ACCESS Beiratssitzung November Dr. G. Laschet and L. Haas ACCESS e.v. Aachen, Germany. FENET Workshop Copenhagen

Transcription

1 Coupling FE Contact and Heat Transfer Analysis in Casting Simulations ACCESS Beiratssitzung November 2001 Dr. G. Laschet and L. Haas ACCESS e.v. Aachen, Germany FENET Workshop Copenhagen

2 About ACCESS e.v. Created in 1986 as Center for Solidification in Space Private research center annexed to RWTH Aachen Simulation and optimization of casting processes 45 employees thereunder 35 scientists Annual turnover : 5 million Euros

3 Coupled Process Modelling (FE/CV Formulation)

4 Thermomechanical Analysis During Solidification with CASTS Special items in stress-strain simulation during casting: phase change for alloys and pure substance weak or strong coupling between thermal and stress-strain analysis coupling between heat transfer and contact or gap formation during shrinkage constitutive models for metal and mould complex 3-D geometries (e.g. investment casting)

5 Thermomechanical Constitutive Models core and mould: isotropic, thermoelastic behaviour thermoviscoplasticity (only 12.4 version) metal: isotropic, thermoelastoplastic behaviour anisotropic elastic behaviour for SX or DS superalloys (12.4 version) isotropic thermoviscoplastic behaviour (Norton law, Robinson model), (12.4 version) liquid: quasi-incompressible elastic behaviour at the solidification front: either stress free or metallostatic pressure liquid / solid density variation

6 Heat Transfer Coefficient as Function of Gap or Contact (1) gap: radiative heat transfer: forming gap is assumed to be parallel and plane h rad 4 4 ( T T ) 1 εc 1 ε ( T T ) + 1 conductive heat transfer term is given by: = c σ m c with I 0 : mean free path of gas molecules m m λg hgas = gn + I0 contact: h con function of the contact pressure: γ p hcon = c * with 0.6 γ 1 p0 c* and p 0 determined experimentally in order to get a smooth transition between contact and gap situation

7 Heat Transfer Coefficient as Function of Gap or Contact (2) hgas = λgas ( gap + l ) 0 hrad = σ 2 2 ( T + T )( T + T ) c m c εc εm m

8 3-D Master-slave Contact Algorithm for Casting Simulation (1) normal contact calculated between two elastoplastic bodies undergoing small deformations friction is actually neglected non-penetration condition: penalty method is implemented single and two-pass options are available augmented lagrangian method is under development specific features for casting simulations: mould surface is specified as master and casting surface as slave if metal is liquid: tied contact between metal and mould master / slave algorithm activated for a slave node if all connecting nodes in the metal are solidified

9 3-D Master-Slave Contact Algorithm (2) normal gap definition: g n = u n -x n g n 0: contact g n > 0: no contact contact pressure: penalty method: t n = C (E) <g n > m m 2 C(E): penalty factor augmented lagrangian method: t n = λ n + C(E) <g n > difficulties: description of master surface: definition of macro-planes or surface smoothing update of the master surface for thin bodies 3-D closest point projection algorithm: crucial near corners, sharp angles

10 Definition of Master Macro-Planes 2-D cut M 1, M 7 : centroid of the element surface n 1, n 7 : normal to the element surface loop over element faces master surface: same macro-plane l if: ( n,n ) arccos i 1,i 1 M1 Mi n1,i 1 < dcr <αcr with default values: α cr = 8.1 or cos α r = 0.99 ; d cr = 100 µm i 1 nk n k 1 1,i 1= = i 1 finally, shift from M 1 to M c (= centroid of these elements) assumption: small deformation macro-planes stay planar during deformation

11 Update of the Master Surface crucial for cast parts with thin walls (mainly in investment casting) definition of a critical updating: ½ of the thinnest section if u > critical updating smaller increments two-pass algorithm

12 Closest Point Projection Algorithm Classical normal projection on master macro-planes l (l= 1,2): if projection point (y 1, y 3 ) is in elements l contact element generation for the plane having smallest gap if Sy 2 -Sy 2' < prec generation of 2 contact elements if projection is in the unreachable domain (y 4, y 4' ): unreachable domain nearest master node (here M1) is adopted as projection point contact elements generated for all planes to which this node belong to if master points are at the same distance from the slave S 5 : the point with the greatest number of connecting planes is selected (here M 5 )

13 Determination of the Normal Gap Loop over the Newton-Raphson iterations at time step t it=1: it>1: update of the master surface for each slave node: compute the new initial gap by closest point projection loop over the slave nodes if contact is active closest point projection else: determination of possible intersection points nearest point is selected compute normal gap for the corresponding master element if no intersection point exists closest point projection Why intersection point? contact with only plane 1 will be considered

