for a non-equiaxed grain structure. P Lt    =   P L   on a tran transve sverse rsely ly ori orient ented ed sur surfac facee for a non-equiaxed grain structure. P Lp   =   P L   on a pl plan anar ar or orien iented ted su surf rfac acee fo forr a no nonnequiaxed grain structure. Q   = correction correction factor for compa comparison rison chart rating ratingss

4.1.2   Planimetric Procedur Procedure—  e— The The planimetric method involves an actual count of the number of grains within a known area. are a. The number number of gra grains ins per uni unitt are area, a,   N  A   , is used to determine the ASTM grain size number,   G. The precision of  the method is a function of the number of grains counted. A precision precis ion of   60. 0.25 25 gr grain ain size un units its can be at attai taine ned d wi with th a reas re ason onab able le am amou ount nt of ef effo fort rt.. Re Resu sults lts ar aree fr free ee of bi bias as an and d repeatability and reproducibility are less than   60.5 grain size units. An accurate count does require marking off of the grains

using a non-standard magnification for microscopically scopi cally determ determined ined grain sizes. correction factor for compa comparison rison chart rating ratingss using a non-standard magnification for macroscopically rosco pically determ determined ined grain sizes. standard stand ard deviati deviation. on. grain bou grain bounda ndary ry sur surfac facee are areaa to vol volume ume rat ratio io for a single phase structure. grain bou bounda ndary ry sur surfac facee are areaa to vol volume ume rat ratio io for a two phase (constituent) structure. studen stu dents’ ts’  t  multiplier for determination of the confidence interval. volume fractio volume fraction n of the  α  phase in a two phase (constituent) microstructure. 95 % co con nfid fiden ence ce in inte terv rval al.. per erce cent nt re rela lati tive ve ac accu cura racy cy..

4.2 4. 2 Fo Forr sp spec ecim imen enss co cons nsis istin ting g of eq equi uiax axed ed gr grain ains, s, th thee method of comparing the specimen with a standard chart is most convenient and is sufficiently accurate for most commercial purposes. For higher degrees of accuracy in determining average grain size, the intercept or planimetric procedures may be use used. d. The int interc ercept ept pro proced cedure ure is par particu ticularl larly y use useful ful for structures struct ures consis consisting ting of elong elongated ated grain grains. s.

 

 N  Ap

 

=

 

= =

Qm

s S V 

 

 

S V α t 

 

=  

V V α 95 % CI %RA

=

= = =

4. Sign Significan ificance ce and Use 4.1 These test methods methods cover procedures procedures for estimating estimating and ruless fo rule forr ex expr pres essin sing g th thee av aver erag agee gr grai ain n siz sizee of all me metal talss consisting entirely, or principally, of a single phase. The test methods may also be used for any structures having appearances similar to those of the metallic structures shown in the comparison charts. The three basic procedures for grain size estimation estimatio n are: 4.1.1   Comparison Procedur The compar comparison ison proce procedure dure Procedure—  e— The does do es no nott re requ quir iree co coun unti ting ng of ei eith ther er gr grai ains ns,, in inter tercep cepts, ts, or intersections but, as the name suggests, involves comparison of  the grain structure to a series of graded images, either in the form of a wall chart, clear plastic overlays, or an eyepiece reticle. There appears to be a general bias in that comparison grain size ratings claim that the grain size is somewhat coarser (1 ⁄ 2   to 1   G   number number lower) lower) tha than n it actu actually ally is (se (seee   X1.3.5). X1.3.5). Repeatability and reproducibility of comparison chart ratings are generally 61 grain size number.

as 4.1.3 they  are counted. Intercept Procedure—  Procedur e— The The intercept method involves an actual count of the number of grains intercepted by a test line or the number of grain boundary intersections with a test line, per unit length of test line, used to calculate the mean lineal intercept length,   ℓ¯.   ℓ¯ is used to determine the ASTM grain size number,  G. The precision of the method is a funct function ion of the number of intercepts or intersections counted. A precision of better than 60.25 grain size units can be attained with a re reas ason onab able le am amou ount nt of ef effo fort rt.. Res Resul ults ts ar aree fr free ee of bi bias; as; repeatability and reproducibility are less than   60.5 grain size units. Because an accurate count can be made without need of  marking off intercepts or intersections, the intercept method is fast fa ster er th than an th thee pl plan anime imetr tric ic me meth thod od fo forr th thee sa same me le leve vell of  precision.

4.3 In case of dispute, the intercept procedure procedure shall be the referee procedure in all cases. 4.4 No attempt should should be made to estimate the average average grain size of heavily cold-worked material. Partially recrystallized wrought alloys and lightly to moderately cold-worked material may be considered as consisting of non-equiaxed grains, if a grain size measurement is necessary. 4.5   Indivi Individua duall gra grain in mea measur sureme ements nts sho should uld not be mad madee based on the standard comparison charts.   These charts were constr con structe ucted d to refl reflect ect the typ typical ical log log-no -norma rmall dis distri tribut bution ion of  grain gr ain sizes sizes th that at re resu sult lt wh when en a pl plan anee is pa pass ssed ed th thro roug ugh h a three-dimensional array of grains. Because they show a distribution of grain dimensions, ranging from very small to very large, depending on the relationship of the planar section and thee th th thre reee-di dime mens nsio iona nall ar arra ray y of gr grain ains, s, th thee ch char arts ts ar aree no nott applicable to measurement of individual grains. 5. Generalities of Application 5.1 It is important, important, in using these test methods, methods, to recognize that th that thee es estim timati ation on of av aver erag agee gr grai ain n si size ze is no nott a pr prec ecise ise measur mea sureme ement. nt. A met metal al stru structu cture re is an agg aggreg regate ate of thr threeeedimensional crystals of varying sizes and shapes. Even if all these crystals were identical in size and shape, the grain cross sections, section s, prod produced uced by a rando random m plane (surface of obser observation vation)) through such a structure, would have a distribution of areas varying from a maximum value to zero, depending upon where

Copyright by ASTM Int'l (all rights reserved); reserved); Tue Sep 3 16:40:18 EDT 2013 3 Downloaded/printed by Center For Library Initiatives pursuant to License Agreement. No further reproductions authorized.

 

 

E112 − 12

the plane cuts each individual crystal. Clearly, no two fields of  observation can be exactly the same. 5.2 The size and location of grains in a microstructure microstructure are normally completely random. No nominally random process of  positio pos itionin ning g a test patt pattern ern can imp improv rovee this randomne randomness, ss, but random processes can yield poor representation by concentrating in g me measu asure reme ment ntss in pa part rt of a sp spec ecime imen. n.   Representative implies that all parts of the specimen contribute to the result, not, as sometimes has been presumed, that fields of average grain size are selected selected.. Visual Visual selectio selection n of fields, or casting out of extreme measurements, may not falsify the average when done by unbiased experts, but will in all cases give a false impression impres sion of high precision. For repres representativ entativee sampli sampling, ng, the area of the spe specime cimen n is men mentall tally y div divide ided d int into o sev severa erall equ equal al coherent cohere nt sub-a sub-areas reas and stage positions prespecified, prespecified, which are approx app roxima imately tely at the cen center ter of each sub-are sub-area. a. The stage is successively set to each of these positions and the test pattern applied blindly blindly,, that is, with the light out, the shutter closed, or the eye turned away. No touch-up of the position so selected is allowable. Only measurements made on fields chosen in this way can be validated with respect to precision and bias. 6. Samp Sampling ling 6.1 6. 1 Sp Spec ecime imens ns sh shou ould ld be se selec lected ted to re repr pres esen entt av aver erag agee conditions within a heat lot, treatment lot, or product, or to assess asse ss var variati iations ons anticipated anticipated across or alo along ng a pro produc ductt or compon com ponent ent,, dep depend ending ing on the nat nature ure of the mate materia riall bei being ng tested test ed and the pur purpos posee of the stu study dy.. Sam Samplin pling g loc locatio ation n and freque fre quency ncy sho should uld be bas based ed upo upon n agr agreem eement entss bet betwee ween n the manufacturers and the users. 6.2 Specim Specimens ens should not be taken from areas affected affected by shearing, burning, or other processes that will alter the grain structure.

magnificat magnifi cation ion.. In mos mostt case cases, s, exc except ept for thin she sheet et or wir wiree 2 specimens, a minimum polished surface area of 160 mm (0.25 in.2) is adequate. 7.4 7. 4 The The sp spec ecim imen en sh shal alll be se sect ctio ione ned, d, mo moun unte ted d (i (if  f  necessary necess ary), ), gro ground und,, and pol polish ished ed acco accordi rding ng to the rec recomommended mende d proce procedures dures in Practic Practicee   E3 E3..   The The spe specime cimen n sha shall ll be etched etch ed usi using ng a rea reagen gent, t, suc such h as list listed ed in Pra Practic cticee   E407, E407, to delineate most, or all, of the grain boundaries (see also  Annex A3). A3 ). TABLE 1 Suggested Comparison Charts for Metallic Materials

NOTE  1—These suggestions are based upon the customary practices in industry.. For speci industry specimens mens prepared accor according ding to speci special al techniq techniques, ues, the appropriate appro priate comparison comparison stand standards ards should be select selected ed on a struc structuralturalappearance appear ance basis in accord accordance ance with 8.2 with  8.2.. Material Aluminum Copper and copper copper-base -base alloys (see Annex A4) A4) Iron and steel: Austenitic Ferritic Carburized Stainless Magnesium and magnesium-base alloys Nickel and nickel-base alloys Super-strength alloys Zinc and zinc-base alloys

Plate Number

Basic Magnification

I III or IV

100X 75X, 100X

II or IV I IV II I or II II I or II I or II

100X 100X 100X 100X 100X 100X 100X 100X

8. Cali Calibrati bration on 8.1 Us 8.1 Usee a sta stage ge mic micro romet meter er to de deter termin minee th thee tr true ue lin linea earr magnifi mag nificat cation ion for each obj objecti ective, ve, eye eyepie piece ce and bel bellow lows, s, or zoom setting to be used within 62 %. 8.2 Us 8.2 Usee a ru ruler ler with a mil millim limetr etree sc scale ale to de deter termin minee th thee actual length of straight test lines or the diameter of test circles used as grids.

