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1 000 Applicaion of Coninuum Damag Modl o Lif Prdicion of Gomrically Nonlinar Srucur in High Tmpraur, 373-1,, 150 ABAQUS Chaboch Absrac In his invsigaion, h basic concp of coninuum damag mchanics was dscribd and h hrmodynamic approach o driv h viscoplasic consiuiv quaions and h consisn mhod of inroducing h damag variabl ino h viscoplasic consiuiv quaions ar discussd Gnral viscoplasic consiuiv laws wih svral sa variabls hav bn implmnd in h gnral-purpos fini lmn cod ABAQUS o prdic h viscoplasic rspons of h srucur subjcd o a cyclic loading Th safy assssmn for a gomrically nonlinar high mpraur srucur subjcd o svr ransin hrmal and mchanical loading was carrid ou Chaboch s viscoplasic modl was adopd o dscrib h marial bhavior of 316 sainlss sl a high mpraur and modifid o inroduc h inrnal damag Th damag conour of h srucur was illusrad and h fficincy of h proposd procdur was discussd 1

2 , Wibull s hory 1958 Kachanov, - 1 Kachanov S D D S S, S D S Rabonov F F σ σ ~ () S S S S D D D 1 1 S F Lmair (Srain Equivalnc Principl) - (3), ε f ( σ, κ,t) (3) (1) - ε f ( σ ~, κ,t) (4) κ, T

3 ε 1 σ~ E 1 σ E (1 D) (5) E E( 1 D) (5), D (6) E D 1 E E, E, E E Fig 1 - (6) (sa ponial) (Concav) (Convx) ϕ ϕ( ε,t, ε, ε p,r, α,d) (7) 1 1 Thrmodynamic variabls (1) Sa variabl Obsrvabl Inrnal Associad variabls ε Srain σ Srss T Tmpraur S Enropy ε Elasic srain σ Srss ε p Plasic srain -σ Srss r Accumulad plasic srain R Drag srss α Back srain nsor X Back srss D Damag Y Damag dissipad nrgy dnsiy ϕ Xγ aklεεkl + R r + xp( br) + αα (8) ρ b 3 (Associad variabls)

4 ϕ σ ρ a ε ε R X kl kl ϕ ρ R r ϕ ρ X γα α 3 [ 1 xp( br) ] (9) (10) (11) (kinic quaion) (ponial of dissipaion) F F( σ,r,x,y; ε,r, α,d) (1) ; s, R, X, Y, r, a,d (kinic quaion) (normaliy rul) p F & λ& (13) s F & r λ& (14) R F a & λ& (15) X (muliplir) λ & (13) ~ (15) (dissipaion ponial) Dissipaiv variabls (1) Flux variabls Dual variabls p & s r& R a& X D & Y ( Y) q r gradt r T Chaboch Modl F J ε & p ( σ ) R σ F 3 σ X λ & λ& σ J( σ X) y 3 + 4X X : X F & r λ & λ& (18) R (16) (17)

5 a& & p 3 X Xλ& (19) R & b(q R)p& (0) X& C & p γ(p) Xp& (1) 3 () (17), (0), (1) λ & f J ( σ Χ ) R k () λ & λ & p& J ( σ X ) R k K n (3) 3 D Y, Xγ ϕ (1 D)aklεεkl + R r + xp( br) + αα (4) ρ b 3 ϕ σ ρ a klεkl(1 D) ε R X ϕ ρ R r ϕ ρ X γα α 3 ϕ Y ρ D [ 1 xp( br) ] 1 a kl ε ε kl F D 3 F J ( ~ s ) R σy + X : X + F (9) D 4X F 3 σ ~ J( ~ X λ& ε& p λ & σ σ X) 1 D (5) (6) (7) (8) (30)

6 R & b( Q R ) λ& (31) & X C & (1 D) γ( p) Xλ& (3) p 3 λ & p& ( 1 D) (33) & F D λ& (34) Y 4 (1) Y FD (Y;(r,D)) H(r pd) (35) S(1 D) (34) Y D& ph & p S ( ) p D (36) Y σ q R ν E( 1 D) (37) R ν E (1 ) 3(1 ) ε + ν ν 3 σq H (38) p, p D H Havisid funcion (Plasic srain hrshold) (Elasic Enrgy dnsiy rlas ra) (Accumulad plasic srain ra) (39) D D C (39) D C (microcrack), Fig 3 Chaboch Fig 3,, Fig 4

