Armstrong Indentation

8/12/2019 Armstrong Indentation

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Indentation Hardness Stress Strain Aspects of

Crystal Elastic/Plastic/Cracking Behaviors

R.. Ar!strong" and .#. El$an""

" %niversity of &aryland' College Park' &( )*+,)""#oyola College' Balti!ore' &( )-)-*

ABSRAC

Single crystal Cl and &g0 indentation hardness test res1lts spanning !acroscopic'

!icrostr1ct1ral' and nanoscale !eas1re!ents are $ro1ght together in a $all2indenter2

$ased stress2strain description. 3or a significant range of hardness !eas1re!ents !adeon &g0 4**-5 crystal s1rfaces' increasingly greater plastic flo6 stresses are deter!ined

at s!aller loads applied to s!aller effective $all si7es at the ro1nded tips of Berkovich

indenters8 and' at the s!allest $all dia!eters of 9)** and ,** n!' the plastic flo6

stresses are sho6n to approach the predicted Hert7ian elastic loading stresses. heres1ltant hardness stress strain description' that is e:tended to cover the elastic' plastic'

and cracking $ehaviors of &g0 crystals' is 1sef1lly applied also to a co!parison ofindentation test res1lts reported for ;aCl and R(< crystals. In general' the dislocation2

ind1ced cracking stress !eas1re!ents are sho6n for &g0 and R(< crystals to $e lo6er

than cracking stresses eval1ated on an 4elastic5 indentation fract1re !echanics 4I3&5$asis.

Introduction

Early designs of hardness testing !achines and indenter shapes 6ere concerned 6ith

achieving relatively large effective strains in the indentation process so as to prod1ce inthe hardness specification a relia$le indication of the !aterial plastic defor!ationproperties separate fro! the !ethod of testing. S1$se=1ent later pioneering researches of

a$or >-? sho6ed connection' at reasona$le plastic straining' $et6een the hardness

property of !etals' 6hen specified as the !ean press1re on a spherical $all' and theplastic stress strain $ehavior of the sa!e !aterial 6hen !eas1red in a co!pression test.

And' later attention 6as directed to deter!ining the f1ll elastic plastic defor!ation

$ehavior of an indented !aterial' for e:a!ple' $y perfor!ing a contin1o1s loading

indentation test 1nder conditions in 6hich the relatively s!all elastic defor!ation$ehavior co1ld $e !eas1red >)?. &ore recently' the e:peri!ental diffic1lty in s1ch a

testing proced1re of !eas1ring the elastic portion of the loading $ehavior for the test

speci!en alone has $een overco!e in a striking !anner' even for relatively hard!aterials' $y the advent of nanoindentation testing !achines and !ethods that provide a

contin1o1s load defor!ation record of the indenting process.

he p1rpose here is to provide a co!parison of s1ch contin1o1s indentation hardness

res1lts' as o$tained 6ith conventional testing !achines and via !icroindentation and

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@ S1$!itted for a Special Iss1e of o1rnal of &aterials Research' 1ly' )**.


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nanoindentation testing' partic1larly' for &g0 crystal hardness val1es. he &g0 plastic

hardness res1lts' o$tained for several different indenter shapes' 6ill $e sho6n to cover a

range of applied loads $et6een a !acroscopic level of * ; and a nanoindentation val1eof *.) !;' and 6ith corresponding plastic hardness val1es ranging fro! D+ Pa to

D) Pa' respectively' in the latter case' near to the eval1ated Hert7ian elastic hardness

stress of D9*.+ Pa at the point of f1ll plastic yielding. he res1lts connect 6ith theo$servation on a hardness stress strain description $asis >9? that' for 4**-5 &g0 crystal

s1rfaces and for harder !aterials' the elastic and plastic strains i!posed in $oth

!icroindentation and nanoindentation tests are co!para$le in val1e.