7. Test Specimens 7.1 In ge 7.1 gene nera ral, l, if th thee gr grai ain n str struc uctu ture re is eq equi uiax axed ed,, an any y specimen orientation is acceptable. However, the presence of  an equiaxed grain structure in a wrought specimen can only be determined by examination of a plane of polish parallel to the deformation axis. 7.2 If the grain structure structure on a longi longitudina tudinally lly oriented specispecimen is equiaxed, then grain size measurements on this plane, or any other, will be equivalent within the statistical precision of  the test meth method. od. If the grain structur structuree is not equiaxed equiaxed,, but elongated, elonga ted, then grain size measur measurements ements on specime specimens ns with differ dif ferent ent ori orient entatio ations ns will var vary y. In this case, the gra grain in size shou sh ould ld be ev evalu aluate ated d on at lea least st tw two o of th thee th thre reee pr prin incip ciple le planes, plan es, tra transv nsvers erse, e, lon longit gitudi udinal nal,, and pla planar nar (or rad radial ial and transverse for round bar) and averaged as described in Section 16 to 16  to obtain the mean grain size. If directed test lines are used, rather than test circles, intercept counts on non-equiaxed grains in plate or sheet type specimens can be made using only two principle test planes, rather than all three as required for the planimetric method. 7.3 The surface surface to be polished polished should should be large enough enough in area to permit measurement of at least five fields at the desired

9. Preparat Preparation ion of Photomicrographs Photomicrographs 9.1 When pho photom tomicro icrogra graphs phs are use used d for esti estimati mating ng the average grain size, they shall be prepared in accordance with Guide E883 Guide  E883.. 10. Comparison Procedure Procedure 10.1 The comparison comparison procedure shall apply to comple completely tely recrystallized or cast materials with equiaxed grains. 10.2 Whe 10.2 When n gra grain in size esti estimat mation ionss are made by the more convenient comparison method, repeated checks by individuals as well as by interlaboratory tests have shown that unless the appearance of the standard reasonably well approaches that of  the samp sample, le, err errors ors may occ occur ur.. To min minimi imize ze suc such h err errors ors,, the comparison charts are presented in four categories as follows:3 10.2.1   Plate I— Untwinned Untwinned grains (flat etch). Includes grain size numbers 00, 0,   1 ⁄ 2, 1, 11 ⁄ 2, 2, 21 ⁄ 2, 3, 31 ⁄ 2, 4, 41 ⁄ 2, 5, 51 ⁄ 2, 6, 61 ⁄ 2, 7, 71 ⁄ 2, 8, 81 ⁄ 2, 9, 91 ⁄ 2, 10, at 100X. 3

Plates I, II, III, and IV are available from ASTM Headquarters. Order Adjunct: ADJE11201P   (Plate (Plate I),   ADJE11202P   (Plate (Plate II),   ADJE11203P   (Plate (Plate III), and ADJE11204P (Plate ADJE11204P  (Plate IV). A combination of all four plates is also available. Order Adjunct:   ADJE112PS. Adjunct: ADJE112PS.

Copyright by ASTM Int'l (all rights reserved); reserved); Tue Sep 3 16:40:18 EDT 2013 4 Downloaded/printed by Center For Library Initiatives pursuant to License Agreement. No further reproductions authorized.

 

 

E112 − 12

FIG. 1 Example of Untwinned Untwinned Grains Grains (Flat Etch) Etch) from Plate I. Grain Size No. 3 at 100X

FIG. 2 Exampl Example e of Twin Grains (Flat Etch) from from Plate II. Grain Size No. 3 at 100X

10.2.2   Plate II— Twinned Twinned grains (flat etch). Includes grain size numbers, 1, 2, 3, 4, 5, 6, 7, 8, at 100X. 10.2.3   Plate III— Twinne winned d grains (contrast etch). Includes nominal grain diameters of 0.200, 0.150, 0.120, 0.090, 0.070, 0.060, 0.050, 0.045, 0.035, 0.025, 0.020, 0.015, 0.010, 0.005 mm at 75X. 10.2.4   Plate IV— Austenite Austenite grains in steel (McQuaid-Ehn). Includes grain size numbers 1, 2, 3, 4, 5, 6, 7, 8, at 100X. 10.3  Table 1 lists 1  lists a number of materials and the comparison charts that are suggested for use in estimating their average grain sizes. For example, for twinned copper and brass with a contrast etch, use Plate III. NOTE 1—Examples of grain-size standards from Plates I, II, III, and IV are shown in Fig. in  Fig. 1, 1,  Fig. 2, 2,  Fig. 3, 3,  and  Fig. 4. 4.

10.4 The estimati estimation on of micros microscopica copically-de lly-determin termined ed grain size should usually be made by direct comparison at the same magnifi mag nificati cation on as the app approp ropria riate te cha chart. rt. Acc Accomp omplish lish thi thiss by comp co mpar arin ing g a pr proj ojec ected ted ima image ge or a ph phot otom omicr icrog ogra raph ph of a representative field of the test specimen with the photomicrographss of the appro graph appropriate priate standard standard graingrain-size size series, or with suitable reproductions or transparencies of them, and select the photomicrograph which most nearly matches the image of the test specimen or interpolate between two standards. Report this estimated grain size as the ASTM grain size number, or grain diameter, of the chart picture that most closely matches the image of the test specimen or as an interpolated value between two standard chart pictures. 10.5 Good judgment judgment on the part of the observer observer is necessary to select the magnification to be used, the proper size of area (num (n umbe berr of gr grain ains) s),, an and d th thee nu numb mber er an and d lo locat catio ion n in th thee specimen of representative sections and fields for estimating

FIG. 3 Example of Twin Twin Grains (Contrast (Contrast Etch) from Plate III. Grain Size 0.090 mm at 75X

the characteristic or average grain size. It is not sufficient to visually select what appear to be areas of average grain size. Recommendations for choosing appropriate areas for all procedures have been noted in  in   5.2 5.2.. 10.6 Grain size estimations estimations shall shall be made on three or more representative areas of each specimen section.

Copyright by ASTM Int'l (all rights reserved); reserved); Tue Sep 3 16:40:18 EDT 2013 5 Downloaded/printed by Center For Library Initiatives pursuant to License Agreement. No further reproductions authorized.

 

 

E112 − 12

FIG. 4 Exampl Example e of Austenite Austenite Grains in Steel from Plate IV. Grain Size No. 3 at 100X TABLE 2 Microscopically Determined Grain Size Relationships Using Plate III at Various Magnifications

NOTE  1—First line—mean grain diame diameter, ter, d, in mm; in paren parentheses theses—equiv —equivalent alent ASTM grain size number, number, G. NOTE  2—Magnification for Plate III is 75X (row 3 data). Magnification

Chart Picture Number (Plate III) 1

2

3

4

5

6

7

8

9

10 10

11

12

13

14

400X

0.015 (9.2) 0.0075 (11.2) 0.005 (12.3) 0.00375 (13.2) 0.0019 (15.2) —

500X

—

0.030 (7.2) 0.015 (9.2) 0.010 (10.3) 0.0075 (11.2) 0.00375 (13.2) 0.0019 (15.1) —

0.045 (6.0) 0.0225 (8.0) 0.015 (9.2) 0.0112 (10.0) 0.0056 (12.0) 0.0028 (14.0) 0.0022 (14.6)

0.060 (5.2) 0.030 (7.2) 0.020 (8.3) 0.015 (9.2) 0.0075 (11.2) 0.0038 (13.1) 0.003 (13.7)

0.075 (4.5) 0.0375 (6.5) 0.025 (7.7) 0.019 (8.5) 0.009 (10.5) 0.0047 (12.5) 0.00375 (13.1)

0.105 (3.6) 0.053 (5.6) 0.035 (6.7) 0.026 (7.6) 0.013 (9.6) 0.0067 (11.5) 0.00525 (12.1)

0.135 (2.8) 0.0675 (4.8) 0.045 (6.0) 0.034 (6.8) 0.017 (8.8) 0.0084 (10.8) 0.0067 (11.5)

0.150 (2.5) 0.075 (4.5) 0.050 (5.7) 0.0375 (6.5) 0.019 (8.5) 0.009 (10.5) 0.0075 (11.1)

0.180 (2.0) 0.090 (4.0) 0.060 (5.2) 0.045 (6.0) 0.0225 (8.0) 0.0012 (10.0) 0.009 (10.6)

0.210 (1.6) 0.105 (3.6) 0.070 (4.7) 0.053 (5.6) 0.026 (7.6) 0.0133 (9.5) 0.010 (10.3)

0.270 (0.8) 0.135 (2.8) 0.090 (4.0) 0.067 (4.8) 0.034 (6.8) 0.0168 (8.8) 0.0133 (9.5)

0.360 (0) 0.180 (2.0) 0.120 (3.2) 0.090 (4.0) 0.045 (6.0) 0.0225 (8.0) 0.018 (8.7)

0.451 (0/00) 0.225 (1.4) 0.150 (2.5) 0.113 (3.4) 0.056 (5.4) 0.028 (7.3) 0.0225 (8.0)

0.600 (00 + ) 0.300 (0.5) 0.200 (1.7) 0.150 (2.5) 0.075 (4.5) 0.0375 (6.5) 0.03 (7.1)

25X 50X 75X 100X 200X

10.7 When the grains grains are of a size outside outside the range covered by the standard photographs, or when magnifications of 75X or 100X 100 X are not sati satisfa sfacto ctory ry,, oth other er mag magnifi nificati cations ons may be employed for comparison by using the relationships given in Note in  Note 2   and and Table  Table 2. 2. It may be noted that alternative magnifications are usually simple multiples of the basic magnifications.

number.. Thu number Thus, s, for a mag magnifi nificat cation ion of 25X 25X,, the tru truee AST ASTM M gra grainin-siz sizee number is four numbers lower than that of the corresponding photomicrograph at 100X (Q = −4). Likewise, for 400X, 400X, the true ASTM grain-size number is four numbers higher ( Q  = +4) than that of the correspondin corresponding g photomicrograph at 100X. Similarly, for 300X, the true ASTM grain-size number is four numbers higher than that of the corresponding photomicrograph at 75X.

NOTE 2—If the grain size is reported in ASTM numbers, it is convenient to use the relationship: (2 )

10.8 The small number number of grains per field at the coarse end of the chart series, that is, size 00, and the very small size of the grain gr ainss at th thee fin finee en end d mak makee acc accur urate ate co comp mpar ariso ison n ra ratin tings gs

log10 ~ M  /  M b ! where Q  is a correction factor that is added to the apparent micro-grain size of the specimen, as viewed at the magnification,  M , instead of at the basic magnification, M b (75X or 100X 100X), ), to yield the true ASTM grain-size grain-size

difficult. When the specimen grain size falls at either end of the chart range, a more meaningful comparison can be made by changing the magnification so that the grain size lies closer to the center of the range.

Q 5 2 log2 ~ M  /  M b ! 5 6.64

 

Copyright by ASTM Int'l (all rights reserved); reserved); Tue Sep 3 16:40:18 EDT 2013 6 Downloaded/printed by Center For Library Initiatives pursuant to License Agreement. No further reproductions authorized.

Center For Library Initiatives pursuant to License Agreement. No further reproductions authorized.  

 

E112 − 12 TABLE 3 Macroscopic Grain Size Relationships Computed for Uniform, Randomly Oriented, Equiaxed Grains

NOTE 1—Macroscopically determined grain size numbers M-12.3, M-13.3, M-13.8 and M-14.3 correspond, respectively, to microscopically determined grain size numbers ( G) 00, 0, 0.5 and 1.0. ¯ A  Grains/Unit Area N 

 

¯   Average Grain Area A

Macro Grain Size No.

