Modeling of a Single Pulse Electric Discharge at Sphere/flat Interface by Coupling Contact Multiphysics and Phase Transformations
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1 Modeling of a Single Pulse Electric Discharge at Sphere/flat Interface by Coupling Contact Multiphysics and Phase Transformations Presented at the COMSOL Conference 2010 Paris Paolo Di Napoli Giovanni Maizza Roberto Cagliero Politecnico di Torino Department of Materials Science and Chemical Engineering November 15, 2010
2 The apparatus Capacitor Discharge Welding Short processing times + high localized energy density Applications: welding of metals, ceramics, composites P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 2/27
3 Modules and features Elasto-plastic solver DC-electrical module Thermal module Contact pair features Solid state transformations by user-defined functions Materials properties definition dependent on temperature and phase content in steel Version 3.5a P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 3/27
4 Outline 1 Model implementation Domain Structural-mechanical Electrical Thermal Phase transformation Solution strategy 2 Results Structural Thermal Phase transformation 3 Conclusions P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 4/27
5 Model implementation Domain P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 5/27
6 Model implementation Domain Axial symmetry, 2D P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 5/27
7 Model implementation Domain Electrode Molybdenum Heigth: 25 mm Diameter: 10 mm Spherical shaped tip P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 6/27
8 Model implementation Domain Sample case AISI 9310 steel case hardened Height: 0.6 mm Diameter: 30 mm P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 6/27
9 Model implementation Domain Sample core AISI 9310 steel annealed Height: 9.4 mm Diameter: 30 mm P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 6/27
10 Model implementation Domain Contact pair P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 6/27
11 Model implementation Domain Mesh data Quadratic lagrangian elements Triangular (advancing front) P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 6/27
12 Model implementation STATIONARY STRUCTURAL-MECHANICAL Elasto-plastic behavior of sample, electrode and contact region Isotropic tangent modulus E Tiso P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 7/27
13 Model implementation Structural Boundary conditions Axial symmetry P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 8/27
14 Model implementation Structural Boundary conditions Axial symmetry Applied pressure: 35 MPa P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 8/27
15 Model implementation Structural Boundary conditions Axial symmetry Applied pressure: 35 MPa Fixed edge of the sample P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 8/27
16 Model implementation Structural Boundary conditions Axial symmetry Applied pressure: 35 MPa Fixed edge of the sample Penalty factor: P n = E smaxi hmin cp1 smaxi min ( 1.e 3 5 aug, 1 ) Initial contact pressure: 10 MPa P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 8/27
17 Model implementation Structural Boundary conditions Axial symmetry Applied pressure: 35 MPa Fixed edge of the sample Penalty factor: P n = E smaxi hmin cp1 smaxi min ( 1.e 3 5 aug, 1 ) Initial contact pressure: 10 MPa Free displacement for the rest P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 8/27
18 Model implementation STATIONARY ELECTRICAL P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 9/27
19 Model implementation Electrical Boundary conditions Axial symmetry P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 10/27
20 Model implementation Electrical Boundary conditions Axial symmetry Voltage drop V P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 10/27
21 Model implementation Electrical Boundary conditions Axial symmetry Voltage drop V Contact resistance σ c = ρ e1 + ρ e2 4 r c [1] r c = contact radius [1] R. Holm, Electrical Contacts, Hugo Gebers,Stockholm, (1936) P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 10/27
22 Model implementation Electrical Boundary conditions Axial symmetry Voltage drop V Contact resistance σ c = ρ e1 + ρ e2 4 r c [1] r c = contact radius Electric insulation [1] R. Holm, Electrical Contacts, Hugo Gebers,Stockholm, (1936) P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 10/27
23 Model implementation Thermal TRANSIENT THERMAL P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 11/27
24 Model implementation Thermal Boundary conditions Axial symmetry P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 12/27
25 Model implementation Thermal Boundary conditions Axial symmetry Fixed temperature (massive copper tooling) P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 12/27
26 Model implementation Thermal Boundary conditions Axial symmetry Fixed temperature (massive copper tooling) Joule heating: Q T = σc d (V 1 V 2 ) [1] R. Holm, Electrical Contacts, Hugo Gebers,Stockholm, (1936) P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 12/27
27 Model implementation Thermal Boundary conditions Axial symmetry Fixed temperature (massive copper tooling) Joule heating: Q T = σc d (V 1 V 2 ) Heat flux: h = 50 W/(K m 2 ) [1] R. Holm, Electrical Contacts, Hugo Gebers,Stockholm, (1936) P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 12/27
28 Model implementation PHASE TRANSFORMATION and INERTIAL EFFECTS Assumptions: high temperature cycling high heating rates rapid reaustenitization narrow heat affected zone Inertial effects without growth kinetics modeling P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 13/27
29 Model implementation Phase transformation A c1 and A c3 curves from experimental data P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 14/27
30 Model implementation Phase transformation A c1 and A c3 curves from experimental data T defines univocally the phase fields P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 14/27
31 Model implementation Phase transformation A c1 and A c3 curves from experimental data T defines univocally the phase fields Ψ i represents a general material property P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 14/27
32 Model implementation Phase transformation A c1 and A c3 curves from experimental data T defines univocally the phase fields Ψ i represents a general material property Properties values in pure α and pure γ phase from experimental data P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 14/27