Continuous indentation hardness test measurements

An early res1lt >9? o$tained on !eas1ring the initial elastic defor!ation acco!panyingspherical indentation of an 4**-5 s1rface of an appro:i!ately -.* c! on2a2side Cl

crystal' 6hen loaded in a cali$rated standards2type Instron esting &achine' is sho6n in

3ig. -. In the fig1re' the a1tographically recorded crosshead displace!ent' h' is plotted as

the a$scissa scale for $1ild21p' at a relatively slo6 crosshead speed of .9 : -*

2,

!!/s' ofa co!pressive load cell force approaching -* ; on a F.9 !! dia!eter hardened steel

$all. he dashed c1rve that is sho6n to fit the !eas1re!ent at the initial loading stage6as co!p1ted in accordance 6ith the Hert7ian elastic loading relationship for the

penetration depth' he' as

heG L)/(J-/9>4- K$

)5/E$J L4- Ks)5/EsJ?

)/9 4-5

In e=. 4-5'Lis the applied load' ( is the $all dia!eter' and the paired !aterial constants'

K$' E$and Ks' Esare the PoissonMs ratio and No1ngMs !od1l1s for the 4steel5 $all and 4Cl5speci!en' respectively8 s1$stit1tion here and else6here of >-/Er? is generally !ade for the

second factor 6ithin s=1are $rackets. In 3ig. -' the !achine deflection'hm' is sho6n to

$e added at the 1nloading section of the defor!ation c1rve and 6as !eas1red $yperfor!ing the test 6ith the steel $all pressed elastically onto a hardened steel platen. As

indicated in the fig1re' the !achine deflection 6as negligi$le d1ring the initial elastic

loading of the crystal.

Additional indentation tests' of the type sho6n in 3ig. -' and for other tests taken to loads

of -** ; and ** ;' 6ere reported for the sa!e crystal and si!ilar speci!ens. At -** ;'

the proOected s1rface dia!eter' d' of the resid1al i!pressed indentation 6as sho6n to fitthe relationship

dG )>h4( h5?-/) 4)5

in 6hich h6as taken as the total indentation depth 1nder load. he relevance of this

deter!ination for h$eing the correct one relates to the i!portant e:peri!entalo$servation that' 1pon 1nloading' the $otto! of the resid1al indentation 6as fo1nd to $e

flattened in the deter!ination of hu$1t the val1e of d6as essentially 1nchanged. 0n the

$asis of e=. 4)5 and specification of the plastic hardness stress as


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HGL/4d)/,5' 495

a val1e of HG D9 &Pa' 6as o$tained for the !a:i!1! load val1e of .+ ; in 3ig. -'and H6as increased to D* &Pa at -** ;' and to D-** &Pa at ** ; load' also

corresponding to 4d/D5 val1es of *.) and *.,' respectively. he slo6er increase of H

6ith change in displace!ent at the larger loads' and corresponding larger indentationsi7es' is in line 6ith the !entioned2a$ove indenter shapes $eing designed to achieve

effective large strains so as to o$tain a representative hardness stress that is relatively

insensitive to the i!posed strain. In this regard' a direct linear dependence in 3ig. - ofthe ordinate val1e ofLon hat relatively s!all hco!pared toD' see e=s. 4)5 and 495'

6o1ld correspond to a constant val1e of H. Close e:a!ination of the load vs.

penetration depth dependence in 3ig. -' ho6ever' reveals the trend for Hto increase

strongly at first fro! an initial plastic yielding val1e' and s1$se=1ently to increase !oreslo6ly at larger straining' pres1!a$ly' in an analogo1s !anner to the !aterial strain

hardening $ehavior in a co!pression test.