No./mm2

No./in.2

mm2

M-0 M-0.5 M-1.0 M-1.5 M-2.0 M-2.5 M-3.0 M-3.5 M-4.0 M-4.5 M-5.0 M-5.5 M-6.0 M-6.5 M-7.0 M-7.5

0.0008 0.0011 0.0016 0.0022 0.0031 0.0044 0.0062 0.0088 0.0124 0.0175 0.0248 0.0351 0.0496 0.0701 0.099 0.140

0.50 0.71 1.00 1.41 2.00 2.83 4.00 5.66 8.00 11.31 16.00 22.63 32.00 45.26 64.00 90.51

1290.3 912.4 645.2 456.2 322.6 228.1 161.3 114.0 80.64 57.02 40.32 28.51 20.16 14.26 10.08 7.13

M-8.0 M-8.5 M-9.0 M-9.5 M-10.0 M-10.5 M-11.0 M-11.5 M-12.0 M-12.3 M-12.5 M-13.0 M-13.3 M-13.5 M-13.8 M-14.0 M-14.3

0.198 0.281 0.397 0.561 0.794 1.122 1.587 2.245 3.175 3.908 4.490 6.349 7.817 8.979 11.055 12.699 15.634

128.0 181.0 256.0 362.1 512.0 724.1 1024.1 1448.2 2048.1 2521.6 2896.5 4096.3 5043.1 5793.0 7132.1 8192.6 10086.3

5.04 3.56 2.52 1.78 1.26 0.891 0.630 0.0445 0.315 0.256 0.223 0.157 0.128 0.111 0.091 0.079 0.064

¯  Average Diameter d 

 

in.2

mm

2.00 1.41 1.00 0.707 0.500 0.354 0.250 0.177 0.125 0.0884 0.0625 0.0442 0.0312 0.0221 0.0156 0.0110 ×10−3 7.812 5.524 3.906 2.762 1.953 1.381 0.977 0.690 0.488 0.397 0.345 0.244 0.198 0.173 0.140 0.122 0.099

35.9 30.2 25.4 21.4 18.0 15.1 12.7 10.7 8.98 7.55 6.35 5.34 4.49 3.78 3.17 2.67 2.25 1.89 1.59 1.33 1.12 0.994 0.794 0.667 0.561 0.506 0.472 0.397 0.358 0.334 0.301 0.281 0.253

in. 1.41 1.19 1.00 0.841 0.707 0.595 0.500 0.420 0.354 0.297 0.250 0.210 0.177 0.149 0.125 0.105 ×10−3 88.4 74.3 62.5 52.6 44.2 37.2 31.2 26.3 22.1 19.9 18.6 15.6 14.1 13.1 11.8 11.0 9.96

 

!¯  Mean

mm 32.00 26.91 22.63 19.03 16.00 13.45 11.31 9.51 8.00 6.73 5.66 4.76 4.00 3.36 2.83 2.38 2.00 1.68 1.41 1.19 1.00 0.841 0.707 0.595 0.500 0.451 0.420 0.354 0.319 0.297 0.268 0.250 0.225

Intercept in. 1.2 1.0 0.89 0.74 0.63 0.53 0.44 0.37 0.31 0.26 0.22 0.18 0.15 0.13 0.11 0.093 ×10−3 78.7 66.2 55.7 46.8 39.4 33.1 27.8 23.4 19.7 17.7 16.6 13.9 12.5 11.7 10.5 9.84 8.87

 

¯ L N 

 

¯  N 

mm−1

100 mm

0.031 0.037 0.044 0.053 0.063 0.074 0.088 0.105 0.125 0.149 0.177 0.210 0.250 0.297 0.354 0.420

3.13 3.72 4.42 5.26 6.25 7.43 8.84 10.51 12.50 14.87 17.68 21.02 25.00 29.73 35.36 42.05

0.500 0.595 0.707 0.841 1.00 1.19 1.41 1.68 2.00 2.22 2.38 2.83 3.14 3.36 3.73 4.00 4.44

50.00 59.46 70.71 84.09 100.0 118.9 141.4 168.2 200.0 221.9 237.8 282.8 313.8 336.4 373.2 400.0 443.8

transparenc parencies ies4 or prints of the standards, 10.9 The use of trans with the standard and the unknown placed adjacent to each other, is to be preferred to the use of wall chart comparison with the projected image on the microscope screen.

magnificat magnifi cation ion,, thr throug ough h bel bellow lowss ext extens ension ion,, or obj object ective ive or 5 eyepiece eyepie ce replace replacement ment betwee between n estimate estimatess   (1).

10.10 particular signi significance ficance attached to the fact thatt No tha differ dif ferent ent obs observ ervers ers often oft en should obtain obt ain be slightly slig htly dif differ ferent ent results, provided the different results fall within the confidence limits reasonably expected with the procedure used.

magnification of 1X, of the properly prepared specimen, or of  a photograph of a representative field of the specimen, with photographs of the standard grain series shown in Plate I (for untwinned material) and Plates II and III (for twinned material). Since the photographs of the standard grain size series were made at 75 and 100 diameters magnification, grain sizes esti es tima mate ted d in th this is wa way y do no nott fa fall ll in th thee st stan anda dard rd AS ASTM TM grain-size grain -size series and hence hence,, prefe preferably rably,, shoul should d be expre expressed ssed eith ei ther er as di diam amet eter er of th thee av aver erag agee gr grai ain n or as on onee of th thee macro-grain size numbers listed in   Table 3. 3. For the smaller macroscopic grain sizes, it may be preferable to use a higher magnifi mag nificat cation ion and the cor correc rection tion fac factor tor giv given en in   Note Note 3, particularly if it is desirable to retain this method of reporting.

10.12 Make the estimati estimation on of macros macroscopica copically-de lly-determin termined ed grain gr ain si sizes zes (e (ext xtre reme mely ly co coar arse se)) by di dire rect ct co comp mpar aris ison on,, at a

10.11 There is a pos 10.11 possib sibilit ility y whe when n an ope operat rator or mak makes es repeated pea ted che checks cks on the sam samee spe specime cimen n usi using ng the com compar pariso ison n method that they will be prejud prejudiced iced by their first estimate. This disadvantage can be overcome, when necessary, by changes in

4 Transparencies of the various grain sizes in Plate I are available from ASTM Headquarters. Order Adjunct:  Adjunct:   ADJE112TS for ADJE112TS  for the set. Transparencies of individual grain size groupings are available on request. Order Adjunct:  ADJE11205T  ADJE11205T (Grain  (Grain Size 00),   ADJE11206T   (Grai (Grain n Si Size ze 0),   ADJE11207T   (Grain (Grain Siz Sizee 0.5) 0.5),, ADJE11208T (Grain ADJE11208T  (Grain Size 1.0), ADJE11209T 1.0),  ADJE11209T (Grain  (Grain Size 1.5), ADJE11210T 1.5),  ADJE11210T (Grain  (Grain Size 2.0),  2.0),   ADJE11211T (Grain ADJE11211T  (Grain Size 2.5),   ADJE11212T (Grain ADJE11212T  (Grain Sizes 3.0, 3.5, and 4.0), ADJE11213T 4.0),  ADJE11213T (Grain  (Grain Sizes 4.5, 5.0, and 5.5),  ADJE11214T  ADJE11214T   (Grain Sizes 6.0, 6.5, and 7.0), ADJE11215T 7.0), ADJE11215T (Grain  (Grain Sizes 7.5, 8.0, and 8.5), and ADJE11216T and ADJE11216T (Grain  (Grain Sizes 9.0, 9.5, and 10.0). Charts illustrating grain size numbers 00 to 10 are on 81 ⁄ 2 by 11 in. (215.9 by 279.4 mm) film. Transparencies for Plates II, III, and IV are not available.

Copyright by ASTM Int'l (all rights reserved); reserved); Tue Sep 3 16:40:18 EDT 2013 Downloaded/printed by

NOTE   3—If 3—If the gra grain in siz sizee is rep report orted ed in ASTM macro-gr macro-grain ain size numbers, it is convenient to use the relationship:

5

The boldface numbers in parentheses refer to the list of references appended to these test methods.

7

Center For Library Initiatives pursuant to License Agreement. No further reproductions authorized.

 

 

E112 − 12 TABLE 4 Grain Size Relationships Computed for Uniform, Randomly Oriented, Equiaxed Grains ¯ A  Grains/Unit Area N 

¯   Average Grain Area A

 

 

¯   Average Diameter d 

 

!¯   Mean

Intercept

¯ L N 

 

Grain Size No. G 

No./in.2 at 10 100X 0X

No./ No ./mm mm2 at 1X

mm2

µm2

mm

µm

mm

µm

No./mm

00 0 0.5 1.0 1.5 2.0 2.5 3.0

0.25 0.50 0.71 1.00 1.41 2.00 2.83 4.00

3.88 7.75 10.96 15.50 21.92 31.00 43.84 62.00

0.2581 0.1290 0.0912 0.0645 0.0456 0.0323 0.0228 0.0161

258064 129032 91239 64516 45620 32258 22810 16129

0.5080 0.3592 0.3021 0.2540 0.2136 0.1796 0.1510 0.1270

508.0 359.2 302.1 254.0 213.6 179.6 151.0 127.0

0.4525 0.3200 0.2691 0.2263 0.1903 0.1600 0.1345 0.1131

452.5 320.0 269.1 226.3 190.3 160.0 134.5 113.1

2.21 3.12 3.72 4.42 5.26 6.25 7.43 8.84

3 4..5 0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0

5 8..6 06 0 11.31 16.00 22.63 32.00 45.25 64.00 90.51 128.00 181.02 256.00 362.04 512.00 724.08 1024.00 1448.15 2048.00 2896.31 4096.00 5792.62 8192.00

18274.6 .080 175.36 248.00 350.73 496.00 701.45 992.00 1402.9 1984.0 2805.8 3968.0 5611.6 7936.0 11223.2 15872.0 22446.4 31744.1 44892.9 63488.1 89785.8 126976.3

.00181046 00.0 0.00570 0.00403 0.00285 0.00202 0.00143 0.00101 0.00071 0.00050 0.00036 0.00025 0.00018 0.00013 0.000089 0.000063 0.000045 0.000032 0.000022 0.000016 0.000011 0.000008

181046055 5703 4032 2851 2016 1426 1008 713 504 356 252 178 126 89.1 63.0 44.6 31.5 22.3 15.8 11.1 7.9

0 0..1 00 86 98 8 0.0755 0.0635 0.0534 0.0449 0.0378 0.0318 0.0267 0.0225 0.0189 0.0159 0.0133 0.0112 0.0094 0.0079 0.0067 0.0056 0.0047 0.0040 0.0033 0.0028

18096..88 75.5 63.5 53.4 44.9 37.8 31.8 26.7 22.5 18.9 15.9 13.3 11.2 9.4 7.9 6.7 5.6 4.7 4.0 3.3 2.8

0 0..0 09 85 01 0 0.0673 0.0566 0.0476 0.0400 0.0336 0.0283 0.0238 0.0200 0.0168 0.0141 0.0119 0.0100 0.0084 0.0071 0.0060 0.0050 0.0042 0.0035 0.0030 0.0025

9 85 0..1 0 67.3 56.6 47.6 40.0 33.6 28.3 23.8 20.0 16.8 14.1 11.9 10.0 8.4 7.1 5.9 5.0 4.2 3.5 3.0 2.5

1 10 2..5 51 0 14.87 17.68 21.02 25.00 29.73 35.36 42.04 50.00 59.46 70.71 84.09 100.0 118.9 141.4 168.2 200.0 237.8 282.8 336.4 400.0

Q m   5 2 log2   M 

 

ASTM gra ASTM grain in size sizess pre presen sented ted in   Tabl Tablee 4.   This coinci coincidence dence makes the fracture grain sizes interchangeable with the austenitic nit ic gra grain in size sizess det determ ermined ined micr microsc oscopi opicall cally y. The size sizess observed ser ved micr microsc oscopi opicall cally y sha shall ll be con consid sidere ered d the pri primar mary y standard, since they can be determined with measuring instruments.

(3 )

5 6.64 log 10   M  where Q M  is a correction factor that is added to the apparent grain size of the specimen, when viewed at the magnification  M , instead of at 1X, to yield the true ASTM macro-grain size number. Thus, for a magnification of 2X, the true ASTM macro-grain size number is two numbers higher (Q  = +2), and for 4X, the true ASTM macro-grain size number is four numbers higher (Q = +4) than that of the corresponding photograph.

