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Modeling residual stresses in Arc Welding
Frédéric Roger – Abderrazak Traidia
ENSTA Paristech
COMSOL Conference 2010 Boston Presented at the
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Consequences of Welding
Arc heating
Weld pool
Metallurgical transformation
Plasticity (incompatibility)
Clamping
Residual stresses distortions)
Heat transfer
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Plasticity (incompatibility)
Clamping
Residual stresses distortions)
Heat transfer
viscosity
Hardening model
Chaboche thermo-elasto- visco-plastic Model (1989)
Evaluation of (visco)plastic strains
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Chaboche elastoviscoplastic model
02 3 2 .1p ptrace T T
Thermoelasticity with (visco)plastic strain
(visco)plastic strain time evolution
K, n, C, Q, g and b Temperature dependent
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Comsol implementation
sr_smaxi= 4*G_smaxi*(er_smaxi-epr_smaxi)/3 -2*G_smaxi*(ephi_smaxi-epphi_smaxi)/3 -2*G_smaxi*(ez_smaxi-epz_smaxi)/3 -p
sz_smaxi= 4*G_smaxi*(ez_smaxi-epz_smaxi)/3 -2*G_smaxi*(er_smaxi-epr_smaxi)/3 -2*G_smaxi*(ephi_smaxi-epphi_smaxi)/3 -p
sphi_smaxi= 4*G_smaxi*(ephi_smaxi-epphi_smaxi)/3 -2*G_smaxi*(er_smaxi-epr_smaxi)/3 -2*G_smaxi*(ez_smaxi-epz_smaxi)/3 -p
srz_smaxi= 2*G_smaxi*(erz_smaxi-eprz_smaxi)
p= -K_smaxi*(evol_smaxi-epr_smaxi-epphi_smaxi-epz_smaxi -3*mat1_alpha*(Temp_smaxi-Tempref_smaxi))
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Non linear Ordinary differential equations = Mode PDE, General form without spatial derivatives
Comsol implementation
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Application : spot arc welding
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Numerical results
Temperature field during welding
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Equivalent plastic strain
Numerical results
End of heating
After cooling
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Residual stresses and distortions
Numerical results
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Extension of the model : metallurgical transformation
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Arc heating
Weld pool
Plasticity (incompatibility)
Clamping Metallurgical
transformation
Residual stresses distortions)
Heat transfer
Conclusion
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Thank you for your attention
Any questions ?
The authors: Frederic Roger And Abderrazak Traidia
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Extension of the model :Fluid flow and metallurgy
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Fluid flow and thermal field
Austenite distribution after heating
Phase fraction time evolution
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Chaboche elastoviscoplastic model
02 3 2 .1p ptrace T T
Thermoelasticity with (visco)plastic strain
(visco)plastic strain time evolution