(eter!ination of the plastic hardness stress at varying 4d/D5 val1es !ay $e co!pared6ith the Hert7ian elastic stress operative at the onset of plastic yielding of the speci!en

$y e!ploying the relationship $et6een $all contact dia!eter deand heas deG >)he(?-/)so

as to o$tain the analogo1s elastic hardness stress' E' as

EG 4,/95Er4de/(5' 4,5

in 6hich 4de/(5 is taken as a !eas1re of the hardness strain. 3or 3ig. -' an elastic

hardness stress of D--* &Pa 6as esti!ated fro! the Hert7ian c1rve load' D*.) ;' and

displace!ent' -. : -*2,!!' deter!ined at the onset of yielding. h1s' Eat the onset ofyielding for Cl crystals is associated 6ith an i!!ediately lo6er val1e of Hthat

increased 6ith plastic straining to a hardness val1e near to that of the Elevel. In f1rther

researches involving other !aterials' the !ethod of perfor!ing a contin1o1s indentationhardness test via a conventional testing !achine 6as e!ployed to o$tain elastic !od1l1s

eval1ations for 6ood2derived lignan !aterial >,? and to o$tain elastic/plastic defor!ation

res1lts on polycrystalline al1!in1! !aterial >?. &ore recent elastic !od1l1s res1lts6ere reported for solid and poro1s polycrystalline al1!in1! !aterials' incl1ding

co!parison of the c1rrent and previo1s loading !eas1re!ents 6ith !od1l1s esti!ations

o$tained fro! the initial part of the 1nloading c1rve >F?.

Nanoindentation test measurements

;anoindentation hardness testing' 6ith its e:ceptional !eas1re!ent sensitivity of loadand displace!ent val1es that are achieved on a contin1o1s loading $asis' nat1rally lends

itself to the st1dy of initial yielding in the indentation process' partic1larly' 6hen acco1nt

is taken of the consideration that the indenter tip' ho6ever shaped' 6ill generally $ero1nded at the !icro2 or nano2di!ensional scale. h1s' fit of the Hert7ian elastic

relationship $et6een heandLin e=. 4-5 to the de!onstrated reversi$le indentation c1rve

reported for an &g0 4**-5 crystal s1rface 6as e!ployed to specify a Berkovich tip

dia!eter of 9.+ !icrons in one test' and' in another test 6as fitted 6ith a tip dia!eter of


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9.) !icrons. In the latter case' the analysis 6as e:tended to a description of higher load

val1es !eas1red $oth for the Hert7ian elastic stress at yield and for the initial plastic flo6

stress defined in e=. 495 and e!ploying the e=. 4)5 relationship $et6een d and h >+?.

3ig1re ) sho6s si!ilar application to an apparently significantly different &g0 crystal

loading c1rve reported $y Cha1dhri >' ?. In this case' too' a Berkovich dia!ondindenter 6as e!ployed for nanoindenting a cleaved 4**-5 &g0 crystal s1rface. he

initial loading $ehavior is sho6n to $e fitted 6ith e=. 4-5 $eginning fro! an ass1!ed

offset displace!ent of ,.* n! and a trial2and2error2deter!ined indenter tip radi1s of ,**n!' also e!ploying the sa!e PoissonMs ratio and No1ngMs !od1l1s val1es of *.*F and

--, Pa for a dia!ond indenter and *.-- and 9-) Pa for the &g0 crystal' as

previo1sly e!ployed in reference >+?. he onset of f1ll plastic yielding at the indentation

site is !arked at the Qpop2in point in 3ig. )8 and' follo6ing the pop2in displace!ent' theesta$lish!ent of a plasticity2infl1enced defor!ation c1rve is seen to take on a

significantly red1ced load dependence in the s1$se=1ent displace!ent. E:cept for the

very different !agnit1des of load and displace!ent scales sho6n in 3igs. - and )' the

overall shapes of the defor!ation c1rves appear reasona$ly si!ilar. In othernanoindentation tests on &g0 crystals' ho6ever' s!aller Qpop2in discontin1ities

representing only interr1ptions of the other6ise elastic loading c1rve have $een reported>-*?. he pre2yield Qpop2in offsets $et6een contin1ed elastic loading seg!ents are

easily recogni7ed in these cases $y si!ply shifting the s1$se=1ent contin1ed elastic

loading c1rve to fit the earlier defor!ation. E=1ation 495 eval1ations for s1ch Qpop2insgive 1nrealistically high val1es of H. Even for Cha1dhriMs test res1lt in 3ig. )' ho6ever'

it 6as not possi$le to locate the resid1al nanoindentation.

