Khảo sát hàm hấp thu trong tính toán ứng suất vật liệu phi đẳng hướng bằng chiếu xạ x quang sử dụng phương pháp đo omega

NGHIEN CIJTU-TRAO Ddl KHAO SAT HAM HAP THU TRONG TINH TOAN UNG SUAT VAT LIEU PHI DANG HU'OfNG B A N G NHlfiU XA X - QUANG SU* DUNG PHU'OnVG PHAP DO OMEGA STUDY OF ABSORPTION FACTOR IN

NGHIEN CIJTU-TRAO Ddl

KHAO SAT HAM HAP THU TRONG TINH TOAN UNG SUAT VAT LIEU

PHI DANG HU'OfNG B A N G NHlfiU XA X - QUANG

SU* DUNG PHU'OnVG PHAP DO OMEGA

STUDY OF ABSORPTION FACTOR IN X-RAY STRESS ANALYSIS OF ANISOTROPY

MATERIAL USING Q-TYPE GONIOMETER

TS Le Chi Cmrag

Khoa Co khi mdy, Trudng Dgi hpc Su phgm Ky tiiuat Thanh phd Hd Chi Minh

TOM TAT

Bdi bdo nghien ciru tinh todn hdm hdp thu trong do ung sudt diing nhieu xg X-quang doi v&i vgt lieu phi dang hu&ng Kit qud mo phong thepferrite v&i ho mat phang nhieu xg {211} diing dgc tinh tia X la Cr-Ka cho thdy mo hlnh Eshelby-Kroner cho gid tri gdn vai thuc nghiem han so v&i mo hinh Voigt vd Reuss

Tir khda: Do ung sudt bdng X-quang; He so hdp thu; Tex-tua; Vgt lieu phi dang hu&ng

ABSTRACT

This research will represent the influence of the anisotropy of material into the generalized absorption function in stress measurement using x-ray diffraction The simulation result offerritic steel {211} plane using Cr-Ka radiation shows that the Eshelby-Kroner give the closer result to the experimental data in comparision to those from the Voigt and Reuss models

Keywords: X-ray Stress Measurement; Absorption Factor; Texture; Anisotropic materials

1 Gidl THI$U neutron, nhidu xa X-quang Trong dd, phuang

phap nhidu xa X-quang la phuang phdp khdng U'ng suit du Id mpt trong nhung nhan td phd hfly cd the xac dinh chinh xdc ung suat, de quan trpng dnh hudng din dp bin, tudi thp cfla chi dang tu dpng hda Dd tinh toan chinh xdc gid tri tidt may iTng suit du dugc phat sflih trong qua flng suit, cucrag do tia X phai dugc hieu chinh trinh gia cdng co, gia cdng dp luc, xu ly nhidt bang he sd hap thu hoac ham hap thu [1,2] Ddi

Vi vdy vipc xac djnh flng suit du cd vai trd rit vdi vat lieu ding hudng, ham nay da dugc tinh quan trpng trong qua trinh xu ly va cdi thien diiu toan[3] Tuy nhidn, ddi vdi vat lieu phi dang hudng ki^n lam vipc ciia cac chi tidt mdy nhu thep can ed td chflc texture, hdm hap thu

vdn chua dupe tinh toan, do dd, bdi nghidn cuu

Cd nhieu phuang phdp xac dinh flng suat ndy se tinh ham hap thu tdng qudt cho vdt lipu phi

du tren be mdt chi tiit nhu phuang phap; Due Id, ding hudng su dung cac gia thiet Voigt, Reuss va

cdt tiet di$n, sidu dm, quang ddn hdi, nhieu xa Elsherby-Kroner dflng phuang phdp do Q ^

NGHIEN CUTU-TRAO Ddl

2 M 6 I Q U A N WE UlSG SUAT - BIEN D ^ ^ G

Xit he toa do nhu Hinh 1, trong do S 14 he

tpa dp gan hen voi mau, trong do 5^, S^ nam trong

b^ mat mlu L^ \k he toa do do, vuong goe voi

hg mat phang nguyen tii {hkl} L^ nam trong mat

phang man t?o voi S^ mpt goe (p BiSn dang xac

dinh duac la biln dang trong h6 tpa dp do, duac

bieu dien thdng qua biSn dang ciia he tpa dp mau

bang he thong ma tran chuyen doi tpa dp

Binh 1 Cdc he true toa do thi nghidm L va mau thuS

BiSn dang tnmg binh dpc true L3 duac

xacdinhbSng {e^,)^ = '''"~''° =a,,a„>!„ (1)