11. Planimetr Planimetric ic (or Jeffries’) Jeffries’) (3 ( 3) Procedure 11.1 In the planimetric procedure 11.1 procedure inscribe inscribe a circle or rectangl an glee of kn know own n ar area ea (u (usu sual ally ly 50 5000 00 mm2 to si simp mplif lify y th thee calcula calc ulation tions) s) on a micr microgr ograph aph,, a mon monito itorr or on the gro ground und-glass screen of the metallograph. Select a magnification which will give at least 50 grains in the field to be counted. When the image is focused properly, count the number of grains within this area. The sum of all the grains included completely within the known area plus one half the number of grains intersected by the circumference of the area gives the number of equivalent whole grains, measured at the magnification used, within the area. If this number is multiplied by the Jeffries’ multiplier,  f , in the second column of   of   Table 5   opposite the appropriate magnification, the product will be the number of grains per squaree millimet squar millimetre re   N  A   . Count a minimum of three fields to ensure a reasonable average. The number of grains per square millimetre at 1X,   N  A  , is calculated from:

10.13 The com 10.13 compar pariso ison n pro proced cedure ure shall shall be app applica licable ble for estim est imati ating ng th thee au aust sten enite ite gr grai ain n siz sizee in fe ferr rrit itic ic ste steel el af afte terr a McQuaid-Ehn testrevealed (see  Annex (see Annex A3,other A3,  A3.2),  A3.2 ), or after austenite grains have been by any means (seethe  Annex A3, A3, A3.3). A3.3 ). Mak Makee the gra grainin-siz sizee mea measur suremen ementt by com compar paring ing the microscopic image, at magnification of 100X, with the standard grain size chart in Plate IV, for grains developed in a McQuaid-Ehn test (see   Annex A3); A3); for the measurement of  austenite grains developed by other means (see   Annex A3), A3), measure by comparing the microscopic image with the plate having the most nearly comparable structure observed in Plates I, II, or IV. 10.14 10 .14 The so so-ca -calle lled d “Sh “Shep ephe herd rd Fr Fract actur uree Gr Grain ain Siz Sizee Method” of jud Method” judgin ging g gra grain in size from the appearanc appearancee of the fractu fra cture re of har harden dened ed stee steell   (2), inv involv olves es com compar pariso ison n of the specimen specime n under investigation investigation with a set of standa standard rd fractures.6 It has been found that the arbitrarily numbered fracture grain

 S

size ser series ies agr agree ee well with the cor corres respon pondin dingly gly num number bered ed

 

(4 )

where  f  is the Jeffries’ multiplier (see  Table 5), 5),  N Inside Inside  is the number of grains completely inside the test circle and   N Intercepted  is the number of grains that intercept the test circle. The ¯ , is the reciprocal of   N  A  , that is, 1/  N  A  , average grain area,   A

6 A photograph of the Shepherd standard fractures can be obtained from ASTM Headquarters. Order Adjunct: ADJE011224 Adjunct:  ADJE011224..

Copyright by ASTM Int'l (all rights reserved); reserved); Tue Sep 3 16:40:18 EDT 2013 Downloaded/printed by

 D

 N  Intercepted  N   A   5  f   N  Inside 1 2

8

Center For Library Initiatives pursuant to License Agreement. No further reproductions authorized.

 

 

E112 − 12

TABLE 5 Relationship Between Magnification Used and Jeffries’ Multiplier,   f , for an Area of 5000 mm 2 (a Circle of 79.8-mm Diameter) (f    = 0.0002   M 2) Magnification Used, M  Used,  M  1 10 25 50 75A 100 150 200 250 300 500 750 1000

 

TABLE 6 Grain Size Equations Relating Measured Parameters to the Microscopically Microscopically Deter Determined mined ASTM Grain Size,   G 

NOTE   1—Determi 1—Determine ne the ASTM Grain Size,   G, usi using ng the fol follow lowing ing equations:

Jeffries’ Multiplier, Multiplier, f   f , to Obtain Grains/mm2 0.0002 0.02 0.125 0.5 1.125 2.0 4.5 8.0 12.5 18.0 50.0 112.5 200.0

NOTE   2—The second and third equations are for single phase grain structures. NOTE   3—To convert micrometres to millimetres, divide by 1000. NOTE  4—A calculated  G  value of − 1 corresponds to ASTM  G  = 00. Equation

Units

¯ A  ) − 2.954 G  =   = (3.321928 log10 N  ¯ L  ) − 3.288 G  =   = (6.643856 log10 N  G  =   = (6.643856 log10 P L  ) − 3.288 G  =   = (−6.643856 log10  ! ) − 3.288

       

N A  in mm−2 ¯ L  in mm−1 N  P L  in mm−1 !  in mm

A

At 75 diameters magnification, Jeffries’ multiplier,   f , becomes unity if the area used is 5625 mm2 (a circle of 84.5-mm diameter).

intersecting each of the four corners are, on average, one fourth within the figur figures es and three-fourths three-fourths outside. These four corne cornerr grains together equal one grain within the test box. 11.5.2 11 .5.2 Igno Ignoring ring the four corner grains, grains, a count is made of  completely within the box, and of  N   N  Inside, the grains completely  N  Interc  Intercepted  epted , the grains intersected by the four sides of the box.   Eq 4   now becomes:

while the mean grain diameter,   d , as listed on Plate III (see ¯ . This grain diameter has no 10.2.3), 10.2.3 ), is the square root of   A physical significance because it represents the side of a square grain of area  A¯ , and grain cross sections are not square. 11.2 To obt obtain ain an accu accurat ratee cou count nt of the num number ber of gra grains ins completely comple tely within the tes testt circ circle le and the num number ber of gra grains ins intersecting the circle, it is necessary to mark off the grains on the template, for example, with a grease pencil or felt tip pen. The precision of the planimetric method is a function of the number num ber of gra grains ins cou counte nted d (se (seee Sec Section tion   19 19). ). The num number ber of  grains within the test circle, however, should not exceed about 100 as counting becomes tedious and inaccurate. Experience sugges sug gests ts that a mag magnifi nificati cation on tha thatt pro produc duces es abo about ut 50 gra grains ins within the test circle is about optimum as to counting accuracy per field. Because of the need to mark off the grains to obtain an accurate count, the planimetric method is less efficient efficient than the intercept method (see Section 12 Section  12). ).

5

 N  A

1

1

0.5 N Intercepted

1)

(5)

where M  is   is the magnification,  A  is the test figure area in mm 2 and   N  A   is the number of grains per square millimeter at 1×. Select the fields at random, as described in 11.3 in  11.3.. It is recommended that enough fields should be evaluated so that a total of  ~700 ~70 0 gra grains ins are cou counte nted d whi which ch will usually usually pro provid videe a 10% relative accuracy (see  (see   Appendix X1, X1,  paragraph  paragraph X1.3.2  X1.3.2). ). 11.5.3 11 .5.3 The average average grain area, A¯ , is the reciprocal of  N   N  A  and the mean grain diameter, d, is the square root of  A¯ , as described in   11.1. 11.1.   The ASTM grain size number,   G, can be estimated using the data in Table in  Table 4, 4, or can be calculated from  N  A  using Eq (1) in Table in  Table 6. 6.

11.3 Fiel Fields ds sho should uld be cho chosen sen at ran random dom,, with without out bias, as described in 5.2 in  5.2..  Do not attempt to choose fields that appear to be typ typical ical.. Cho Choose ose the field fieldss blin blindly dly and sele select ct the them m fro from m different locations on the plane of polish.

12. General Intercept Intercept Procedures Procedures 12.1 Inter Intercept cept procedures procedures are more convenient to use than the planimetric procedure. These procedures are amenable to use with various types of machine aids. It is strongly recommended that at least a manual tally counter be used with all interce int ercept pt pro proced cedure uress in ord order er to pre preven ventt nor normal mal err errors ors in counting and to eliminate bias which may occur when counts appear to be running higher or lower than anticipated.

11.4 11 .4 By origin original al defini definition, tion, a micros microscopica copically-de lly-determine termined d grain size of No. 1 has 1.000 grains/in. grains/in.2 at 100X, hence 15.500 grains/mm2 at 1X. For areas other than the standard circle, determine the actual number of grains per square millimetre,  N  A , and find the nearest size from   Table 4. 4.  The ASTM grain size number,   G, can be calculated from  N  A  (number of grains per mm2 at 1X) using ( using  (Eq Eq 1) in in Table  Table 6. 6.

12.2 Intercept procedures are recommended particularly for all structures that depart from the uniform equiaxed form. For anisotropic structures, procedures are available either to make separate size estimates in each of the three principal directions, or to rationally estimate the average size, as may be appropriate.

11.5 Thi Thiss app approa roach ch ass assume umess tha that, t, on ave averag rage, e, hal halff of the grains intersecting the test circle are within the circle while half  are outside the circle. This assumption is valid for a straight line through a grain structure, but not necessarily for a curved line.. The bias cre line created ated by thi thiss ass assump umptio tion n inc increa reases ses as the numberr of grain numbe grainss inside the test circle decreases. decreases. If the number of grains within the test circle is at least 50, the bias is about 2%. 11.5.1 11 .5.1 There is a simple simple way ( way (4 4)  to avoid this bias, irrespective of the number of grains inside the test figure - use a square or rectangulat test area. However, the counting procedure must be mo modi difie fied d sli sligh ghtly tly.. Fi Firs rst, t, it is as assu sume med d th that at th thee gr grain ainss Copyright by ASTM Int'l (all rights reserved); reserved); Tue Sep 3 16:40:18 EDT 2013 Downloaded/printed by

2

( M   ⁄  A ) ( N Inside

12.3 There is no direct mathematical relationship relationship between the ASTM grain size number,  G , and the mean lineal intercept, unlike the exact relationship between  G ,  N  AE  ,  N  A and  A¯   (Eq 1) 1) for the planimetric method. The relationship

S ¯ D  π

ℓ5

9

4

 A

 ½

(6 )

Center For Library Initiatives pursuant to License Agreement. No further reproductions authorized.  

 

E112 − 12

between the mean lineal intercept,   ℓ, and the average grain area,  A¯ , is exact for circles but not quite exact for a structure of  uniform equiaxed grains (see A2.2.2 (see  A2.2.2). ). Consequently, the relationship tionsh ip between the ASTM grain size number G  and the mean lineal intercept has been defined so that ASTM No. 0 has a mean intercept size of precis precisely ely 32.00 mm for the macros macroscopicopically determined grain size scale and of 32.00 mm on a field of  view at 100X magnification for the microscopically determined grain size scale. Thus:

grain boundary. Either may be counted, with identical results in a single phase material. When counting intercepts, segments at the end of a test line which penetrate into a grain are scored as half intercepts. When counting intersections, intersections, the end points of  a test line are not intersections and are not counted except when the end appears to exactly touch a grain boundary, when   1 ⁄ 2 intersection should be scored. A tangential intersection with a grain gr ain bo boun unda dary ry sh shou ould ld be sc scor ored ed as on onee in inte ters rsect ectio ion. n. An intersection apparently coinciding with the junction of three 1

G 5 2log2

ℓ0

Hℓ

 

(7 )

G 5 10.00 2 2log2  ℓH

¯  L G 5 10.001 2log 2  N 

grains should be scoredtwo as 1intersections  ⁄ 2 . With irregular grain shapes, test line may generate with different partsthe of  the same gra grain, in, tog togeth ether er with a thi third rd int inters ersecti ection on wit with h the intrud int ruding ing gra grain. in. The two add additio itional nal int inters ersecti ections ons are to be counted.

(8 )  

(9 )

13.4 The ef 13.4 effec fects ts of mod modera erate te dep departu arture re fro from m an equ equiax iaxed ed structure may be eliminated by making intercept counts on a line array containing lines having four or more orientations. The four straight lines of  Fig.  Fig. 57 may be used. The form of such arrays is not critical, provided that all portions of the field are measured with approximately equal weight. An array of lines radiating from a common point is therefore not suitable. The number of intercepts is to be counted for the entire array and single values of  N   N  L and  ℓ  determined for each array as a whole.