7 (1) 3 Chaboch σ σ~ 1 D p 3 σ ~ X ε& ~ p& ( σ Χ ) q R & b( R R)(1 D ) p& Χ & p γ(1 D) Χε& Χ p& 3 Y D& ph & ( p p D ) S σ q R ν E H Y R (1 ) 3(1 ) ε ν + ν ν E( 1 D) 3 σq N ( σ ~ Χ ) q R σ y p & H ( σ ~ Χ ) q R σ K ( ) y 3 GMR (40),, & & + & + & h in (40) (41)~(4) 1+ ν & s~ & ν Tr[ s~ & ]I (41) E E & h γt& I (4) E ν, g (40)~(4) p p [ & & ] I + (1 D) λ( & & ) s& (1 D) µ r (1 D) γ( µ + 3λ)T& I λ µ Lam (4) 3 ξ (4) σ& G( s, x,t) (43) x& H( s, x,t) (44)

8 Chaboch ξ (X, R, D) 31 (45) y & f ( y, ) ABAQUS (45) GTR(gnralizd rapzoidal rul) (46) (45) y [ 1 θ) f( y, ) + θf( y, + ) ] ( + (46) y + y + [( 1 θ) f (, y ) + θ f ( +, y + y) ] (47) θ 0 1 yθ y + θ y (43), (43) (47) σ ξ [( 1 θ) G + θ ] (48) G + [( 1 θ) H + θ ] (49) H + G G(s, ξ,t ), G G(s,,T ) + + ξ + + [( θ) + θg, ξ, T )] s G ( (50) ξ + s s [( θ) + θh( ξ,t )] + ξ + 1 +, + + H s (51) ( ) ( T ) + + (5) T + T + θ T (53) (50)~(51), ξ +, ξ +

9 (Lin sarch) () 3 ABAQUS UMAT ABAQUS,, (dformaion gradin nsor) ABAQUS ABAQUS (3) Jaumann Ra (Rigid Body Roaion) ( + )(50) (51) (50) (51) (4) 4 Y- - Y- Y- 41 Y- Fig 5 Y-,, Fig o C 550 o C Y-, Y- 8 Y-

10 316 4 Y- 5833*10-3 J/mm o C sc Fig 7 Fig, Y- 4 Y- ABAQUS 5 6 Fig8 333 Fig 9 - Fig 10 - Fig Y- Fig cycl ASME Cod Scion III Subscion NH - 5

11 ABAQUS UMAT 1 JLmair, A Cours on Damag Mchanics, Springr-Vrlag, 199 Numrical rcips in Forran, 199, Cambridg Prss 3 ABAQUS, Usr s manual, Vrsion 54, 1995, HKS, USA 4 Samson Youn, Soon-Bok L, Jong Bum Kim, Hyong-Yon L, Bong Yoo, Implmnaion of visco-plasic consiuiv quaions ino h fini lmn cod ABAQUS, Procdings of h Koran Nuclar Sociy, 98 Auumn, JLmair and JLChaboch, Mchanics of solid marials, Cambridg Univrsiy Prss, (kg/mm 3 ) (J/kg o C) (J/sc mm 3 ) Marial paramrs of h Chaboch modl for h 316 sainlss sl (4) Marial T( C o ) N K σ y X o γ Q b 316 sainlss sl Elasic propris and Marial paramrs of h Damag voluion quaion for h 316 sainlss sl (3) Marial E (MPa) ν T(C o ) S (MPa) ε pd D 1C 316 Sainlss Sl 140,

12 05 04 Damag Numbr of cycl Fig 1 Low cycl faigu srss-srain parn for AISI 316 L Fig Damag voluion a low cycl faigu sing B 100 B Srss (Mpa) Srss Tim Fig3 Effc of Damag voluion o h marial bhavior: im vrsus srss rang Srain Fig 4 Effc of Damag voluion o h marial bhavior; srss-srain curv involving damag Fig 5 (vssl) Y

13 Fig Fig 7 Y Fig 8 Fig9 - Fig10 -

14 Fig 11 Fig 1

DBPIA-NURIMEDIA

DBPIA-NURIMEDIA 22 특집 : 용접산업의시뮬레이션기법활용 Wlding Simulaion Incororaing h Mchanical Rlaxaion du o Mling Myoung-Soo Han 1. 서론 철강재료에대한아크용접공정은용융지 (mling ool) 근방의집중적열투입으로발생하는비선형적온도변화에따른천이적응력및변형률의변화와더불어복잡한상변태등을동반한다. 용융용접에서발생하는이러한역학적현상을유한요소법을사용한수치해석적방법으로평가하기위한시도는종래부터다양하게연구되어져왔으며최근컴퓨터성능의비약적인발전에따라그수법및다루어지는문제의크기도점차적으로대영역문제에대한현상규명에가깝게다가서고있다.

歯295윤삼손.PDF

歯295윤삼손.PDF