Trong do: d^ la khoang each giCa cac mat

m ^ g khi chua co iJng suat; a^j , j^, la cosin chi

hudng cia L^, S, va Lj, S,; a^ li ma trjn chuyen

giiSa he thong miu S va he thong do L Thay a^,,

a^ vio phiiang trinh (1) ta co biSn d^ng:

^eJ3J =£„cos psin <i/+£^^sin(psva if + e^^sm tpsm^ili

+53jCos^t(^+f,3Cos^sin2(/+£:j3Sinpsin2((/ (2)

TClbiendang, tacothexacdinh dupe iJng

suat thong qua m6i quan he ling suat bien dang

Trong v4t lif u phi dang hudng cac tinh the khong

sap xep mpt each nglu nhien, tinh chat tai mpt

dilm nao dp eiia no khong giong nhau theo cac

phuong khae nhau Dl dje trUng cho tinh chat

phi dang hudng, he so ling suat tia X dupe sil

dung, va dupe xac dinh bang [4,5]:

v6i/Cg; li him phan bo hudng (ODF); S,^ ket hpp

don tinh the phi dang hudng; A la gdc quay quanh

vecta vuong gdc vdi hp mat nhieu xa {hkl}

Trpng bii nghien eilu nay, ta gia djnh vat lifu phi dang hUdng la dong nhat, co t6 chiic tex-tua manh, tiic li phin be cua tinh the

ly tudng hda chi vii hildng Uu tien Khi dd h? s6 ling suat dilpe tinh qua trung binh ciia h | so dan hpi dan tinh t h i phi dang hudng, tiic li h| s6 din hoi dan tinh the trpng h^ trilc tpa d$ L

HI SP ling suat dUpe xac dinh li:

F(M;,<P,V/ )=s^a J+^s^m,fs,,j (4)

Trong do 5','", 5'*' li he sd dan hoi dOn tmh the

ciia mat (hkl), 5^ Ii cac delta Kronecker, vi oj la

cac cosin chi hudng ciia h? true

3 H A M H X P THU DOI VOI VAT LIEU PHI DANG HUdNG

Xet ehiun tia tdi phan to ed the tieh Sdz va

nhieu x^ ra khdi mau thii Ddi vdi vat H|u phi d4ng hiidng, chieu dii xuyen than cua chum tia tdi vi tia nhilu xa can phii hieu chinh bang hi s6 ling suat TrUdng hpp niy, cUdng do nhieu xa eua phan to la:

p{hkl,if,\^)- ~2it

J/te¥>

(3)

Co djnh I/O C6 dinh;;

Hinh 2 Phuong phdp do Q

NGHIEN cufu - TRAO BOI

<S = a/, exp{,-fi(F,fAB+F^BC)]Sdz

vdi AB = —^,BC = — ^ • Lay tich ph^n ta cd:

cosa cos^

= J/oiiexp -^1

cosa " cosjS ^.hdz

Ddy la cdng thuc tmh hdm hap thu tdng

qudt khdng gidi han didn tieh nhidu xg ddi vdi vat

li^u phi ding hudng Trong do he sd flng sudt tia

X trdn tia tdi AB la F-^ Tfl (4) ta cd:

cosVsinV -sm2psinV -cos^sin2j?

-sin2psin^^ sin^psin^^ -sin^sin^^

-cos^sin2^ -sin

(10)

/ g a cos a cos jg

~ // *^ F,f^ cos ^+Fg^ cos a

Luge bd cdc h i n g sd, ham h i p thu dupe

xdc dinh bing:

7 : " ' ^ F , - " o o s f l + F , ' " ^ c o s a ^ '

Thay thd /|=l/cosi|' vd /^ = l/cosq vdo (5),

ta cd hdm hap thu tong qudt dUpc tinh theo cdng thflc:

1 cosa cos jg

c o s ^ c o s ; ; i^^ c o s a + Z^^ cos^ff (11)