¯  L  are in millimetres at 1X or where  ℓ 0  is 32 mm and  ℓ¯ and  N  number of intercepts per mm for the macroscopically determined grain size numbers and in millimetres or number per mm on a fiel field d at 100 100X X for the micr microsc oscopi opicall cally y dete determi rmined ned grain gra in size numbers. numbers. Usi Using ng this scale, meas measure ured d gra grain in siz sizee numbers are within about 0.01   G  units of grain size numbers determined by the planimetric method, that is, well within the precision precisi on of the test method methods. s. Additional Additional details concerning concerning grain size relationships are given in Annex in  Annex A1 and A1  and  Annex A2. A2.

13.5 For distinctly non-equiaxe non-equiaxed d structures such as moder moder-ately atel y wor worked ked metals, metals, mor moree inf inform ormatio ation n can be obt obtain ained ed by making separate size determinations along parallel line arrays that coincide with all three principal directions of the specimen. Longitudinal and transverse specimen sections are normally used, the normal section being added when necessary. Either of the 100-mm lines of  Fig.  Fig. 5 may 5  may be applied five times, using parallel parallel displacements, displacements, placing the five “ + ” marks at the same point on the image. Alternatively, a transparent test grid with systematically spaced parallel test lines of known length can be made and used.

12.4 The mean intercept distance, distance,   ℓ¯, measured on a plane section is an unbiased estimate of the mean intercept distance within the solid material in the direction, or over the range of  directi dir ections ons,, mea measur sured. ed. The gra grain in bou bounda ndary ry sur surfac facee are area-t a-toovolume ratio is given exactly by  S v   = 2  N  L when N  L is averaged over three dimensions. These relations are independent of grain shape. 13. Heyn (4) Line Lineal al Intercept Intercept Procedure Procedure 13.1 Esti 13.1 Estimate mate the ave averag ragee gra grain in size by cou countin nting g (on the ground-glass screen, on a photomicrograph of a representative field of the specimen, a monitor or on the specimen itself) the number num ber of gra grains ins int interc ercept epted ed by one or mor moree str straigh aightt lin lines es sufficiently long to yield at least 50 intercepts. It is desirable to select a combination of test line length and magnification such

14. Circular Intercept Intercept Procedures Procedures 14.1 Use of circular test lines rather than straight straight test lines has bee been n adv advoca ocated ted by Und Underw erwood ood   (6), Hil Hilliar liard d   (7), an and d Abrams ( Abrams  (8 8). Circular test arrays automatically compensate for departures from equiaxed grain shapes, without overweighting any local portio portion n of the field. Ambiguou Ambiguouss interse intersections ctions at ends of test lines are eliminated. Circular intercept procedures are most suitable for use as fixed routine manual procedures for grain size estimation in quality control.

that a single field will yield the required number of intercepts. One such test will nominally allow estimation of grain size to the nearest whole ASTM size number, at the location tested. Additional lines, in a predetermined array, should be counted to obtain obt ain the pre precisi cision on req requir uired. ed. The pre precisi cision on of gra grain in siz sizee estimates by the intercept method is a function of the number of grain interceptions counted (see Section   19 19)). Because the ends of straight test lines will usually lie inside grains (see 14.3), 14.3 ), precision will be reduced if the average count per test line is low. If possible, use either a longer test line or a lower magnification.

14.2   Hilliard Single-Circle Procedure   (7)   : 14.2.1 14.2. 1 When the grain shape shape is not equiaxed but is distorted by deformation deformation or other proce processes, sses, obtaining an averag averagee lineal intercept value using straight test lines requires averaging of  values made at a variety of orientations. If this is not done carefully, bias may be introduced. Use of a circle as the test line eliminates this problem as the circle will test all orientations equally and without bias. 14.2.2 14.2. 2 Any circle size of exactly known circumferen circumference ce may

13.2 Make counts counts first on three to five blindly selected and widely separated fields to obtain a reasonable average for the specimen. If the apparent precision of this average (calculated as indicated in Section   15 15)) is not adequate, make counts on sufficient additional fields to obtain the precision required for the specimen average.

be used. Circumferences of 100, 200, or 250 mm are usually

13.3 An  intercept  is a segment of test line overlaying one 13.3 grain. An   intersection   is a point where a test line is cut by a Copyright by ASTM Int'l (all rights reserved); reserved); Tue Sep 3 16:40:18 EDT 2013 Downloaded/printed by

7

A true-size transparency of Fig. 5 is available from ASTM Headquarters. Order Adjunct:ADJE11217F.

10

Center For Library Initiatives pursuant to License Agreement. No further reproductions authorized.  

 

E112 − 12

NOTE  1—If reproduced to make straight lines marked length: Straight lines total: 500 mm Circles are:

Circumference, mm, 250.0 166.7 83.3 Total 500.0

Diameter, mm 79.58 53.05 26.53

NOTE  2—See Footnote 9. FIG. 5 Test Pattern for Intercept Intercept Counting Counting

convenient. The test circle diameter should never be smaller than the largest observed grains. If the test circle is smaller than about three times the mean lineal intercept, the distribution of  the number of intercepts or intersections per field will not be Gaussian. Also, use of small test circles is rather inefficient as a great many fields must be evaluated to obtain a high degree of precision. precision. A small reference reference mark is usually placed placed at the top of the circle to indicate the place to start and stop the count. Blindly apply the selected circle to the microscope image at a convenient known magnification and count the number of grain boundaries intersecting the circle for each application. Apply the circle only once to each field of view, adding fields in a representative manner, until sufficient counts are obtained to yield the required precision. The variation in counts per test circle application decreases as the circle size increases and, of  course, is affected by the uniformity of the grain size distribution. Copyright by ASTM Int'l (all rights reserved); reserved); Tue Sep 3 16:40:18 EDT 2013 Downloaded/printed by

14.2.3 As with all intercept procedures 14.2.3 procedures,, the precision of the measurement increases as the number of counts increases (see Section 19 Section  19). ). The precision is based on the standard deviation of  the counts of the number of intercepts or intersections per field. In general, for a given grain structure, the standard deviation is improved as the count per circle application and the total count (that is, the number of applications) increase. Hilliard recommended mende d test conditions conditions that produce about 35 counts per circle with the test circle applied blindly over as large a specimen areaa as fea are feasib sible le unt until il the desired desired tota totall num number ber of cou counts nts is obtained. 14.3   Abrams Three-Circle Procedure   (8)  : 14.3.1 14.3. 1 Based on an experimental experimental finding finding that a total of 500 counts per spe counts specim cimen en nor normal mally ly yie yields lds acce accepta ptable ble pre precisi cision, on, Abrams Abr ams dev develo eloped ped a spe specifi cificc pro proced cedure ure for rou routin tinee ave averag ragee grain size rating of commercial steels. Use of the chi-square 11

Center For Library Initiatives pursuant to License Agreement. No further reproductions authorized.

 

 

E112 − 12 counting correctly at the count density recommended. Completely count each circle in turn, using a manually operated counter cou nter to accu accumul mulate ate the tota totall num number ber of gra grain in bou bounda ndary ry inter in tersec sectio tions ns wi with th th thee tes testt pa patt tter ern. n. Th Thee ma manu nual al co coun unter ter is necess nec essary ary to avo avoid id bia biass tow toward ard unr unreal eal agr agreem eement ent bet betwee ween n appl ap plic icati ation onss or to towa ward rd a de desi sire red d re resu sult, lt, an and d to mi mini nimi mize ze memory errors. The operator should avoid keeping a mental score. When a tally counter is used, score any intersection of  the circle with the junction of three grains as two rather than 1

the14.3. correct value 1  ⁄ 2 count,  ; the introduced very small. 14.3.3 3 For eachoffield cou nt,error calcula calculate te  N  L or  Pis  L  according to:

¯  L   5  N  ¯  P  5  L

Pi  L /  M 

 

(10)

 

(11)

where  N i  and  P i  are the number of intercepts or intersections counted on the field,  L  is the total test line length (500 mm) and  M  is   is the magnification. 14.3.4 14. 3.4 Calc Calcula ulate te the mean lin lineal eal inte interce rcept pt val value ue for each ¯ field,   ℓ by:

FIG. 6 Aver Average age Intercept Intercept Counts on 500 mm Test Pattern

test on real data demonstrated that the variation of intercept counts cou nts is clos closee to nor normal mal,, allo allowin wing g the obs observ ervatio ations ns to be treated by the statistics of normal distributions. Thus both a measuree of variab measur variability ility and the confid confidence ence limit of the result are computed for each average grain size determination. 14.3.2 14. 3.2 The test patt pattern ern con consis sists ts of thr three ee con concen centric tric and equally spaced circles having a total circumference of 500 mm, as shown in  Fig. 5. 5.  Successively apply this pattern to at least five blin blindly dly sele selected cted and wid widely ely spa spaced ced field fields, s, sep separa arately tely recording the count of intersections per pattern for each of the tests. Then, determine the mean lineal intercept, its standard deviation, 95 % confidence limit, and percent relative accuracy. For most work, a relative accuracy of 10 % or less represents an acc accepta eptable ble deg degree ree of pre precis cision ion.. If the calc calcula ulated ted rel relativ ativee accuracy is unacceptable for the application, count additional fields until the calculated percent relative accuracy is acceptable. The specific procedure is as follows: 14.3.2.1 14.3. 2.1 Examin Examinee the grain structure structure and select a magnification that will yield from 40 to 100 intercepts or intersection counts per placement of the three circle test grid. Because our goal is to obtain a total of about 400 to 500 counts, the ideal magni mag nific ficati ation on is th that at wh which ich yi yield eldss ab abou outt 10 100 0 co coun unts ts pe perr placeme plac ement. nt. How Howeve ever, r, as the cou count nt per pla placem cement ent inc increa reases ses from fr om 40 to 10 100, 0, er erro rors rs in co coun untin ting g be beco come me mo more re lik likel ely y. Because the grain structure will vary somewhat from field to field,, at leas field leastt five widely widely spa spaced ced fields sho should uld be sel selecte ected. d. Somee meta Som metallog llograp rapher herss fee feell mor moree com comfor fortab table le cou counti nting ng 10 fields with about 40 to 50 counts per field. For most grain structures, a total count of 400 to 500 intercepts or intersections over 5 to 10 fields produces better than 10 % relative accuracy. Fig. 6   shows shows the relatio relationship nship between the averag averagee interc intercept ept count and the microscopically microscopically determined ASTM grain size number as a function of magnification. 14.3.2.2 14.3. 2.2 Blindly select select one field for measurement measurement and apply the test patter pattern n to the image. A transparenc transparency y of the pattern may be applied directly to the ground glass, or to a photomicrograph when permanent records are desired. Direct counting using a properly sized reticle in the eyepiece is allowable, but it may heree be exp her expect ected ed tha thatt som somee ope operat rators ors will find diff difficu iculty lty in Copyright by ASTM Int'l (all rights reserved); reserved); Tue Sep 3 16:40:18 EDT 2013 Downloaded/printed by

 N i  L /  M 

Hℓ 5 1

¯  L  N 

5

1

(12)

¯  P

 L

The average value of   n   determinations of   N  L   ,   P L   , or   ℓ¯ is used to determine the microscopically measured ASTM grain size using the equations in Table in  Table 6, 6, the data shown graphically in Fig. in  Fig. 6, 6,  or the data in  Table 4. 4. 15. Statistical Analysis 15.1 No determination determination of average average grain size can be an exact measurement. Thus, no determination is complete without also calcula calc ulating ting the pre precisi cision on wit within hin whi which ch the det determ ermine ined d size may, with normal confidence, be considered to represent the actu ac tual al av aver erag agee gr grain ain siz sizee of th thee sp spec ecime imen n ex exami amine ned. d. In accorda acco rdance nce with com common mon eng engine ineerin ering g pra practic ctice, e, this sect section ion assumes normal confidence to represent the expectation that the actual error will be within the stated uncertainty 95 % of  the time. 15.1.1 15.1. 1 of Many specim ens vary measurably measurably in grain size from one field viewspecimens to another, this variation being responsible for a major portion of the uncertainty. Minimum effort in manual methods meth ods,, to obt obtain ain a req requir uired ed pre precisi cision, on, jus justifi tifies es ind indivi ividua duall counts whose precision is comparable to this natural variability (7). The high local precision that may be obtained by machine meth me thod odss of often ten wi will ll yi yiel eld d on only ly a sm small all in incr crea ease se in ov over erall all precision unless many fields also are measured, but does help distinguish natural variability from inaccuracies of counting. 15.2 After the desired number of fields have been measured, ¯  A   or   ℓ¯ from the individual field calculate the mean value of   N  values according to:

¯ 5  X 

( X 

i

n

 

(13)

where  X i  represents an individual value,  X  ¯  is the mean and  n is the number of measurements. 15.3 Calculate 15.3 Calculate the stan standar dard d dev deviati iation on of the ind indivi ividua duall measurements according to the usual equation: 12

Center For Library Initiatives pursuant to License Agreement. No further reproductions authorized.