3ig1re 9 sho6s the previo1sly 1nreported elastic c1rve for fit of a Berkovich tip dia!eterof 9)** n! to an other6ise f1lly analy7ed &g0 nanoindentation test res1lt reported $y

ro!as et al. >--? and $y Co1pea1 et al. >-)?. he fitted indenter tip dia!eter of 9)**

n! is eight ti!es greater than the ,** n! val1e deter!ined for 3ig. ). he difference ineffective ( val1es acco1nts for the significantly different load and displace!ent

!eas1re!ents that are sho6n in the t6o defor!ation c1rves. ith the ass1!ption that

the onset of f1ll yielding in 3ig. 9 6as deter!ined $y the designated Qpop2indisplace!ent' hpG 9- n! at a val1e ofLG F.9 !;' and hpG hin e=. 4)5' then a val1e of

HG )*.F Pa 6as co!p1ted for the yield stress $ased on the co!p1ted dG F)+ n! and a

val1e' then' of 4d/D5 G *.). A val1e of EG )-.9 Pa' only slightly greater than H' 6as

co!p1ted 1sing e=. 4,5. he plastic hardness res1lt co!pares in 3ig. ) fro! Cha1dhri6ith a co!p1ted val1e of HG ).- Pa deter!ined for the lo6er val1es ofhpG .) n!

andLG *.) !;. And a val1e of EG D9*.+ Pa is o$tained for this test res1lt O1st

prior to the yield2type Qpop2in. ery interestingly' 6ith co!p1tation of d G --9.+ n!for the 3ig. ) test res1lt' a relatively high val1e of 4d/D5 G *.), is o$tained for the

sharper indenter tip. h1s' the contin1ation of f1ll plasticity in this case is soon

controlled $y the trigonally2shaped indentations o$tained at a relatively lo6 load of D!;' or less' and leads to the Cha1dhri2reported hardness val1es of .F Pa' o$tained at a

load of )* !;' and ., Pa' at * !;.


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A log/log hardness stress strain !ethod of co!parison of Eand Hstresses 6as

deter!ined as a f1nction of (d/D)for &g0 crystal !eas1re!ents $y Ha!!ond and

Ar!strong >-9? and 1pdated in reference >+? $y addition of the closed circle!icroindentation res1lts reported previo1sly $y Ar!strong and Ragh1ra! >-,? and $y

addition of the co!p1ted hardness val1es o$tained fro! 3ig. 9. 3ig1re , sho6s the

f1rther 1pdate of res1lts' especially involving co!parison of $oth Hand Edeter!inations o$tained fro! 3igs. ) and 9. In 3ig. ,' the plotted (d/D)val1es 6ere

either directly deter!ined fro! the !eas1re!ents' as descri$ed a$ove' or 6ere

deter!ined $y kno6n conversion val1es' for e:a!ple' (d/D)G *.9+ for the dia!ondpyra!id indentation 4as co!pared 6ith *.,) for the Berkovich indenter5. As indicated in

3ig. ,' the total plastic hardness res1lts 6ere o$tained for applied load val1es ranging

fro! * ; to *.) !;' th1s prod1cing an increasing hardness val1e 6ith decreasing

load 1ntil in the t6o s!allest load tests' the plastic hardness stresses' H' approach theHert7ian elastic stresses' E' for 6hich the applied loads are only elastically s1pported.

he open circle point on the Hert7ian elastic loading line in 3ig. ,' atDG F.9 !!' and

open s=1are point' atDG 9.+ !icrons' are for hardness stress val1es esti!ated on an

indentation fract1re !echanics 4I3&5 $asis' as 6ill $e descri$ed later in connection 6ithother test res1lts.