33 Model implementation Phase transformation A c1 and A c3 curves from experimental data T defines univocally the phase fields Ψ i represents a general material property Properties values in pure α and pure γ phase from experimental data Properties values in two-phase region obtained by sigmoidal function flc1hs P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 14/27
34 Model implementation SOLUTION STRATEGY P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 15/27
35 Model implementation Solution strategy P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 16/27
36 Model implementation Solution strategy P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 16/27
37 Model implementation Solution strategy P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 16/27
38 Model implementation Solution strategy P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 16/27
39 Model implementation Solution strategy P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 16/27
40 Model implementation Solution strategy P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 16/27
41 Model implementation Solution strategy P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 16/27
42 Model implementation Solution strategy P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 16/27
43 Model implementation Solution strategy P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 16/27
44 Model implementation Solution strategy P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 16/27
45 Model implementation Solution strategy P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 16/27
46 Model implementation Solution strategy P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 16/27
47 Model implementation Solution strategy P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 16/27
48 Model implementation Solution strategy P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 16/27
49 Results Structural Thermal Phase transformation P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 17/27
50 Results Structural Pre-loading No Applied voltage Elapsed time: 0 ms 3V 2V 1V P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 18/27
51 Results Thermal CDW step: Applied voltage V : 1 V Elapsed time: 0.2 ms 3V 2V 1V 0.2 ms P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 19/27
52 Results Thermal CDW step: Applied voltage V : 2 V Elapsed time: 2.0 ms 3V 2V 1V 2 ms P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 20/27
53 Results Thermal CDW step: Applied voltage V : 3 V Elapsed time: 3.0 ms 3V 2V 1V 3 ms P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 21/27
54 Results Phase transformation CDW step: focus on sample case Applied voltage V : 3 V Elapsed time: 2.2 ms 3V 2V 1V 2.2 ms P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 22/27
55 Results Phase transformation CDW step: focus on sample case Applied voltage V : 3 V Elapsed time: 2.8 ms 3V 2V 1V 2.8 ms P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 23/27
56 Results Phase transformation CDW step: focus on sample case Applied voltage V : 3 V Elapsed time: 3.0 ms 3V 2V 1V 3 ms P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 24/27
57 Results Yield strength ELECTRODE (1) (2) (3) SAMPLE CASE SAMPLE CORE 1V 0.2 ms TIME (1) (2) (3) P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 25/27
58 Results Yield strength ELECTRODE (1) (2) (3) SAMPLE CASE SAMPLE CORE 1V 0.4 ms TIME (1) (2) (3) P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 25/27
59 Results Yield strength ELECTRODE (1) (2) (3) SAMPLE CASE SAMPLE CORE 1V 0.6 ms TIME (1) (2) (3) P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 25/27
60 Results Yield strength ELECTRODE (1) (2) (3) SAMPLE CASE SAMPLE CORE 1V 0.8 ms TIME (1) (2) (3) P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 25/27
61 Results Yield strength ELECTRODE (1) (2) (3) SAMPLE CASE SAMPLE CORE 1V 1 ms TIME (1) (2) (3) P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 25/27
62 Results Yield strength ELECTRODE (1) (2) SAMPLE CASE 2V (3) SAMPLE CORE 1.2 ms TIME (1) (2) (3) P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 25/27
63 Results Yield strength ELECTRODE (1) (2) SAMPLE CASE 2V (3) SAMPLE CORE 1.4 ms TIME (1) (2) (3) P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 25/27
64 Results Yield strength ELECTRODE (1) (2) SAMPLE CASE 2V (3) SAMPLE CORE 1.6 ms TIME (1) (2) (3) P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 25/27
65 Results Yield strength ELECTRODE (1) (2) SAMPLE CASE 2V (3) SAMPLE CORE 1.8 ms TIME (1) (2) (3) P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 25/27
66 Results Yield strength ELECTRODE (1) (2) SAMPLE CASE 2V (3) SAMPLE CORE 2 ms TIME (1) (2) (3) P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 25/27
67 Results Yield strength ELECTRODE 3V (1) (2) SAMPLE CASE (3) SAMPLE CORE 2.2 ms TIME (1) (2) (3) P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 25/27
68 Results Yield strength ELECTRODE 3V (1) (2) SAMPLE CASE (3) SAMPLE CORE 2.2 ms TIME (1) (2) (3) P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 25/27
69 Results Yield strength ELECTRODE 3V (1) (2) SAMPLE CASE (3) SAMPLE CORE 2.4 ms TIME (1) (2) (3) P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 25/27
70 Results Yield strength ELECTRODE 3V (1) (2) SAMPLE CASE (3) SAMPLE CORE 2.4 ms TIME (1) (2) (3) P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 25/27
71 Results Yield strength ELECTRODE 3V (1) (2) (3) SAMPLE CASE SAMPLE CORE TIME 2.4 ms (1) (2) (3) P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 25/27
72 Conclusions 1/2 A coupling strategy suitable for general COMSOL architectures and solvers is designed to solve contact multiphysics involving steel samples The essential multiphysics of the real CDW process is taken into account by coupling mechanical, electrical, thermal and metallurgical fields A novel concept in the definition of non-linear properties of materials undergoing phase transformations is developed P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 26/27
73 Conclusions 2/2 The overall model is able to capture a realistic behavior of steel sample during rapid CDW heating in terms of temperature and microstructure. The model allows to follow the behaviors of all the materials properties upon CDW, thus highlighting the peculiar aspects behind the physical problem Extension to spot welding, electrical circuitry and current-assisted powder metallurgy is possible Strong convergence difficulties are encountered when severe localized strain gradients develop P. Di Napoli G. Maizza R. Cagliero COMSOL Paris 27/27
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