 

 

E112 − 12

~

TABLE 7 95 % Confidence Internal Multipliers,   t  No. of Fields, n Fields,  n

t 

5 6 7 8 9 10 11 12

2.776 2.571 2.447 2.365 2.306 2.262 2.228 2.201

s5

 

 ( ~ X 

F

i

No. of Fields Fields,,  n

t 

13 14 15 16 17 18 19 20

2.179 2.160 2.145 2.131 2.120 2.110 2.101 2.093

¯ !   2

  2  X 

n21

 G

(14)

15.4 Calc 15.4 Calculat ulatee the 95 % con confide fidence nce inte interva rval, l, 95 % CI, of  each measurement according to:

=n

(15)

where the · indica indicates tes a multip multiplication lication operation. operation. Table  Table 7 lists 7  lists values of   t   as a function of  n  n . 15.5 Calculat Calculatee the percen percentt relative accuracy, accuracy, % RA, of the measurements dividing the 95 % CI that value expressing the by results as a percentage, is:by the mean and % RA 5

95% CI ¯    · 100  X 

(17)

(15.1-15.5 15.1-15.5)) only on the indiv individual idual measurements measurements on each field. 16.3   Intercept Method: 16.3 16 .3.1 .1 To To ass asses esss th thee gr grai ain n si size ze of no nonn-eq equi uiax axed ed gr grai ain n structures, struct ures, measurements measurements can be made using circular test grids or randomly placed test lines on each of the three principal principal test planes, or by use of directed test lines in either three or six of  thee pr th prin inci cipa pall di dire recti ction onss us usin ing g eit eithe herr tw two o or th thre reee of th thee princi pri ncipal pal tes testt plan planes, es, see   Fig. Fig. 7. Fo Forr sp spec ecim imen enss wh wher eree th thee departure from an equiaxed shape is not severe ( ≤3:1 aspect ratio) rat io),, a rea reason sonabl ablee est estimat imatee of the gra grain in size can be mad madee using a circular test grid on the longitudinal plane only. 16.3.2 The grain size can be be determined from measurements measurements of the mean number of grain boundary intersections per unit length,  P¯  L  , or the mean number of grains intercepted per unit ¯  L  . Both methods yield the same results for a single length,   N 

  ½

t · s

1/ 3

where whe re · ind indicat icates es a mul multip tiplica licatio tion n ope operat ration ion and the bar above each quantity indicates an average value. 16.2.2 16.2. 2 A reasonable reasonable estimate estimate of the grain size can be made ¯  from  N  Aℓ  alone if the departure from an equiaxed shape is not excessive (≤3:1 aspect ratio). ¯  A   from 16.2.3 16.2. 3 Calculat Calculatee   G   from the mean value of   N  from the averages made on each field. Perform the statistical analysis

where   s  is the standard deviation.

95% CI 5

!

¯   5  N  ¯  A ℓ  · N  ¯  At  · N  ¯  Ap  N 

phase grain structure.  P¯  L  or  N  ¯  L  can be determined using either test circles on each of the principal planes or directed test lines in either three or six of the principal test directions shown in Fig. 7. 7. 16.3.3 16.3. 3 For the case of rando randomly mly determined determined values of  P  P¯  L  or ¯  L   on the three principal planes, compute the average value  N  according to:

(16)

15.6 15 .6 If th thee % RA is co cons nsid ider ered ed to be to too o hi high gh fo forr th thee intended application, more fields should be measured and the calculations in 15.1-15.5 in  15.1-15.5 should  should be repeated. As a general rule, a 10 % RA (or lower) is considered to be acceptable precision for most purposes. ¯   or  ℓ¯ to the ASTM grain 15.7 Conve Convert rt the mean value value of  N   N 

¯  P 5 ~ ¯  P

 L ℓ

1/ 3

!

1/ 3

(18)

or

 A

~

¯   5  N  ¯  L ℓ  · N  ¯  Lt  · N  ¯  Lp  N 

size number,  G , using Table using  Table 4 or 4  or the Eqs in  Table 6. 6.

(19)

¯  L values Alternatively, calculate  ℓ¯ℓ,  ℓ¯t  and  ℓ¯ p from the P¯  L or  N  on each plane using (Eq ( Eq 12) 12). Then, calculate the overall mean ¯ value of   ℓ from:

16. Speci Specimens mens with Non-e Non-equiax quiaxed ed Grai Grain n Shape Shapess 16.1 If the grain shape shape was altered by processing processing so that the grains are no longer equiaxed in shape, grain size measurements should be made on longitudinal ( ℓ), transverse (t  )   ) and planar ( p) oriented surfaces for rectangular bar, plate or sheet type material. For roun round d bars, radial longitudinal longitudinal and transverse sections are used. If the departure from equiaxed is not too great (see  16.2.2  16.2.2)), a reasonable estimate of the grain size can be det determ ermine ined d usi using ng a lon longit gitudi udinal nal spe specime cimen n and the circularr test grid. If directed test lines are used for the analysis, circula measure meas uremen ments ts in the thr three ee pri princi ncipal pal dir directi ections ons can be mad madee using only two of the three principal test planes.

Hℓ 5 ~ Hℓ  · Hℓ  · Hℓ !   1/ 3 ℓ t   p

(20)

16.3.4 If directed test lines are used in the principal 16.3.4 principal directions on the principal planes, only two of the principal planes are required to perform directed counts in the three principal directions and obtain an estimate of the grain size. 16.3.5 16. 3.5 Add Additio itional nal inf inform ormatio ation n on gra grain in sha shape pe may be ob¯ tained by determining  ℓ parallel (0°) and perpendicular (90°) to the deformation axis on a longitudinally oriented surface. The grain gra in elo elonga ngatio tion n rat ratio, io, or the anis anisotr otropy opy ind index, ex,   AI , can be determined from:

16.2   Planimetric Method: 16.2.1 16.2. 1 When the grain shape is not equiaxed but elongated, elongated, make grain counts on each of the three principal principal planes, that is, planes of polish on longitudinal, transverse and planar-oriented surfaces. Determine the number of grains per mm2 at 1X on the longitudinal, transverse, and planar oriented surfaces,  N  ¯  A   ℓ,  N  ¯  At  ¯  and  N  Ap , respectively, and calculate the mean number of grains ¯  A  , from the three  N  ¯  A  values from the principal per unit area,  N  planes: Copyright by ASTM Int'l (all rights reserved); reserved); Tue Sep 3 16:40:18 EDT 2013 Downloaded/printed by

!

P Lt  · ¯  P Lp  · ¯ 

 AI ℓ   5 H ℓ ℓ ~ 0 ° !  / H ℓ ℓ ~ 90° !

 

(21)

16.3.5.1 16.3. 5.1 The three-dimension three-dimensional al mean grain size and shape may al may also so be de defin fined ed by th thee di dire recte cted d me mean an lin lineal eal in inter tercep ceptt values on the three principal planes. These values would be expressed as: Hℓ

13

ℓ ~0 °!

 : H ℓ ℓ ~ 90° !  : H ℓ ℓ ~ 90° !

 

(22)

Center For Library Initiatives pursuant to License Agreement. No further reproductions authorized.

 

 

E112 − 12 computing   ℓ¯ from this mean value; or, by calculating directed values es in each of the three pri princip ncipal al dir directi ections ons and the then n ℓ¯ valu averaging them according to (Eq (Eq 24): 24):

~

¯ 5 P¯  L ℓ ~0 ° !  · P¯  Lt ~90° !  · P¯  Lp~90° ! P

!

1/ 3

(23)

¯  L . For computing the grand This is done in like manner for N  mean   ℓ¯ from the directed mean values, use:

~

Hℓ 5 Hℓ

ℓ ~0° !

 · H ℓ

t ~ 90° !

 · H ℓ p ~ 90° !

!

1/ 3

(24)

where the · indicates a multiplication operation. 16.3.7 16.3. 7 The mean grain size is determ determined ined from the overall ¯ ¯  ¯  averages of  P  P L ,  N  L or  ℓ using using Table  Table 4 or 4  or the equations in Table in  Table 6. Additional information on the measurement of grain size for non-equiax nonequiaxed ed struct structures ures can be foun found d in   Annex A1   of Test Methods E1382 Methods  E1382.. 16.4 Sta 16.4 Statist tistical ical ana analys lysis is sho should uld be per perfor formed med on the dat dataa from each plane or each principal test direction according to the procedure in  15.1-15.5  15.1-15.5.. 17. Specimen Specimenss Conta Containin ining g Two or Mor Moree Phas Phases es or Constituents 17.1 Min 17.1 Minor or amo amount untss of sec second ond pha phase se par particl ticles, es, whe whethe therr desire des ireabl ablee or und undesir esireab eable le fea featur tures, es, may be ign ignore ored d in the determination of grain size, that is, the structure is treated as a single phase material and the previo previously usly described planimetric planimetric or inte interce rcept pt meth methods ods are use used d to dete determi rmine ne the grain siz size. e. Unless stated otherwise, the effective average grain size shall be presumed to be the size of the matrix phase. 17.2 The identity of each measured phase phase and the percen percenttage of field area occupied by each phase shall be determined and reported. The percentage of each phase can be determined according to Practice E562 Practice  E562.. 17.3   Compariso Comparison n Method Method—  — The The com compar pariso ison n cha chart rt rat rating ing procedure may provide acceptable precision for most commercial applications if the second phase (or constituent) consists of  islands   or   patches   of essentially the same size as the matrix grains; or, the amount and size of the second phase particles are both small and the particles are located primarily along grain boundaries. 17.4   Planimetric Method— The The planimetric method may be applied if the matrix grain boundaries are clearly visible and the sec second ond pha phase se (co (const nstitu ituent) ent) par particl ticles es are mai mainly nly pre presen sentt betw be twee een n th thee ma matr trix ix gr grain ainss ra rath ther er th than an wi with thin in th thee gr grain ains. s. Determ Det ermine ine the percentag percentagee of the test area occ occupi upied ed by the second phase, for example, by Practice   E562. E562.  Always determine the amount of the phase of least concentration, usually the second phase or constituent. Then, determine the matrix phase by difference. Next, count the number of matrix grains comple com pletely tely within within the test are areas as and the num number ber of mat matrix rix grains gra ins int inters ersecti ecting ng the tes testt area bou bounda ndary ry,, as des descri cribed bed in Section 11 Section  11..  The test area must be reduced to that covered only by the matrix phase grains. The effective average grain size is then determined from the number of grains per unit net area of  the matrix phase. Statistically analyze the number of grains per unit un it ar area ea of th thee   α   matrix matrix pha phase, se,   N  A   α, fr from om ea each ch fie field ld measur mea sureme ement nt usi using ng the app approa roach ch des descri cribed bed in Sec Sectio tion n   15 15..