3.1 Phfldng phdp c6 dinh i^j,

„ rcosa = cosK/sinft, , , , ,

Thay J ^ " vao (11), [cos^ = cos(i/sin(2^-^o)

ta daoc ham hap thu trong phiiong phdp c6 djnh

(7)

cosVsin^a -sin2psin'Q: -cos^siii2a

1 , ! : ! 1 J

-sm2$jsm o sin f sm a -sin^sin a

1

(8)

juspsinza -sinpsin2a cos^a

Hp sd flng sudt tia X tren tia nhidu xa BC

ld7=;/"^.Tfl(4)tacd:

e**^ _ v"iis ^ c**'^^«c,,»c (9)

«?;<;"

sin(2e-61,)

Vdi cac t h i n h phan cua ma t r i n chuyin

d 6 i « :

i^j-" sin(2e -e,) + F''^ sin B, (12)

a Mo hinh Reuss

Reuss gid dinh flng suat trong m ^ g da tinh the la nhU nhau H^ s6 ddn hdi tia X trong

md hinh Reuss dflpc tinh bang [6,7l:

5f(Mo=%+Jor; -s^ihki) = sj,-s,^-3sar (13)

Vdi tham sd hudng r

Thay (8) vdo (7) vdi a^o:^ la ma trdn chuyen tfl

tpa do 5 sang tia tdi AB, ta tinh dugc cdc thanh

p h i n ciia he sd dan hdi tia X tren tia tdi AB: Cdc thdnh phan cua ma trgn chuyen doi

c(«)AB ,

-{R)AS -HKSAB -HKSAB

33311 03312 d3313

-{K)J& {R)AB —(R)AB

^3322

-WAS

03332

53323

iR)AB

(14)

NGHIEN CJJU - TRAO DOI

Tuong tvr ta tmh dupe he s5 ling suat tren

tia nhilu x?i BC tic cac thinh p h k cua hing so

dan hdi tia X tii (7) va (9) vdi <^1'^<af/14 ma tran

chuyin t i tpa dp S sang tia nhidu x? BC The hd

sd ling suit niy vio cdng thiic (11), ham hap thu

tinh theo md hinh Reuss trd thanh:

sin(2e-e,)

' F / ' - " sin(2S - 6i„) + F™"'sin 6I„ (16)

b.Mdhinh Voigt

FJhkI,ip,yf) = \S„,j+t„ (21)

Trong md hinh Voigt, bien dang ciia cae

hgit tinh thi trong vat Ii|u li nhu nhau H | sd din

hdi tia X trong md hmh Voigt li:

^i _ 2s„(j,| +2s„)+5s„s„ 1 51- _ SJ«.(J|I - J „ ) {j7)

' 6J0+5J44 2 ^ 6sg+5s^

Trong dd S33,) Ii hing s6 din hdi don tmh the da biet, dilpc tinh theo md hinh Reuss vi (,3,^

la phin tiidng tic din hdi ciia h?t vdi ma trin din hdi bao quanh, dildc tinh nhu sau:

lm,=[E{c(.g)-C}+lJ'-I (22)

*

Vdi c (g) la hang sd dg cflng ddi vdi mpt hgt troi^ vgt h^u; / la ma trgn hang tfl, dflgc tinh theo cdng thflc:

C = S-1: dp cflng ddn tinh the

Tenxg E dflgc tinh:

(23)

vdi*o=*ii-*i2—^^^44 [8].'Ihay(17)vao

(7), ta tinh dflgc cdc thdnh phan cfla hp sd ddn hdi

tia X trdn tia tdi AB va tia nhieu xa BC lan Iflpt la:

jp(V}AB _

p(V)BC _

f-(V)AB -{y)AB -(r)AB'

03311 03312 03313

'-z^yiBC ^y)BC —{r)BC

03311 03312 03313

(18)

(19)

Him hip thu eho phUdng phap c6 djnh r]^

theo md hinh Voigt li:

siii(2g-6i,)

/^7>'"siii(2»-».)+fW5in6i (20)

c Mo hinh Esheiby-Kroner

Vdi md hinh Eshelby-Kroner, ngoii thinh

phin ling suit edn cd tUdng tic gifla cac hat Do

dd, F(hkl,(p,yi) dupe tinh [9]

