HVA KAN VI OPPNÅ MED FE BEREGNINGER *HVORDAN VAR DET? *HVORDAN ER DET? *HVORDAN BLIR DET?
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The JQM Approach M =, T = 0 Q M σ σ + Q σ f θ ) + M σ f ( θ + 12 ij ij 0 ( β 0 _1 ij 0 _ 1 ij ) Geometry t i t specimen crack loading Mismatch t i t strength hardening general J-Q theory BM or HAZ J-M th WM J-Q-M theory
ACCRIS 1997 (σ y = 500 MPa) PRESS 2001 (σ y = 700 MPa) STRAIN BASED DESIGN Temperature Toughness Brittle fracture - constraint correction Brittle fracture - ccriterion Ductile crack growth Plastic collapse J-Q-M
PRESS-project MATERIAL BASE MATERIAL 50 mm thick QT steel plate Prescribed yield strength of minimum 690 MPa. Yield and tensile strength in the mid-thickness position were 655 MPa and 745 MPa respectively. ALLOY: C Si Mn P S Al N Cu.16.430 1.20.013.001.039.008.035 Mo Ni Cr V Nb Ti B.31.34.425.043.026.003.0002 TWO DIFFERENT WELDING PROCEDURES Flux-Cored Arc Welding (FCAW) Submerged Arc Welding (SAW)
Typical macro section of the welded joints
690 MPa steel PRESS-project Notched tensile testing Stress-strain curves 1.0 mm FL
FRACTURE MECHANICS SPECIMENS Specimen B [mm] W [mm] SENT (a/w=0.2) 46 (37) 46 SENB (a/w=0.2) 46 (37) 46 SENB (a/w=0.5) 46 (37) 46 Crack tip position BM FL (FCAW) FL (SAW) BM FL (FCAW) FL (SAW) BM FL (FCAW) FL (SAW) No. of parallels 6 12 12 6 12 12 6 12 12 Crack orientation Surface notch Surface notch Surface notch
Examination of three test geometries bending pin-loaded clamped
bending pin-loaded clamped
bending pin-loaded clamped
Effekt av geometri SPREKKENS DRIVENDE KRAFT SENT clamped (a/w=0.2) SENB (a/w = 0.2) APPLIED J SENB (a/w = 0.5) CONSTRAINT [Q,T,M]
Kvantifisering av material-mismatch (J applied) m=1.3, 30% weld metal overmatch when HAZ is the critical material
Duktil sprekkvekst a) b)
Increase in local crack tip constraint due to ductile crack growth Ductile crack growth initiation
BRUDDSEIGHET SENT clamped (a/w=0.2) SENB (a/w = 0.2) RESISTANCE J SENB (a/w = 0.5) CONSTRAINT [Q,T,M]
BRUDD SEIGE MATERIALER BRUDD I SEIGE MATERIALER *gurson-skademekanikk *dynamisk gurson *cohesiv sone *sprøtt-duktilt omslagsområde *rørledninger *japan
Initiering og vekst av porer a) b) a) b) c) d) Increment df = df + df growth nucleation
PRESS-project. High strength steel. Scatter
Applied J (crack driving force) Resistance J (toughness) All we need are test data and 3D FE calculations...
All we need are test data and 3D FE calculations... Hvordan få overført alle de flotte FE beregningene til design? Hvordan etablere et effektivt bindeledd mellom Material og Design?
