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Alflow Model for Work Hardening and Dynamic Recovery: A Comprehensive Study

Explore the Alflow model, developed by Erik Nes from NTNU, for understanding work hardening and dynamic recovery in metals. This model describes the behavior of materials at different strain rates and temperatures using microstructural parameters like cell size, dislocation density, and sub-boundary misorientation. The model delves into the stages of work hardening and recovery, offering insights into the dynamic stress response, dislocation storage, and the inhomogeneous nature of material deformation. By considering various input parameters and process history, the Alflow model provides a detailed framework for predicting microstructure evolution and flow stress in materials. This comprehensive study also discusses future improvements and the potential integration of the Alflow model into Finite Element Method simulations.

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Alflow Model for Work Hardening and Dynamic Recovery: A Comprehensive Study

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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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