Elastic vs.plastic strains

he resid1al dislocation defor!ation patterns s1rro1nding aligned dia!ond pyra!id!icroindentations p1t into 4**-5 &g0 crystal s1rfaces have $een e:tensively st1died' for

e:a!ple' as descri$ed in >-?' partic1larly for resid1al plastic indentations having

conve:2like shapes acco!panying the indenter sides $eing aligned parallel to T--*U

directions and for concave2like shapes for the indenter sides $eing aligned parallel toT-**U directions. Beyond the descri$ed scanning electron !icroscopy 4SE&5 and :2ray

diffraction topography res1lts descri$ed in >-F?' !ore recent ato!ic force !icroscopy

res1lts have $een reported also for dislocation etch2pitted nanoindentation res1lts !ade ine:tension of original pioneering etch2pit res1lts o$tained at !icroindentations >-+?. 3or

the T-**U align!ent case' 3ig. sho6s sche!atically the generally agreed 1pon !odel

dislocation distri$1tion that has $een investigated to 1nderstand $etter' for s1fficientlylarge applied load val1es' the fo1r2fold pattern of cracking that occ1rs on vertical --*J

planes containing the indentation direction >-?. As 6ill $e disc1ssed' the !odel for the

dislocation pile21p ind1ced --*J cracking' that has $een investigated !ost recently in a

spherical $all2type nanoindentation testing proced1re >-*?' occ1rs at a lo6er hardnessstress than predicted on an elastic I3& $asis $1t the i!!ediate point of interest here is

the relatively co!para$le contri$1tions of $oth the plastic dislocation displace!ents and

the 41nloading5 elastic recovery strains to the resid1al indentation shapes. 3or e:a!ple'even at an applied load of * ; for the lo6est hardness test res1lts in 3ig. ,' the elastic

strain is esti!ated as 4d/(5 G D*.*+' and this co!pares 6ith the $all2e=1ivalent plastic

strain val1e of 4d/(5 G *.9+ for the dia!ond pyra!id indentation.

At the increasing hardness val1es plotted in 3ig. ,' the ratio of elastic2to2plastic strains

for dia!ond pyra!id indentations increases significantly as the Hert7ian elastic loading

c1rve is approached. Ha!!ond and Ar!strong >-9? had de!onstrated a red1ction of the


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indentation depth on 1nloading of dia!ond pyra!id !icroindentations thro1gh !eas1red

changes in the angle $et6een opposite indentation facets. oirgard et al. have

co!!ented on the flat nat1re of resid1al nanoindentations !ade in aAs as part of aresearch investigation also involving &g0 nanoindentations >-?. Also' Co1pea1 et al.

>-)? reported ato!ic force !icroscopy i!ages and s1rface depth !eas1re!ents for the

resid1al indentation test res1lt descri$ed in 3ig. 9 that !atch the very s1$stantial depthrecovery sho6n in the 1nloading c1rve. 3or e:a!ple' the =1antitative !eas1re!ent

reported of a do6n6ard tro1gh2like displace!ent of D-, n! of the crystal s1rface O1st

o1tside of the resid1al indentation' along the >*-*? direction' is in agree!ent 6ith thedislocation !odel description of 3ig. ' 6here$y the !eas1re!ent is acco1nted for $y the

indentation2for!ing T*--U B1rgers vector dislocations spreading in a scre6 orientation

along the >*-*? direction >+?.

Crystal comparisons on a hardness stress-strain basis

3ig1re F sho6s a co!pilation of hardness val1es of vario1s crystals 6ithin the fra!e6ork

of the proposed $all2type indentation stress 2 strain description' incl1ding for &g0 the D+Pa average dia!ond pyra!id !icroindentation hardness val1e' involving --*J plane

cracking of the type !odeled in 3ig. . In the present case' different co!p1ted Hert7ianelastic loading lines are sho6n on the left2side of the fig1re on the $asis of e!ploying a

steel $all indenter 6hereas the collected dia!ond pyra!id hardness val1es are plotted at

their $all2e=1ivalent val1e of 4d/D5 G *.9+. In the fig1re' a solid Hert7ian line ands1$se=1ent plastic flo6 c1rve is sho6n for an ;aCl crystal indented 6ith a F.9 !! steel