Direkte beregninger: Skall-modell +linespring =LINK PIPE
3D with crack Shell element with linespring Line Springs connecting the shell elements
Line spring finite element: simplify 3D crack problem to 2D, has a sound fracture mechanics basis from slip line analysis of the crack ligament
Line spring relationships
Line spring FE discretization, 8 DOF, elongation and rotation (opening of the crack)
LINK ftr THE LINK BETWEEN LOCAL FAILURE AND STRUCTURAL RESPONSE LINK failure LINK transfer LINK respons D D D D 11 21 31 41 D D D D 12 22 32 42 ( ) D ep ij A B q, i Q i D D D D 13 23 33 43 a ( ) h D D D D 14 24 34 44 q q q q A 1 A 2 B 1 B 2 Q = Q Q Q A 1 A 2 B 1 B 2 Line Spring Tangent stiffness matrix Generalized displacements at nodes A and B Generalized Force at nodes A and B, in tension and in bending (N,M),
LINKresponse load fracture? displacement
LINKfailure
LINKtransfer
SENB
PIPE
Global strain - CTOD PIPE (tension): OD=400mm, WT=20mm, a/wt=0.5, σ ys =400MPa, E=200GPa, n=0.1 2.5 2.25 2 2c a 1.75 CTOD [mm] 1.5 1.25 1 0.75 3D (2c/O=0.04) 3D (2c/O=0.1) Link PIPE (2c/O=0.04) Link PIPE (2c/O=0.1) 0.5 0.25 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 Strain [%]
a 2c Calculation time 3D 60.000 sec (cpu) LINKpipe 100 sec (cpu)
COST BENEFIT Preprosessing 3D - calculation 20 hours LINKpipe 10 seconds Processing Postprocessing 17 hours calculation time, gives 3 hours inefficiency 2 hours 2 minutes 10 minutes TOTAL 25 hours 25.000 NOK 12min and 10sec 200 NOK
Visulatisation of J-integral/CTOD in crack
Local buckling versus fracture?
LINK PIPE FEATURES 1.The calculations are performed directly on the structure with realistic: -size and location of defect -geometry -tensile/bending loading -internal/external pressure 2.LINK PIPE combines structural analysis (plastic collapse, buckling) and local defect analysis (fracture) 3.LINK PIPE is merging the competence of materials- and structural engineering in a user-friendly way. No in-depth expert knowledge is needed 4.The speed of calculation is extremely high, close to real time. The defect size and dimensions of the structure can be changed within a few seconds
LINK PIPE FEATURES... 5.LINK PIPE opens up for statistical evaluations -no analytical equations are neede -scatter in material data, loads, dimensions etc can be examined -sensitivity analysis -Monte Carlo simulations -partial safety factors for a given system or project OPTIMISATION OF COST AND SAFETY 6. Real time processing of data opens up for efield applications
3D FE calculations Shell elements FE calculations with line spring Analytical equations Accuracy Accuracy Costs Costs
Beregning av constraint med LINKpipe SENT
SENT
690 Steel
Applied J (crack driving force) Resistance J (toughness) All we need are test data and 3D FE calculations...
LINK PIPE BENEFITS 1.Dramatic reduction in man-hours EXAMPLE: Surface defects in pipelines 3D calculations 25.000 NOK LINK PIPE 200 NOK 2. Direct calculations are more realistic than analytical approaches (CrackWise...) This gives better utilization of materials and design solutions 3. Extremely high speed of calculation and generation of new models Scatter can be treated realistic Cost and Safety can be optimised 4.Data from a monitoring system can directly be transformed to concequences Reduced need to store and transmitt data Reduced need for monitoring, inspection and control
4.PROBABILISTISK BRUDDMEKANIKK Sannsynlighet for å få brudd APPLIED Påført belastning, K I FREKVENS RESISTANCE Materialets bruddseighet, K IC SANNSYNLIGHETEN FOR BRUDD SPENNINGSINTENSITETSFAKTOR
Partial safety factors γ γ... 1 2 L A R γ γ... 1 2 R L - applied load R - resistance ( ) γ γ... - partial saftey factors applied load 1 2 A ( ) γ γ... - partial safety factors resistance 1 2 R Design against fracture with a given safety level achieved
EKSEMPEL 304 Rustfritt rør, Diameter 700 mm, tykkelse 34 mm ustabilt initiering Monte Carlo er basert på 10.000 analyser Sannsynligheten for brudd øker med økende belastning
BRUDDMEKANIKK I UTVIKLING NYE TRENDER 1.Numerisk bruddmekanikk: gjenskape virkeligheten med en FE modell 2.Constraint-korrigert bruddmekanikk: effekt av geometri 3.Miljø assistert bruddmekanikk: effekt av prøvebetingelser og miljø 4.Probabilistisk bruddmekanikk: sannsynligheten for å få brudd 5.Direkte beregninger: bruddmekaniske FE beregninger utført direkte på den aktuelle konstruksjonen/komponenten