14 Crisfield Contact Patch Test Evaluation of the performance of the contact model in term of accuracy and convergence capability (pure mechanical test) 1 y interface x 1 incompatible meshes Analytical stress solution (plane strain assumption) σ x = 0, σ y = E / (1-ν 2 ), τ xy = 0, σ z = νσ y

15 Crisfield Patch Test: Results for a Straight Contact Surface Stress σ y Stress σ x Contact pressure (deformation x10) Simulation results: analytical solution σ y = MPa verified with an error of 0.1% analytical solution σ x = 0 is verified normal contact pressure equal to the uniform compression in y-direction

16 Second Crisfield Patch Test: Curved Contact Surfaces initial penetration Contact pressure (CASTS) Solution σ x [MPa] σ y [MPa] σ z [MPa] τ xy [MPa] min max min max min max min max Analytical CASTS ABAQUS 84, error in σ y Crisfield : min 2.3% ; max 3.0% CASTS: min 13.4% ; max 49.4% ABAQUS: min 2.8% ; max 44.9% both programs show poor prediction of the analytical solution ABAQUS a little more accurate than CASTS

17 Simulation of a Dummy Blade Subjected to a Thermal Cycle Geometry of the dummy blade Applied temperature profile mould: Al 2 O 3 casting: AlSi 7 Mg model: 2680 nodes elements Shrinkage and dilatation of the dummy blade leading to gap formation and contact between metal and mould N.B.: 15 master macro-planes are defined

18 Dummy Blade Results: Evolution of the Gap t= 1200 s t= 3700 s t= 5000 s deformation scale: 20

19 Dummy Blade Results: Prediction of the Contact Pressure t= 1200 s t= 5000 s t= 3700 s deformation scale: 20

20 Dummy Blade Results: Evolution of the Heat Transfer Coefficients t= 60 s t= 1200 s t= 3700 s

21 Dimensional Stability of an Investment Casting Part Specified size = 329,0 ± 2,4 mm VDG-Merkblatt P690 (March 1999) Objective: scaling of the CAD-model dimension of cast part within allowed tolerance

22 Description of the Process CAD-model (CATIA): Wax injection Mould production Pouring Cast part Rapid-Prototyping 3D-measurement, comparison CAD-model 3D-data of the cast part FE-model Simulation

23 Volume Model and FE Mesh Discretized geometry (69335 nodes, elements)

24 Calculation of the Shell Mould Pre-heating Temperature calculation specifying radiation with view factors t = 840 s Restart conditions for the second calculation (the mould filling phase is neglected)

25 Thermomechanical Simulation of the Solidification Process (1) Evolution of the temperature distribution in the cast part t = 1000 s

26 Thermomechanical Simulation of the Solidification Process (2) Apparition of contact in locally solidified regions t = 995 s t = 1000 s Contact pressure (deformation scale: 10)

27 Thermomechanical Simulation of the Solidification Process (3) t = 1000 s t = 1005 s Contact pressure (deformation scale: 2) at time step 1005 s and subsequent : no convergence of N-R iterations definition of a new benchmark test for thin investment casting parts implementation of a more robust augmented lagrangian algorithm

28 Outlook: New Thermomechanical Benchmark for Thin Cast Parts Geometry of crossed shells Tetrahedron mesh (2408 nodes, 1198 elements) Hexahedron mesh (1854 nodes, 2862 elements) ceramic mould (Al 2 O 3 ) of 3 mm is generated on the metal (AlSi 7 Mg) surface I-DEAS universal file is available temperature dependence of thermophysical data of mould and metal is given

29 Boundary and Initial Conditions of the Thermomechanical Benchmark mechanical BC: bottom shell face fixed in normal direction fixation of the rigid body modes at this face thermal BC: bottom shell face isolated free radiation + convection (ε = 0.5, α=10-3 W/cm 2 K, T room = 20 C) 3 problems can be specified as function of initial temperature: a) T met = 620 C >T liq = 613 C and T mould = 550 C > T sol = 548 C test for PROCASTS, THERCASTS, CASTS b) T met = 500 C and T mould = 430 C: challenging test for FE codes c) preheating of the shell in a cubic furnace (20 x 20 x 20 cm 3 ) at 750 C by radiation (ε = 0.9) during 800 s non uniform initial mould temperature due to shadowing

30 Thermomechanical Benchmark: First Results for Case A evolution of the gap prediction (deformation x 5) t= 65 s temperature at t= 65 s torsion of the body t= 70 s 37 master macro-planes are specified gap / contact oscillations