NOTE   1—Measurements of rectangular bar, plate, strip or sheet type specimens with non-equiaxed grain structures. FIG. 7 Schematic Showing the Six Possible Directed Test Line Orientation Orient ations s for Grain Size Measurement

16.3. 16.3.5.2 5.2 Anoth Another er approach approach that can be used is to norma normalize lize the three results by dividing each by the value of the smallest with the results expressed as ratios. 16.3.6 16. 3.6 The mean value of   ℓ¯ for the measurements in the three thr ee pri princi ncipal pal test dir directi ections ons is obt obtain ained ed by ave averag raging ing the ¯  L   , or   P ¯  L   values (as shown in (Eq directed   N  ( Eq 23) 23)) and then Copyright by ASTM Int'l (all rights reserved); reserved); Tue Sep 3 16:40:18 EDT 2013 Downloaded/printed by

14

Center For Library Initiatives pursuant to License Agreement. No further reproductions authorized.  

 

E112 − 12

¯  A   α, determine the effective Then, from the overall average,   N  grai gr ain n si size ze of th thee ma matr trix ix us usin ing g   Tabl Tablee 4   or the app approp ropriat riatee equation in Table in  Table 6. 6.

of the planar measurements, and the computed or estimated ASTM grain size number. 18.6 For a two-phase structure, structure, list the method of analysis, the amount of the matrix phase (if determined), the grain size measurement of the matrix phase (and the standard deviation, 95 % confidence interval, and percent relative accuracy), and the computed or estimated ASTM grain size number.

17.5   Interc Intercept ept Method Method—  — The The sam samee res restric trictio tions ns reg regard arding ing applicability, as stated in  17.4  17.4,,  pertain to this method. Again, thee amo th amoun untt of th thee ma matr trix ix ph phas asee mu must st be de deter termin mined ed,, as described in   17.4. 17.4.   A test grid consisting of one or more test circles, such as shown in  Fig. 5, 5,  is used. For this application, count the number of matrix grains,   N α, intercepted by the test

18.7 18. 7 If it is desired desired to exp expres resss the average average grain grain size of a

line. Determine the mean intercept length of the matrix phase according to: Hℓ

α

 5

~ V V  !~ L /  M ! α

 N α

gr grou oup pM ofgra speci sp mens from fr om lot, lo t,tead, do, no not t sim simpl ply aver erag age e th the e ASTM AST grain inecime size siz ensnum number bers. s.a Ins Instead comput com pute e yanav arithme arit hmetic tic ¯  A or  ℓ  values average of the actual measurements, such as, the N  per specimen. specimen. Then, from the lot average, calculate or estimate ¯  A  or the ASTM grain size for the lot. The specimen values of  N   N  ℓ  may also be statistically analyzed, according to the approach in Section  Section   15 15,,  to evaluate the grain size variability within the lot.

(25)

where the volume fraction of the  α  matrix, V V α  , is expressed as a fraction,  L   is the test line length and  M  is the magnification. The grain size of the  α  grains is determined using Table using  Table 4 or the equation in   Table 6. 6.   In practice, it is inconvenient to manually determine the volume fraction of the  α  phase and the number of   α   grains intercepting the test line for each field. If  this is done, the mean lineal intercept length of the  α  phase for each field can be determined and this data can be statistically analyzed for each field according to the procedure described in Section 15 Section  15.. If  V   V V α  and  N α  are not measured simultaneously simultaneously for

19. Pre Precisi cision on and Bias 19.1 The pre 19.1 precisi cision on and bias of gra grain in siz sizee mea measur suremen ements ts depend on the representativeness of the specimens selected and the areas on the plane-of-polish chosen for measurement. If the grain size varies within a prod product, uct, specimen and field selectio selection n must adequately sample this variation.

the sam the samee fie field lds, s, th then en th thee st stati atist stica icall anal analys ysis is can on only ly be performed on the  V V α  and  N α  data. 17.6 It is also possible to determine determine   ℓ¯α  by measurement of 

19.2 The relative relative accuracy of the grain size measurement measurement of  the product improves as the number of specimens taken from the product increases. The relative accuracy of the grain size measur mea sureme ement nt of eac each h spe specime cimen n imp improv roves es as the num number ber of  fields sampled and the number of grains or intercepts counted increase.

individual intercept lengths using parallel straight test lines individual applied randomly to the structure. Do not measure the partial intercepts at the ends of the test lines. This method is rather tedious unless it can be automated in some way. The individual intercepts are averaged and this value is used to determine   G from   Tabl Tablee 4   or th thee eq equa uati tion on in   Table Table 6.   The indivi individual dual intercepts may be plotted in a histogram, but this is beyond the scope of these test methods.

19.3 Bias in measurements measurements will occur if specime specimen n preparation is inadequate. The true structure must be revealed and the grain boundaries must be fully delineated for best measurement precision and freedom from bias. As the percentage of nondelinea del ineated ted gra grain in bou bounda ndaries ries inc increas reases, es, bia biass incr increase easess and precision, repeatability, and reproducibility become poorer.

18. Repor Reportt 18.1 18. 1 The test rep report ort should should doc docume ument nt all of the pertinen pertinentt identify ident ifying ing inf infor ormat mation ion reg regard arding ing th thee spe specim cimen en,, its

19.4 Inaccu Inaccurate rate determination determination of the magnification magnification of the grain structure will produce bias.

composition, specification designation or trade name, customer or dat dataa req reques uester ter,, dat datee of tes test, t, hea heatt trea treatmen tmentt or pro process cessing ing history histor y, specime specimen n locatio location n and orientation, orientation, etchan etchantt and etch method, grain size analysis method, and so forth, as required.

19.5 If th 19.5 thee gr grain ain str struc uctu ture re is no nott eq equi uiax axed ed in sh shap ape, e, fo forr exam ex ampl ple, e, if th thee gr grain ain sh shap apee is elo elong ngat ated ed or fla flatt tten ened ed by deformation, measurement of the grain size on only one plane, particu par ticularl larly y the plan planee per perpen pendicu dicular lar to the def deform ormatio ation n direction, will bias test results. Grain shape distortion is best detected using a test plane parallel to the deformation direction. The size of the deformed grains should be based on measurements made on two or three of the principal planes which are averaged as described in Section  16  16..

18.2 List the number of fields measur measured, ed, the magnification, magnification, and field area. The number of grains counted or the number of  intercepts or intersections counted, may also be recorded. For a two-phase structure, list the area fraction of the matrix phase. 18.3 A photomicrogr photomicrograph aph illustrating the typica typicall appea appearance rance of the grain structure may be provided, if required or desired.

19.6 Specim Specimens ens with a unimo unimodal dal grain size distribution distribution are measured for average grain size using the methods described in these test methods. Specimens with bimodal (or more complex) size distributions should not be tested using a method that yield yi eldss a sin singl glee av aver erag agee gr grain ain si size ze va valu lue; e; th they ey sh shou ould ld be characterized charac terized using the method methodss descri described bed in Test Metho Methods ds E1181   and meas measure ured d usi using ng the meth methods ods des descri cribed bed in Test Methods E112. The size of individual very large grains in a fine grained matrix should be determined using Test Methods E930 Methods E930..

18.4 List 18.4 List th thee me mean an me meas asur urem emen entt va valu lue, e, it itss st stan anda dard rd deviation, deviati on, 95 % confid confidence ence interv interval, al, percen percentt relativ relativee accura accuracy cy,, and the ASTM grain size number. 18.4.1 18.4. 1 For the comparison comparison method, list only the estimate estimated d ASTM grain size number. 18.5 For a non-equiaxed non-equiaxed grain structure, structure, list the method of  analysis, planes examined, directions evaluated (if applicable), the grain size estimate per plane or direction, the grand mean Copyright by ASTM Int'l (all rights reserved); reserved); Tue Sep 3 16:40:18 EDT 2013 Downloaded/printed by

15

Center For Library Initiatives pursuant to License Agreement. No further reproductions authorized.  

 

E112 − 12

19. 19.7 7 Whe When n usi using ng the com compar pariso ison n cha chart rt meth method, od, the cha chart rt selected should should be consis consistent tent with the nature of the grains (that is, twinned or non-twinned, or carburized and slow cooled) and thee etc th etch h (t (tha hatt is, flat et etch ch or gr grai ain n co cont ntra rast st etc etch) h) fo forr be best st precision.

and reproducibility of measurements improved as the number of grains or interc intercepts epts counted increased increased and was better for the intercept method than for the planimetric method for the same count. 19.13 The planimetric planimetric method requires requires a markin marking g off of the grains during counting in order to obtain an accurate count. The intercept method does not require marking in order to get an accurate count. Hence, the intercept method is easier to use and faster. Further, the round robin test showed that the intercept

19.8 Grain size ratings using the comparison comparison chart method by an individual metallographer will vary within 60.5  G  units. When a number of individuals rate the same specimen, the spread in ratings may be as great as 1.5 to 2.5   G  units.

method meth od pr prov ovid ides es be bette tterr sta statis tistic tical al pr preci ecisio sion n fo forr th thee sa same me numberr of counts and is, theref numbe therefore, ore, the prefer preferred red measurement measurement method.

19.9 The fracture 19.9 fracture gra grain in size method method is onl only y app applica licable ble to hardened, relatively brittle, tool steels. Specimens should be in the asas-que quench nched ed or ligh lightly tly temp tempered ered conditio condition n so tha thatt the fracture surface is quite flat. An experienced metallographer can rate the prior-austenite grain size of a tool steel within 60.5   G  units by the Shepherd fracture grain size method.

19.14 An individual individual metallo metallograph grapher er can usuall usually y repeat planimetric or intercept grain size measurements within   60.1   G units. When a number of metallographers measure the same specimen, specim en, the sprea spread d of grain sizes is usuall usually y well within 60.5 G  units.

19.10 19.1 0 A ro roun und d ro robi bin n tes testt pr prog ogra ram m (s (see ee   Appendi Appendix x X1 X1), ), analyzed analyze d accord according ing to Practic Practicee  E691  E691,,  revealed a rather consistent bias between comparison chart ratings using Plate I and grain size measurements using both the planimetric and intercept methods. Chart ratings were 0.5 to 1  G  unit coarser, that is, lower   G  numbers, than the measured values.

19.15 If the number of grains completely completely within within a test circle decreases below 50, the grain size estimate using the planimetric method will be biased, with the degree of bias increasing as  N inside  decreases from 50. To avoid this problem, select the magnification so that   N inside   is   ≥   50, or use a rectangular or square test figure and the counting method described in  11.5  11.5..

19.11 19. 11 Gra Grain in siz sizes es det determ ermine ined d by eith either er the pla planim nimetr etric ic or intercept methods produced similar results with no observed bias.

inside   of ~100 and above lead to Magni Magnification fications s that yield   N errors. imprecision due to counting A 10% relative accuracy in G   will be obtained when at least 700 total grains are counted using multiple fields selected at random.