(24)

vdi A,

sin ^ cos ^ sin ^ cos ^ cos^

Him hip thu dupe tinh theo md hinh Eshelby-Kroner:

sia(29-g.) (25) i^"""sin(2e-9,)+J^™»=cos6!,

Vdi cae thinh phan cua hing sd din hoi tia X tren tia tdi AB vi tia nhilu xa BC dupe tmh trong md hinh Reuss v i them thinh phan tUdng tic din hdi ciia h^t

lf'''=Fr""+'m (27)

3.2 Phiidng phip cd dinh 1) Khi c6 dinh q gdc nhilu xa fl° = 9, nen

thay e„ bang 6 trong edng thije (6) tinh him hJp

NGHIEN cufu - TRAO DOI

tiiu vd hing sd ddn hoi tia X trong phuong phap cd dinh gdc T\:

cd dinh gdc TI„, ta dugc ham hip tiiu phuong phap ^(^j^ ^ ^^gy^ ^ ^

cd dinh gdc ij: ir ? s

plK)BC _pmBC

g g 3

^ = _ / - (28)

(33) (34)

a Theo md hinh Reuss

Thayd(, = dvao(14)va(15) ta tinh dugc

cdc thdnh phan cfla hang sd dan hdi tia X tren tia

tdi AB va tia nhieu xg BC:

Fr^ =

r e^*' "^<''> c*^*

03311 03312 03313

-{R) -iR^ -iR)

•3 3321 0 3322 0 3323

•^(.R) -^(fi) -ziR)

0 3331 0 3332 03333

(29)

Him hap thu theo md hinh Reuss dupe

tinh theo

A = - 1

h MS hlnh Voigt

(30)

Thay 6^ = 9 vio (18), (19) ta tmh dupe

cic thinh phin ciia hing sd din hdi tia X trln cic

tiaABviBC:

p(y)._

f-^v) -Tin -^v) ^

03311 03312 03313

- ( f ) - ( F ) - ( F )

0332I 03322 03323

•^(F) - ( F ) - ( F )

03331 t>3332 0 3333

(31)

A = - 1

e Mo hinh Eshelby-Kroner

Ham hip thu theo md hlnh Eshelby-Kioner dupe tinh theo phuong trinh:

1

pi.y)AB ^ piV)BC (35)

4 KHAO SAT BIEN THIEN CUA HAM HAP THU VOfI GOC 0 , T VA O

Hmh 3 cho thiy ham hip thu A d6i vdi

phuang phap do cd dinh gdc i^O trong pham vi gdc nhidu xa 20 tu 140° ddn 180°, Id pham vi cho sai sd phep do nhd vd thdng thudng dugc dflng

dd do ung suit, sfl dung ddc tflih tia X cfla CrKa cho mat nhidu xa (211) cfla thdp ferrite Tfl kit qua tinh todn, ta thiy h ^ hip thu gidm khi gdc nhidu xa tang ldn Ddi vdi md hinh Reuss vd Voigt, A gidm nhanh d cdc gdc 9^ thip, vd gidm chdm d cdc gdc 9^ cao Bien thien ndy ngugc lai, vdi md hinh Eshelby-Kroner Didu ndy phfl hgp vdi kdt qud cfla cac nghien euru trudc vd hdm hip thu cho vgt lipu ding hudng [3,4], khdng dinh md hinh Elsherby - Kroner phfl hpp vdi kdt qud ki^m nghiem bdng thirc nghidm hem Id md hinh Reuss

va Voigt Do dd, md hinh Elsherby-Kroner dugc

de xuat sfl dung trong do ludng - tinh todn flng

Ham hip thu theo md hinh Voigt dugc

tinh theo phuong trinh:

(32)

Hp sd dan h6i tia X tren tia tdi AB va tia

nhieu xg BC dugc tinh trong md hinh Reuss vd

them thdnh phin tuong tdc dan hdi cua hgt dugc

tinh d md hinh Eshelby-Kroner cho phuang phap (a) M6 hinh Reuss

06ciihiSo]if2e,d$

NGHIEN cufu - TRAO D(!>l

(b) Mo hinh Voigt

m

1

1-T

• ^

^r J l

3"

— f — i

;

« w

1 j

• n s

1 1

• •

06c •

1

f — 1 — ^

j

420,

p —

It m

"

i!

