Slip System based Model for Work Hardening of Aluminium, including Transient Effects during StrainPa

1
Slip System based Model for Work Hardening of
Aluminium, including Transient Effects during
Strain-Path Changes.

• Steven Van Boxel, Marc Seefeldt, Bert Verlinden,
  Paul Van Houtte
• Department of Metallurgy and Materials
  Engineering (MTM),
• Katholieke Universiteit Leuven,
• Kasteelpark Arenberg 44 bus 2450, B-3001
  Heverlee, Belgium

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Outline

• Introduction
• Experimental observations
• Cross-test behaviour
• Reverse test
• Work hardening model multiscale approach
• Cross-type strain path changes
• Model equations
• Results
• Strain reversal
• Model equations
• Results
• Conclusions

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Introduction

• Work hardening is still an important issue in
  deformation modelling
• Various models are able to predict work hardening
  behaviour for monotonic strain paths
• Transient hardening and softening effects during
  strain path changes
• Complex deformation processes could be much
  better simulated if these effects are taken into
  account

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Experimental observations

• Simple Shear tests
• AA3103_O

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Experimental observations

• Cross test behaviour

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Experimental observations

• Cross test behaviour
• yield stress after strain path change higher
• Latent hardening of inactive slip systems
• Anisotropy of built up substructure
• Lower hardening (even softening) in transient
  region
• Hardening returns to monotonic hardening curve

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Experimental observations

• Reversal test behaviour

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Experimental observations

• Cross test behaviour
• yield stress after strain path change higher
• Latent hardening of inactive slip systems
• Anisotropy of built up substructure
• Lower hardening (even softening) in transient
  region
• Hardening returns to monotonic hardening curve
• Reversal test behaviour
• yield stress after strain reversal is lower
  (Bauschinger effect)
• Back stresses of the built op microstructure
• in transient region a plateau in hardening
  behaviour
• Polarisation of the substructure is reversed
• Hardening returns to monotonic hardening curve

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Multiscale approach
Texture ODF? discrete set of orientations
Macro
Crystal lattice structure Applied velocity
gradient ? active slip systems
Meso
Dislocation substructure Microstructural
contributions to workhardening
Micro
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Mesoscopic part

• Evolution equations for

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Mesoscopic part

• Evolution equations for

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Mesoscopic part

• Evolution equations for

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Mesoscopic part

• Evolution equations for

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Mesoscopic part

• Evolution equations for

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Cross type SPC

• Transient behaviour in cross test
• Every slip system a contributes to the hardening
  of the grain, proportional to
• In cross-type strain path change substructure
  of the prestrain is converted into a new
  substructure according to the new strain mode
• Previous contributions of s to s have
  to be partially removed
• Transient softening
• Parameter for every slip system related to
  previous
• Previous contribution of slip system a

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Cross type SPC

• Transient behaviour in cross test
• Hardening during strain path change

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Cross type SPC

• Results with latent hardening

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Cross type SPC

• Results with latent hardening

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Cross type SPC

• Results with substructural hardening

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Reversal type SPC

• Transient behaviour in strain reversal test
• Lower yield stress due to back stresses of
  dislocation substructure
• If slip system a is active, in opposite
  direction will harden to a lesser extent

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Reversal type SPC

• Transient behaviour in strain reversal test
• Assumptions
• At strain reversal, due to the back stresses
  dislocation glide is initially easy newly
  formed dislocations interact in the same way as
  in the monotonic case at the same
• A part of the dislocations of opposite sign,
  stored in the microstructure can gradually be
  reactivated, leading to increasing annihilation,
  effect of polarisation of the microstructure
• Polarity of a slip system a scales with

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Reversal type SPC

• Transient behaviour in strain reversal test
• Assumptions
• This softening scales with the hardening which
  was realised during prestrain
• As long as there are polarised dislocations
  available, the hardening of the forward direction
  is compensated by an equal softening of the
  backward direction

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Reversal type SPC

• Result

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Conclusions

• Multiscale model for work hardening
• Transient effects during strain path changes
  modelled at mesoscopic level
• Substructural evolution modelled with two fitting
  parameters and
• Cross test
• The higher yielding in cross test can not come
  from latent hardening alone, most likely also
  substructural anisotropy
• Two fitting parameters give adequate transient
  behaviour
• Better prediction of the substructural anisotropy
  necessairy
• Reversal test
• Hardening and softening contributions as a
  function of existing polarised substructure
• Three fitting parameters give adequate transient
  behaviour

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Experimental results

• Shear tester

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Experimental results

• Shear tester
• Strain mapping (al50 20-03-07 1 al50-000-1)

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Experimental results

• Shear tester
• Strain mapping (al50 20-03-07 1 al50-050-1)

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Experimental results

• Shear tester
• Strain mapping (al50 20-03-07 1 al50-088-1)

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Experimental results

• Shear tester
• Strain mapping (al50 20-03-07 1 al50-088-1)