$all in a conventional !acroscopic loading test as descri$ed for the Cl defor!ation

c1rve sho6n in 3ig. -. Also appearing in the fig1re are individ1al open2s=1are

!icrohardness !eas1re!ents !ade on a 4cyclotri!ethylentrinitra!ine5 R(< 4)-*5crystal s1rface e!ploying a -. !! dia!eter steel $all8 see reference >-F? for f1rther

details a$o1t R(< crystal properties. And' at the 1pper end2points of the Hert7ian elastic

loading lines are a n1!$er of open2circle points co!p1ted in accordance 6ith the I3&relationship reported $y #a6n >-? as

CG ,EsV/>D4- Ks)54W-

)L W))5?J-/)4d/D52-/) 45

In e=. 45' V is the crack s1rface energy' 4W-)L W)

)5 G ). : -*26as specified as a

n1!erical factor' and the other para!eters 6ere already defined for e=. 4-5. E:a!ination

of e=. 45 sho6s that the cracking stress' C' decreases asDincreases and this is sho6n to$e the case in 3ig. F for theDG F.9 !! andDG *.-), !! points p1t onto the &g0

line8 the 1pper *.-), !!Dval1e is the $all2dia!eter e=1ivalent of the dia!ond pyra!id

!eas1re!ent that is plotted.

3ig1re F !akes clear the increasing i!portance of the elastic defor!ation part of the

hardness property as the hardness itself increases a!ong the !aterial val1es that aresho6n. he ;aCl contin1o1s indentation stress strain and dia!ond pyra!id res1lt is

sho6n to have a negligi$le elastic strain contri$1tion of 4d/D)G D*.**+ for the hardness

at 4d/D5 G *.9+. Also' the ;aCl stress strain c1rve follo6s the trend of Eand H

eval1ations that have $een descri$ed for the Cl loading res1lt in 3ig. -. In addition'


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co!parison of the elastic and plastic properties of ionically2$onded ;aCl and the

!olec1larly2$onded energetic crystal' R()*?. 0f greater interest in

the present case' ho6ever' is co!parison in 3ig. F of the esti!ated elastic I3& crackingstresses' say' either for the effective 4dia!ond pyra!id5 s!all2$all res1lt ofDG *.-),

!! sho6n for &g0 or the calc1lated -. !! dia!eter $all cracking stress esti!ation

!ade for R()-?. Ar!strong and El$an have recently revie6ed

the case for s1ch pile21ps playing an i!portant role in the e:plosive deco!position ofR(< and other energetic !aterials >))?.

Summary

Indentation hardness !eas1re!ents covering !acroscopic' !icrostr1ct1ral' and

nanoindentation test !ethods have $een co!pared on a hardness stress 2 strain $asis'partic1larly involving !eas1re!ents !ade on Cl' &g0' ;aCl' and R(< crystals. 3or

&g0 in partic1lar' a =1antitative assess!ent has $een !ade of the elastic' plastic' and

cracking $ehaviors deter!ined fro! !icro2 and nano2indentation hardness test res1lts.he hardness stress 2 strain description is sho6n to provide a 1sef1l $asis for co!paring

different !aterial $ehaviors over the f1ll defor!ation range fro! elastic loading to

plasticity2ind1ced cracking.

Acknowledgement

0ne of the co2a1thors' Ron Ar!strong' thanks (r. Nves aillard for providing $othhelpf1l reprints and infor!ation concerning his co!prehensive !eas1re!ents !ade 6ith

colleag1es on nanoindenting &g0 4**-5 crystal s1rfaces.

References

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crystals' in &icroindentation echni=1es in &aterials Science and Engineering'

edited $y P.. Bla1 and B.R. #a6n 4A!er. Soc. est. &ater.' Philadelphia' PA'-F5 AS& SP ' p. -*.

-+. N. aillard' C. ro!as' and . oirgardX St1dy of the dislocation str1ct1re involved

in a nanoindentation test $y ato!ic force !icroscopy and controlled che!icaletching. Acta &ater.' -' -* 4)**95.