^«

fj

s '••

'

'

4-1 ••\

• » • » •

4-Si

1

1 M 1 1 1 1 1

OdcnhiSDXfie,^

(&j Afa /lin/i Voigt

G6cnluSDX92e,d$

(cj iW5 /iJn/i Eshelby-Kroner

Hinh 3 Hdm hdp thu A cho phtidng phdp c6 dinh ri^

Suit vdt lieu phi ding hudng dung nhidu

xa X-quang

Tuang tu, hinh 4 Id hdm h i p tiiu tuong

flng dugc tinh toan cho phuang phdp do cd dinh

gdc ?/ Dgc biet, ddi vdi md hinh Reuss va Voigt,

A khdng phu thude vdo gdc nghieng y/ vd gdc

nhidu xa 29, thdng nhit vdi ket qua nghien cuu

trudc [3] Mgt khac, md hinh Eshelby-Kroner cho

hdm hap thu bien thien nhieu ph\i thugc vao gdc

nghieng ij/, tuong tu nhu phuong phap cd dinh

gdc?/

„ "

• ? '

St

K

T

i 1 j 1

p 1 1 1

• f « i

i 1 i

i 1 i

t ^

(a) Mo hinh Reuss

(c) Md hinh Eshelby-Kroner Hinh 4 Hdm hdp thu vdi phUdngphdp c6^nh t}

5 KET L U A N

Nghien cflu da dat dflgc nhflng ket qui

n h u sau: Tinh toan va xay dUng dflgc cdc cdng thflc tong qudt cho h a m hap thu trong vdt Hdu phi dang hfldng thdng qua cac md hinh Reuss, Voigt

vd Eshelby-Kroner

Md phdng cdc dgng dd thi tdng quat va khao sdt sfl bien thidn cfla hdm hap thu tia X cua

vdt lidu tex-tua lam ca sd cho viec tinh todn chinh

xac dinh nhi^u xa va flng suat cua vgt U?u, dgc bi§t

la cac vgt lidu sat thep thdng dung

Md hinh Eshelby-Kroner cho gia tri h ^ hdp thu phu h g p vdi mgng tinh the thflc, nSn dflgc sfl dung trong do Ifldng tinh toan flng sillt dung nhiSu xa X-quang • ^

NGHIEN eu'u - TRAO D(!)l

Ngiy nhin bii: 10/9/2012

Ngiy phan bipn: 22/10/2012

Nguiyi phan biSn: TS DJng Thifn NgSn,

Trupng Dai hpc Su pham Ky thuat Thinh phd Hd CU Minh

Tai liSu tham khao:

[1] B.D Cullity, (2001), Elements of X-ray Diffaction, 3rd Edition, Prentice Hall Upper Saddle River, NJ 07458,258-262

[2] Ismail C Noyan, Jerome B Cohen, (1987), Residual Stress-Measurement by Diffraction and Interpreta-tion, Springer - Verlag, 30-42

[3] Le Chi Cuong and M Kurita, (2004), Absorption Factor and Influence of LPA on Stress and Diffraction Line Width in X- Ray Stress Measurement, Joumal of Japanese Society for Experimental Mechanics, 7-14 [4] V Hauk, (1997), Structural and Residual Stress Analysis by Nondestructive Methods, Elsevier, 25-33, 114-125

[5] Shouichi Ejiri, Toshihiko Sasaki, Hirofiimi Inoue, Yoshio Shirasuna and Yuido Hirosi, (2001), X-Ray Stress Determination of Cold-Rolled Steel Sheet Using Orientation Distribution Function, Advances in X-ray Analysis, Vol 44,43-49

[6] Jian Lu, (1996), Handbook of Measurement of Residual Stresses, Pegamon, 12-40

[7] Ch Genzel, (1994), FonnaHsm for the Evaluation of Strongly Non-Linear Surface Stress Fields by X-Ray Diffraction Performed in the Scattring Vector Mode, Phys Stat Sol (a) 146, 629

[8] S J Skrzypek, et al, (2005), Progress in X-ray Diilraction of Residual Macro-stress Determination Related

to Surface Layer Gradients and Anisotropy, Advances in X-ray Analysis, Vol 44, 66-72

[9] K Perry, I C Noyan, R J Rudnik, J B Cohen, (2004), The Measurement of Elastic Constants for The Determination of Stresses by X-rays, Department of Material Science, The Technological Instistute, North-westem University, 60601, 93-103