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Material models

Material models. Work-hardening. mechanical-threshold-strength (MTS). Different Models. M icrostructural Metal Plasticity (MMP). Nes-Marthinsen-Holmedal. Kocks. Nes model. 3 internal variable model (3IVM). MTS Model. 1 microstructural parameter

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Material models

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  1. Material models Work-hardening

  2. mechanical-threshold-strength (MTS) Different Models Microstructural Metal Plasticity(MMP) Nes-Marthinsen-Holmedal Kocks Nes model 3 internal variable model (3IVM)

  3. MTS Model • 1 microstructural parameter • total dislocation density => r (The way they are arranged is not considered) Dynamic stress Work hardening Storage of dislocations Dynamic recovery

  4. “Alflow” - Erik Nes - NTNUwork-hardening and dynamic recovery Principle and inputs

  5. Alflow: model principle • From Erik Nes - NTNU • [E. Nes, ‘Modelling of work-hardening and stress saturation in FCC metals', Progress in Materials Science, Vol. 41 (1998) pp.129-193] • Only for pure metals • For work hardening and dynamic recovery: any strain rate and temperature • Describes the 4 stages of work-hardening

  6. j d ri NTNU model (ALFLOW) • 3 microstructural parameters • cell size => d • dislocation density within the cell => ri • small strain: • cell wall thickness => h • wall dislocation density => rb • large strain: sub-boundary misorientation => j

  7. Alflow: model description small strain large strain • 3 microstructural parameters sub-boundary misorientation j cell wall thickness h cell size d dislocation density within the cell ri wall dislocation density rb

  8. WORK-HARDENING (V) II IV III qIII0 qII qIV ts tIII tIII* tIV tIIIs t

  9. II to III (V) high T° II III IV t ts tIV tIII* tIII Def becomes inhomogeneous (locolised slip => shear banding) g Recovery becomes significant g saturation Cells more or less equiaxed Pancake like structure saturates g

  10. II to III (V) high T° II III IV g f h g j jIV jIII g

  11. II to III (V) high T° II III IV S Ssc SIV g g g

  12. NTNU model (ALFLOW) • 3 microstructural parameters • cell size => d • dislocation density within the cell => ri • small strain: • cell wall thickness => h • wall dislocation density => rb • large strain: sub-boundary misorientation => j Dispersoids bypass l: particle spacing Dynamic stress

  13. Alflow: model description • Flow stress Dynamic stress Neglected work -hardening dynamic recovery

  14. General principle of work-hardening • Athermal storage of dislocations: • In cell interiors • In old boundaries • Forming new boundaries Dislocation slip length: Storage probability of a moving dislocation Dislocation in new boundaries: Storage probability of a moving dislocation in a new boundary Fraction of dislocation loops trapped in old boundaries

  15. Alflow: input • Material constant (x5) • From literature • Burgers vector: 2.86 A • Shear Modulus: GPa • Self diffusion activation energy: 120 kJ/mol • Debye frequency: • Model Parameters (x13) • To be determined • Stress - microstructure constants: a1, a2 • Geometric constant: k • Scaling constants: qb, qc, qh, qIV, • Storage parameters: C, SIV • Dynamic recovery parameters: Bd, xd, Br, xr

  16. Alflow: input • Microstructure variable (x2) • Depend on process history • Initial microstructure: r0, d0, ri0, h0, rb0, • Saturation stress: js • Process parameters • From FEM • Temperature • Strain rate Total: 19 input parameters

  17. Alflow: next steps • Precipitate and solute effects on work-hardening grain size + particles • Precipitate effect on the flow stress Dispersoids bypass l: particle spacing

  18. Alflow: next steps Grain size

  19. Conclusion Alflow • More consistent theoretical approach • More realistic microstructure prediction • Code available • Possibility to integrate into FEM 3IVM • Validated for a larger temperature range and composition Future improvements • Combined effect of Mg, Mn, Si • Shearable particles

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