Finite Element Modeling for the Structural Analysis of Al-Cu Laser Beam Welding

PDWHULDO

SRZHU

ZHOGLQJVSHHG

IRFDOGLDPHWHU

ZHOGVHDPOHQJWK

VKLHOGLQJJDV

P v 

G

I

 l  

(homogeneous material, sheet metal specimens)

$O

:

PPLQ

—P

PP

$U

&X(73

:

PPLQ

—P

PP

$U

723

%27720

(heterogeneous material connections, Al-Cu overlap joint sheet metal specimens) 

$O

&X(73

:

PPLQ

—P

PP

QRQH

$O

&X(73

:

PPLQ

—P

PP

QRQH

)LQLWH(OHPHQW0RGHOLQJRIWKH/DVHU%HDP:HOGLQJ3URFHVV

3.1.

 

Governing Equations and Constitutive Modeling  

7R SUHGLFW UHVLGXDO VWUHVVHV DQG ZHOGLQJ GLVWRUWLRQV DFFXUDWHO\ LQIRUPDWLRQ DERXW WKH WHPSHUDWXUH ILHOG

GLVWULEXWLRQZLWKLQWKHKHDWDIIHFWHG]RQHLVFUXFLDO)RUVWUXFWXUDODQDO\VLVVHTXHQWLDOO\FRXSOHGWKHUPRPHFKDQLFDO

)LQLWH (OHPHQW DQDO\]HV DUH SHUIRUPHG 7KH H[DFW SK\VLFDO PRGHOLQJ RI WKH ZHOGLQJ SURFHVV LV VWLOO D FKDOOHQJLQJ

WDVNGXHWRKLJKO\QRQOLQHDUFRXSOLQJVRIGLIIHUHQWSK\VLFDOGRPDLQVWKXVWKHFRPSOH[IOXLGG\QDPLFSURFHVVHVDUH

RIWHQ VLPSOLILHG E\ D KHDW FRQGXFWLRQ SUREOHP (T  ZLWK

T

 EHLQJ WKH WHPSHUDWXUH DQG WHPSHUDWXUH GHSHQGHQW

PDWHULDOSURSHUWLHVIRUGHQVLW\

ȡ

KHDWFDSDFLW\

c

DQGWKHUPDOFRQGXFWLYLW\

k

q

/

LVWKHODWHQWKHDWGXHWRVROLGOLTXLG

SKDVHWUDQVIRUPDWLRQDQG

q

$SS

WKHQHWKHDWLQSXWRIWKHKHDWVRXUFHPRGHOV

ߩሺܶሻܿሺܶሻ

డ்

డ௧

ൌ ߘ ή ሺ࢑ሺܶሻߘܶሻ ൅ ݍ

௅

ሺܶሻ ൅ ݍ

஺௣௣

ݍ

஺௣௣

ா௟௟௜௣௦௢௜ௗ

ൌ ൞

ݍ

஺௣௣ǡ௙

ሺݔǡ ݕǡ ݖሻ ൌ

଺ξଷ௉

ಽ

௙

೑

௔௕௖

೑

గξగ

݁ݔ݌ ቀെ

ଷ௫

మ

௔

మ

ቁ ݁ݔ݌ ቀെ

ଷ௬

మ

௕

మ

ቁ ݁ݔ݌ ൬െ

ଷ௭

మ

௖

೑

మ

൰ ǡ ݔ ൏ Ͳ

ݍ

஺௣௣ǡ௥

ሺݔǡ ݕǡ ݖሻ ൌ

଺ξଷ௉

ಽ

௙

ೝ

௔௕௖

ೝ

గξగ

݁ݔ݌ ቀെ

ଷ௫

మ

௔

మ

ቁ ݁ݔ݌ ቀെ

ଷ௬

మ

௕

మ

ቁ ݁ݔ݌ ቀെ

ଷ௭

మ

௖

ೝ

మ

ቁ ǡ ݔ ൐ Ͳ

 

ݍ

஺௣௣

஼௢௡௘

ሺݔǡ ݕǡ ݖሻ ൌ

ଷ௉

ಽ

గ௭

బ

ൣோ

಼

మ

ା௥

಼

మ

ା௥

಼

ோ

಼

൧

 

 

+HDW VRXUFHV DUH XVHG WR PRGHO WKH KHDW LQSXW IRU ODVHU EHDP ZHOGLQJ 'HILQHG LQ (T  DQG  WKH YROXPWHULF

SRZHUGLVWULEXWLRQRIWKHGRXEOHHOOLSVRLGDODQGFRQLFDOKHDWVRXUFHFDQEHVHHQDFFRUGLQJWR

Goldak

>@:KHUH

a

b

c

I

c

U

r

N

R

N

DQG

z

DUHDVHWRIJHRPHWULFDOSDUDPHWHUV

f

DQG

f

f

f

 UHSUHVHQWWKHHQHUJ\GLVWULEXWLRQWRWKH

IURQW DQG UHDU VHFWLRQ RI WKH GRXEOH HOOLSVRLG DQG

P

/

 GHQRWHV WKH QRUPDO GLVWULEXWHG HIIHFWLYH ODVHU SRZHU 7KHVH

PRGHOVDUHVXSHULPSRVHGPXOWLSOHWLPHVIRUWKHWHPSHUDWXUHILHOGDQDO\VLVRIWKH$O&XRYHUODSMRLQWV)LJ

)LJ+HDWVRXUFHPRGHOVDGRXEOHHOOLSVRLGDODQGFRQLFDOKHDWVRXUFHPRGHOLQDFFRUGDQFHWR*ROGDN>@DSSOLHGIRUWHPSHUDWXUHILHOG

UHFRQVWUXFWLRQEKHDWVRXUFHPRGHOFRPELQDWLRQIRUEDVHPDWHULDOVHJ$OFPXOWLSOHKHDWVRXUFHVXSHUSRVLWLRQIRURYHUODSMRLQWV

---

 Udo Hartel et al.  /  Physics Procedia   83  ( 2016 )  1404 – 1414 

1407

)RU WKH PHFKDQLFDO DQDO\VLV WKH JRYHUQLQJ HTXDWLRQ LV JLYHQ E\ WKH PRPHQWXP EDODQFH 1HJOHFWLQJ LQWHUWLD

IRUFHV WKLV OHDGV WR WKH IRUPXODWLRQ LQ (T  ZLWK