19.12 The rel 19.12 relativ ativee acc accura uracy cy of gra grain in siz sizee meas measure uremen ments ts impro imp rove ved d as th thee nu numb mber er of gr grai ains ns or in inter terce cept ptss co coun unted ted increased. For a similar number of counts, the relative accuracy of intercept measurements was better than that of planimetric measurements of grain size. For the intercept method, 10 % RA (or less) was obtained with about 400 intercept or intersection counts while for the planimetric method, to obtain 10 % RA, or less, about 700 grains had to be counted. Repeatability

20. Keyw Keywords ords 20.1 ALA grain size; anisotrop anisotropy y index; area fraction; fraction; ASTM grain size numb number; er; calibra calibration; tion; equiaxed grains; etchan etchant; t; grain boundary; grains; grain size; intercept count; intercept length; intersection inters ection count; nonnon-equiax equiaxed ed grain grains; s; twin boun boundaries daries

ANNEXES (Mandatory Information) A1. BASI BASIS S OF ASTM GRAIN SIZE NUMBERS NUMBERS

A1.1 Descriptions of Terms Terms and Symbols

A1.1.1.1   N  = Number of grain sections counted on a known test area,   A, or number of intercepts counted on a known test array arr ay of len length gth =  L , at som somee stat stated ed mag magnifi nificati cation, on,   M . The ¯ . average of counts on several fields is designated as   N 

A1.1.1 The general A1.1.1 general ter term m   grain size   is commonly used to design des ignate ate siz sizee est estimat imates es or mea measur sureme ements nts mad madee in sev severa erall ways, employing various units of length, area, or volume. Of  the various systems, only the ASTM grain size number,   G, is essentially essenti ally independent independent of the estimating system and measurementt uni men units ts use used. d. The equ equatio ations ns use used d to det determ ermine ine   G   from recommended measurements, as illustrated in Fig. in  Fig. 6 and 6  and Table  Table 2   and   Tabl Tablee 4,   are given given in   A1.2   and   A1.3. A1.3.   The nomin nominal al relationships between commonly used measurements are given

A1.1.1.2 After correction A1.1.1.2 correction for magnification, magnification, N  A  is the number of grain sections per unit test area (mm2) at 1X;   N  L  is the number of grains intercepted per unit length (mm) of test lines at 1X; and  P L is the number of grain boundary intersections per unit length (mm) of test line at 1X. A1.1.1.3   ℓ¯ = 1/  N    = 1/ P  where   ℓ¯ is the mean lineal inter L

in in Annex A2.in A2.  Measurements  Measurem that appearr in these equatio appea equations, ns, or in  Annex equations the text, ents are as follows:

Copyright by ASTM Int'l (all rights reserved); reserved); Tue Sep 3 16:40:18 EDT 2013 Downloaded/printed by

cept length in mm at 1X.

16

 L

Center For Library Initiatives pursuant to License Agreement. No further reproductions authorized.

 

 

E112 − 12

¯   = 1/  N  A   where   A ¯   is the mean area of the grain A1.1.1.4   A 2 ¯ , is the square sections (mm ) at 1X. The mean grain diameter,  d  root of  A  A¯ . Grain size values on Plate III are expressed in terms ¯  of   d . Note that  Table 2   lists the equivalent ASTM grain size number for each chart picture and for several different magnifications. A1.1.1.5 A1.1. 1.5 The letters letters   ℓ,  t   and  p  are used as subscripts when assessing the grain size of specimens with non-equiaxed grain structures. The three subscripts represent the principal planes

G 5 1 10. 000 2 2 log2  ℓH m

 

(A1.3)

For microscopically determined grain sizes,  ℓ¯ is in millimetres at 1X and: G 5 2 3.2877 2 6.6439 log10  ℓH

(A1.4)

G 5 2 3.28771 2 log 2   ¯  N  L

 

(A1.5)

G 5 2 3.28771 6.6439 log10   N  L

 

¯ 

(A1.6)

¯  L  , substitute  P¯  L  for  N  ¯  L  in If  P  P¯  L  is determined instead of  N   N   in Eq  Eq A1.5   and A1.5 and Eq  Eq A1.6. A1.6.

A1.3   Planimetric Method: ¯  AE  in number per square inches at A1.3.1 Englis English h units,   N  100X for microscopically determined grain sizes and at 1X for macros mac roscop copical ically ly det determ ermine ined d gra grain in siz sizes, es, are use used d with the ¯  AE  t following equations relating  N   to o  G :

A1.2   Intercept Methods: A1.2.1 A1.2. 1 Metric units,   ℓ¯ in millimetres at 100X for microscopically determined grain sizes and  ℓ¯m at 1X for macroscopically cal ly de deter termin mined ed gr grain ain si sizes zes,, ar aree us used ed wi with th th thee fo follo llowi wing ng ¯ ¯ equation relating  ℓ or  ℓ m  to  G . For macroscopically determined grain sizes,ℓ¯m  is in mm at 100X:

G 5 1.0001 log 2   ¯  N  AE 

 

G 5 1.0001 3.3219 log10   ¯  N  AE 

(A1.7)  

(A1.8)

¯  A is expressed in terms of the number of grains per square If  N   N 

millimetres at 1X, for microscopically determined grain sizes, then:

(A1.1)

H ℓ m

(A1.2)

G 5 1 10.0000 2 6.6439 log10 ℓH m

for rectangular bar, plate, sheet, or strip specimens, that is, the longitudinal (ℓ), transverse (t ) and planar ( p) surfaces. They are mutually mutuall y perpe perpendicu ndicular lar to each other. other. On each plane, there are two principal directions that are perpendicular to each other (as illustrated in Fig. in  Fig. 7) 7). A1.1.1.6 A1.1. 1.6 The number of fields measured measured is designated by n . A1.1.1.7 A1.1. 1.7 Other specific designations designations are defined by equations which follow.

0 G 5 2 log2 ℓ

 

G 5 2 2.95421 3.321 N  A 3.3219 9 log10   ¯ 

for  G   = 0,   ℓ0  is established as 32.00 and log 2  ℓ 0   = 5.

 

(A1.9)

A2. EQUA EQUATIONS TIONS FOR CONVERSION CONVERSIONS S AMONG VARIOUS VARIOUS GRAIN SIZE MEASUREM MEASUREMENTS ENTS

A2.1   Chang Changee of Magnification Magnification—If the apparent grain size has been observed at magnification  M , but determined as if at the basic magnification  M b (100X or 1X), then the size value at the basic magnification is as follows:

= 2 (l (log og2  M  −  − log2  M b  ) = 6.6 6.6439 439 (lo (log g10  M  −  − log10  M b  ) where   G0   is th thee ap appa pare rent nt ASTM gr grain ain si size ze nu numb mber er at magnification  M b  .

A2.1.1   Planimetric Count:

2

 N  A   5  N   A 0  ~ M  /  M b ! 2

(A2.1)

 N  A   5  N  AE  ~ 100/25.4! 2

where   N  A 0   is th thee nu numb mber er of gr grai ains ns pe perr un unit it ar area ea at magnification  M b  .  

(A2.6)

(A2.2)

A2.2 Other A2.2 Other me measu asure reme ment ntss sh show own n in th thee ta tabl bles es may be computed from the following equations: A2.2.1   Area of Average Grain:

A2.1.3   Any Length:  

 

where  N  A  is the number of grains per mm2 at 1X and  N  AE  is the number of grains per in. 2 at 100X.

where N i 0 is the number of grains intercepted by the test line (the equation for  P i  and  P i 0  is the same) at magnification  M b  .

¯  ℓ 5 ¯  ℓ 0  M b  /  M   M 

(A2.5)

 N  A   5 15.5 N  AE 

A2.1.2   Intercept Count:  N i   5  N i 0 ~ M  /  M  b !

2

A2.1.5 A2.1. 5 Grain Grainss per mm at 1X from grains per in. at 100X:

¯ 5 1/  N   A  N  A

(A2.3)

 

(A2.7)

¯  is the average grain cross sectional area. where   A

where   ℓ¯0  is the mean lineal intercept at magnification  M b  .

A2.2.2  Intercept Width of a Circular Grain Section:

A2.1.4  ASTM Grain Size Number:

1/ 2

G 5 G0

1Q

 

(A2.4)

ℓ H5

where: Q   = 2 lo log g2  ( M/M b  ) Copyright by ASTM Int'l (all rights reserved); reserved); Tue Sep 3 16:40:18 EDT 2013 Downloaded/printed by

S ¯ D  π   A

4

(A2.8)

The mean int interc ercept ept dis distan tance ce for pol polygo ygonal nal gra grains ins var varies ies about this theor theoretical etical value, being decrea decreased sed by anisot anisotropy ropy but 17

Center For Library Initiatives pursuant to License Agreement. No further reproductions authorized.  

 

E112 − 12

increased by a range of section sizes. The width computed by (Eq A2.8) A2.8) is 0.52 % smaller than the width assigned to   G   by (Eq A1.4) A1.4) in in A1.2.1  A1.2.1   (∆  = + 0.015 0.015 ASTM No.).

formulae, such as equation (Eq (Eq A2 A2.7 .7), ), have been proposed with differ dif ferent ent mul multipl tiplyin ying g fact factors ors.. A rea reason sonabl ablee esti estimat matee of the ¯ , based upon the tetrakaidecahedron shape spatial diameter,   D model and a grain size distribution function   (9)  , is:

A2.3 Other useful useful size indications indications are given by the following equations:

¯ 

 D  5 1.571 ¯  ℓ

¯ 

(A2.10)

A2.3.2 For a single phase microstructu microstructure, re, the grain boundboundary surface area per unit volume,  S V  , has been shown to be an exact function of  P  P L  or  N  L  :

¯ , of similar size A2.3.1 The volumetric A2.3.1 volumetric (spatial) diameter, diameter,  D spheres in space is:  D  5 1.5H ℓ

 

(A2.9)  L S  V    5 2 P L   5 2 N  L

Similar relatio relationship nshipss betwee between n   ℓ¯, de deter termi mine ned d on th thee tw twoo¯  dimensional plane of polish, and the spatial diameter,  D  , have been derived for a variety of potential grain shapes, and various assu as sump mptio tions ns ab abou outt th thei eirr si size ze di dist stri ribu butio tion. n. A nu numb mber er of 

 

(A2.11)

while for a two phase microstructure, the phase boundary surface area per unit volume of the   α  phase,   S V   α, is: S V α   5 2 P  L   5 4 N  L

 

(A2.12)

A3. AUSTENITE GRAIN SIZE, FERRITIC AND AUSTENITIC AUSTENITIC STEELS

A3.1 Scope

14°C) for 8 h or until a case of approximately 0.050 in. (1.27 mm) is obtained. The carburizing compound must be capable of pr prod oduc ucin ing g a hy hype pere reut utect ectoi oid d ca case se in th thee tim timee an and d at th thee temperature specified. Furnace cool the specimen to a temperature below the lower critical at a rate slow enough to precipitate cementite in the austenite grain boundaries of the hypereutectoid toi d zon zonee of the case case.. Whe When n coo cool, l, sect section ion the spe specim cimen en to provide a fresh-cut surface, polish, and suitably etch to reveal the grain size of the hypereutectoid zone of the case. Make a microscopical examination in compliance with Table with  Table 1. 1.  While the McQuaid-Ehn test was designed for evaluating the grain growt gr owth h cha charac racter terist istics ics of ste steels els int intend ended ed fo forr car carbu buriz rizing ing applica app licatio tions, ns, usu usually ally stee steels ls with