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
, 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
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) ฯ ฯ( 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 ฯ 1 1 1 Xγ aklεεkl + R r + xp( br) + αα (8) ρ b 3 (Associad variabls)
ฯ σ ρ a ε ε R X kl kl ฯ ρ R r ฯ 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)
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, 1 1 1 Xγ ฯ (1 D)aklεεkl + R r + xp( br) + αα (4) ρ b 3 ฯ σ ρ a klεkl(1 D) ε R X ฯ ρ R r ฯ ρ X γα α 3 ฯ 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)
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
(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)
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 + 1 + s + + + [( θ) + θh( ξ,t )] + ξ + 1 +, + + H s (51) ( ) ( T ) + + (5) T + T + θ T (53) (50)~(51), ξ +, ξ +
(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 6 - - 50 o C 550 o C Y-, Y- 8 Y-
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 - Fig11 333 Y- Fig 1 - - - - 100 0005 10 4 cycl ASME Cod Scion III Subscion NH - 5
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, 1998 5 JLmair and JLChaboch, Mchanics of solid marials, Cambridg Univrsiy Prss,1990 4 (kg/mm 3 ) (J/kg o C) (J/sc mm 3 ) 316 8-6 500 15-3 178-9 51 13318-3 5 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 600 1 150 6 867 300 80 10 6 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 140,000 03 600 0 00 05
05 04 Damag 03 0 01 00 0 100 00 300 400 500 600 700 Numbr of cycl Fig 1 Low cycl faigu srss-srain parn for AISI 316 L Fig Damag voluion a low cycl faigu sing 00 00 100 B 100 B Srss (Mpa) 0-100 Srss 0-100 -00-00 0 000 4000 6000 8000 10000 1000 14000 Tim Fig3 Effc of Damag voluion o h marial bhavior: im vrsus srss rang -0010-0005 0000 0005 0010 Srain Fig 4 Effc of Damag voluion o h marial bhavior; srss-srain curv involving damag Fig 5 (vssl) Y
Fig 6 - - Fig 7 Y Fig 8 Fig9 - Fig10 -
Fig 11 Fig 1