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ATHENS – Course MP06 – 16 – 20 March 2009 Elasto-viscoplasticity ELASTO-VISCOPLASTICITY Jean-Louis Chaboche ONERA, 29 av. de la Division Leclerc 92320 Châtillon, France [email protected] ATHENS Course MP06 Nonlinear Computational Mechanics March 16 to 20, 2009

ELASTO-VISCOPLASTICITYmms2.ensmp.fr/msi_paris/archives-transparents/JLC-Viscoplasticity.… · athens – course mp06 – 16 – 20 march 2009 elasto-viscoplasticity. various viscosity

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  • ATHENS – Course MP06 – 16 – 20 March 2009 Elasto-viscoplasticity �

    ELASTO-VISCOPLASTICITY

    Jean-Louis Chaboche

    ONERA, 29 av. de la Division Leclerc92320 Châtillon, France

    [email protected]

    ATHENS Course MP06

    Nonlinear Computational MechanicsMarch 16 to 20, 2009

  • ATHENS – Course MP06 – 16 – 20 March 2009 Elasto-viscoplasticity �

    � VARIOUS VISCOSITY AND CREEP EFFECTS

    � NOTION OF VISCOPLASTIC POTENTIAL

    � EXAMPLES OF SECONDARY CREEP AND MULTIPLICATIVE HARDENING RULE

    � ELASTO-VISCOPLASTICITY BASED ON NON-LINEAR KINEMATIC HARDENING

    � STATIC RECOVERY EFFECTS

    � IDENTIFICATION OF UNIFIED VISCOPLASTIC CONSTITUTIVE EQUATIONS

    Classical elasto-viscoplasticity

  • ATHENS – Course MP06 – 16 – 20 March 2009 Elasto-viscoplasticity �

    σσσσ

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    Viscosity effects

  • ATHENS – Course MP06 – 16 – 20 March 2009 Elasto-viscoplasticity �

    σσσσ

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    Strain rate effects on the monotonic and cyclic behaviour

  • ATHENS – Course MP06 – 16 – 20 March 2009 Elasto-viscoplasticity '

    Two strain rates test

    Final state, T 7351 - 173°C

    conical panel

    mold

    Modelling of « creep-forming » process : Metal forming by simultaneous creep andheat treatment��� ���

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  • ATHENS – Course MP06 – 16 – 20 March 2009 Elasto-viscoplasticity �

    constant stress and temperature

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    Creep tests

  • ATHENS – Course MP06 – 16 – 20 March 2009 Elasto-viscoplasticity �

    1�εεεε�

    σσσσ

    12

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    Secondary creep – Norton’s law (1930)

  • ATHENS – Course MP06 – 16 – 20 March 2009 Elasto-viscoplasticity

    �σσσσ

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    Strain-hardening and time-hardening assumptions

  • ATHENS – Course MP06 – 16 – 20 March 2009 Elasto-viscoplasticity .

    � VARIOUS VISCOSITY AND CREEP EFFECTS

    � NOTION OF VISCOPLASTIC POTENTIAL

    � EXAMPLES OF SECONDARY CREEP AND MULTIPLICATIVE HARDENING RULE

    � ELASTO-VISCOPLASTICITY BASED ON NON-LINEAR KINEMATIC HARDENING

    � STATIC RECOVERY EFFECTS

    � IDENTIFICATION OF UNIFIED VISCOPLASTIC CONSTITUTIVE EQUATIONS

    Classical elasto-viscoplasticity

  • ATHENS – Course MP06 – 16 – 20 March 2009 Elasto-viscoplasticity ��

    Elastoplasticity and viscoplasticity : equipotential surfaces

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  • ATHENS – Course MP06 – 16 – 20 March 2009 Elasto-viscoplasticity ��

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    Strain rate effect and equipotentials

  • ATHENS – Course MP06 – 16 – 20 March 2009 Elasto-viscoplasticity ��

    7σσσσ

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    Strain rate – stress relationship at fixed hardening

  • ATHENS – Course MP06 – 16 – 20 March 2009 Elasto-viscoplasticity ��

    potential :

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    ∂∂∂∂∂∂∂∂====��

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    normality :

    hardeningvariables

    Viscoplasticity equations – Normality rule

  • ATHENS – Course MP06 – 16 – 20 March 2009 Elasto-viscoplasticity ��

    � VARIOUS VISCOSITY AND CREEP EFFECTS

    � NOTION OF VISCOPLASTIC POTENTIAL

    � EXAMPLES OF SECONDARY CREEP AND MULTIPLICATIVE HARDENING RULE

    � ELASTO-VISCOPLASTICITY BASED ON NON-LINEAR KINEMATIC HARDENING

    � STATIC RECOVERY EFFECTS

    � IDENTIFICATION OF UNIFIED VISCOPLASTIC CONSTITUTIVE EQUATIONS

    Classical elasto-viscoplasticity

  • ATHENS – Course MP06 – 16 – 20 March 2009 Elasto-viscoplasticity �'

    secondary creep

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  • ATHENS – Course MP06 – 16 – 20 March 2009 Elasto-viscoplasticity ��

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  • ATHENS – Course MP06 – 16 – 20 March 2009 Elasto-viscoplasticity ��

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    Modelling of creep tests

  • ATHENS – Course MP06 – 16 – 20 March 2009 Elasto-viscoplasticity �

    � VARIOUS VISCOSITY AND CREEP EFFECTS

    � NOTION OF VISCOPLASTIC POTENTIAL

    � EXAMPLES OF SECONDARY CREEP AND MULTIPLICATIVE HARDENING RULE

    � ELASTO-VISCOPLASTICITY BASED ON NON-LINEAR KINEMATIC HARDENING

    � STATIC RECOVERY EFFECTS

    � IDENTIFICATION OF UNIFIED VISCOPLASTIC CONSTITUTIVE EQUATIONS

    Classical elasto-viscoplasticity

  • ATHENS – Course MP06 – 16 – 20 March 2009 Elasto-viscoplasticity �.

    potential :

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  • ATHENS – Course MP06 – 16 – 20 March 2009 Elasto-viscoplasticity ��

    DB,�>����H��

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  • ATHENS – Course MP06 – 16 – 20 March 2009 Elasto-viscoplasticity ��

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    Modelling of creep tests

  • ATHENS – Course MP06 – 16 – 20 March 2009 Elasto-viscoplasticity ��

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  • ATHENS – Course MP06 – 16 – 20 March 2009 Elasto-viscoplasticity ��

    � VARIOUS VISCOSITY AND CREEP EFFECTS

    � NOTION OF VISCOPLASTIC POTENTIAL

    � EXAMPLES OF SECONDARY CREEP AND MULTIPLICATIVE HARDENING RULE

    � ELASTO-VISCOPLASTICITY BASED ON NON-LINEAR KINEMATIC HARDENING

    � STATIC RECOVERY EFFECTS

    � IDENTIFICATION OF UNIFIED VISCOPLASTIC CONSTITUTIVE EQUATIONS

    Classical elasto-viscoplasticity

  • ATHENS – Course MP06 – 16 – 20 March 2009 Elasto-viscoplasticity ��

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    Strain recovery

  • ATHENS – Course MP06 – 16 – 20 March 2009 Elasto-viscoplasticity �'

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  • ATHENS – Course MP06 – 16 – 20 March 2009 Elasto-viscoplasticity ��

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  • ATHENS – Course MP06 – 16 – 20 March 2009 Elasto-viscoplasticity ��

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  • ATHENS – Course MP06 – 16 – 20 March 2009 Elasto-viscoplasticity �

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  • ATHENS – Course MP06 – 16 – 20 March 2009 Elasto-viscoplasticity �.

    � VARIOUS VISCOSITY AND CREEP EFFECTS

    � NOTION OF VISCOPLASTIC POTENTIAL

    � EXAMPLES OF SECONDARY CREEP AND MULTIPLICATIVE HARDENING RULE

    � ELASTO-VISCOPLASTICITY BASED ON NON-LINEAR KINEMATIC HARDENING

    � STATIC RECOVERY EFFECTS

    � IDENTIFICATION OF UNIFIED VISCOPLASTIC CONSTITUTIVE EQUATIONS

    Classical elasto-viscoplasticity

  • ATHENS – Course MP06 – 16 – 20 March 2009 Elasto-viscoplasticity ��

    E��������/

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  • ATHENS – Course MP06 – 16 – 20 March 2009 Elasto-viscoplasticity ��

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  • ATHENS – Course MP06 – 16 – 20 March 2009 Elasto-viscoplasticity ��

    ��

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    Intrinsic dependancy between threshold and exponent

  • ATHENS – Course MP06 – 16 – 20 March 2009 Elasto-viscoplasticity ��

    σσσσ−−−−σσσσ�

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    Intrinsic dependancy between threshold and exponent

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  • ATHENS – Course MP06 – 16 – 20 March 2009 Elasto-viscoplasticity ��

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  • ATHENS – Course MP06 – 16 – 20 March 2009 Elasto-viscoplasticity �'

    ����(E��(������� (��� � ���� !

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  • ATHENS – Course MP06 – 16 – 20 March 2009 Elasto-viscoplasticity ��

    ��&/

    Zener – Hollomon master curve

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