-. . oirgard' C. ro!as' . A1d1rier' and .C. irardX ;anoindentation st1dy of

very lo6 stress plasticity' in 31nda!entals of ;anoindentation and ;anotri$ology'

4&ater. Res. Soc.' arrendale' PA' -5 ol. ))' p. F.-. B.R. #a6nX Hert7ian fract1re in single crystals 6ith the dia!ond str1ct1re. . Appl.

Phys.' 9' ,) 4-F5.

)*. R.. Ar!strong and .#. El$anX (islocations in energetic crystals' in (islocationsin Solids' edited $y 3.R.;. ;a$arro and .P. Hirth 4Elsevier B..' 0:ford' %'

)**,5 ol. -)' Ch. F' p. ,*9.

)-. R.. Ar!strongX (islocation pile21psX 3ro! --*J cracking in &g0 to !odelstrength eval1ations. &ater. Sci. Eng. A' ,*' ), 4)**5.

)). R.. Ar!strong and .#. El$anX &aterials science and technology aspects of

energetic 4e:plosive5 !aterials. &ater. Sci. ech.' ))' 9- 4)**F5.


9/15

#ist of 3ig1res

3ig. -. &acroscopic load vs. indentation depth for a Cl crystal in a $all2type contin1o1sloading test' adapted fro! res1lts reported $y Ar!strong and Ro$inson >9?.

3ig. ). ;anoindentation load vs. depth for an &g0 4**-5 crystal s1rface indented 6ith aBerkovich indenter of tip dia!eter ,** n!' as deter!ined for a test res1lt reported $y

Cha1dhri >' ?.

3ig. 9. ;anoindentation load vs. depth for an &g0 crystal indented 6ith a Berkovich

indenter of tip dia!eter 9)** n!' as deter!ined for a test res1lt reported $y ro!as et al.

>--?.

3ig. ,. Hardness stress 2 strain relationship for co!$ined &g0 crystal res1lts' adapted

fro! res1lts reported $y Ar!strong et al. >+? to incl1de 4closed triangle5 eval1ations

derived fro! a test res1lt reported $y Cha1dhri >' ?.

3ig. . (islocation !odel of plastic flo6 at a dia!ond pyra!id indentation in an &g0

4**-5 crystal s1rface' after Ar!strong and 1 >-? and Ar!strong and El$an >-F?.

3ig. F. Hardness stress 2 strain res1lts for a variety of crystal !aterials' adapted fro!

Ar!strong and El$an >))?8 -.* kgf/!!)G .- &Pa.


10/15

3ig. -. &acroscopic load vs. indentation depth for a Cl crystal in a $all2type contin1o1sloading test' adapted fro! res1lts reported $y Ar!strong and Ro$inson >9?.


11/15

3ig. ). ;anoindentation load vs. depth for an &g0 4**-5 crystal s1rface indented 6ith a

Berkovich indenter of tip dia!eter ,** n!' as deter!ined for a test res1lt reported $y

Cha1dhri >' ?.


12/15

3ig. 9. ;anoindentation load vs' depth for an &g0 crystal indented 6ith a Berkovich

indenter of tip dia!eter 9)** n!' as deter!ined for a test res1lt reported $y ro!as et al.

>--?.


13/15

3ig. ,. Hardness stress strain relationship for co!$ined &g0 crystal res1lts' adapted

fro! res1lts reported $y Ar!strong et al. >+? to incl1de 4closed triangle5 eval1ations

derived fro! a test res1lt reported $y Cha1dhri >' ?.


14/15

3ig. . (islocation !odel of plastic flo6 at a dia!ond pyra!id indentation in an &g0

4**-5 crystal s1rface' after Ar!strong and 1 >-? and Ar!strong and El$an >-F?.


15/15

3ig. F. Hardness stress strain res1lts for a variety of crystal !aterials' adapted fro!Ar!strong and El$an >))?8 -.* kgf/!!)G .- &Pa.

Documents

Armstrong Indentation