1. Effect of the loading mode on the evolution of the dislocation structure in magnesium
Kristián Máthis1, G. Csiszár2, J. Čapek1, J. Gubicza2, B. Clausen3, P. Lukáš4, A. Vinogradov5
1Department of Physics of Materials, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic
2 Department of Materials Physics, Eötvös Loránd University, Budapest, Hungary
3Los Alamos National Laboratory, Lujan Neutron Scattering Center, Los Alamos, NM USA
4Nuclear Physics Institute, Řež, Czech Republic
5 LPSM-IDS Togliatti State University, Togliatti, Russia

2. Motivation Study of the loading mode dependence of the
twinning evolution (see previous lecture of J. Čapek)
activity of slip systems
in random textured magnesium
Methods:
Theoretical: Elasto-plastic self-consistent (EPSC) modeling
Experimental: acoustic emission
neutron diffraction

3. AE in cast polycrystalline magnesium
Specimen – polycrystalline magnesium
as-cast, random texture
Mg wt.% Zr – grain size: 110 µm
Strain rate
210-3 s-1
Testing temperature
20ºC
Methods
EPSC, AE, EBSD, neutron diffraction

4. In-situ acoustic emission & neutron diffraction
Real-time, non-destructive techniques
Suited for global monitoring – information from the entire volume
ACOUSTIC EMISSION
NEUTRON DIFFRACTION
Twin nucleation
Dislocation movement
Twin growth
Activity of slip systems

5. Time of Flight (TOF) neutron diffraction
Set up (LANSCE)
∡ 45° loading direction and incident beam
∡ 90° incident beam and diffracted beam
Axial and radial planes
Recording time of a single pattern ~70 min.
Neutron Source
Incident Neutron Beam
Loading direction
Radial detector
𝑄 ⊥
𝑄 ∥
Axial detector

6. Basic principles of AE measurements
DATA STREAMING – new approach
The classical AE measurements – getting AE parameters in real-time BUT sensitivity on set-up parameters, overlapping events
Data streaming – continuous sampling and storing of the signal
AE parameters from post-processing – no data loss, better fit of set-up parameters
Large data files (~1 Gb/min), long computing time

7. Statistical analysis of AE data
New method– adaptive sequential k-means (ASK) analysis
Pomponi, Vinogradov, Mech. Syst. Sig Proc., November 2013
Analysis of streaming data – definition of analysis window (time interval)  calculation of the power spectral density (PSD) for  windows  characteristic values of PSD used for clustering

8. Statistical analysis of AE data
New method– adaptive sequential k-means (ASK) analysis
Pomponi, Vinogradov, Mech. Syst. Sig Proc., November 2013
Analysis of streaming data – definition of analysis window (time interval)  calculation of the power spectral density (PSD) for  windows  characteristic values of PSD used for clustering

9. Statistical analysis of AE data
New method– adaptive sequential k-means (ASK) analysis
Pomponi, Vinogradov, Mech. Syst. Sig Proc., November 2013
Analysis of streaming data – definition of analysis window (time interval)  calculation of the power spectral density (PSD) for  windows  characteristic values of PSD used for clustering

10. Statistical analysis of AE data
New method– adaptive sequential k-means (ASK) analysis
Pomponi, Vinogradov, Mech. Syst. Sig Proc., November 2013
Analysis of streaming data – definition of analysis window (time interval)  calculation of the power spectral density (PSD) for  windows  characteristic values of PSD used for clustering

11. Statistical analysis of AE data
New method– adaptive sequential k-means (ASK) analysis
Pomponi, Vinogradov, Mech. Syst. Sig Proc., November 2013
Analysis of streaming data – definition of analysis window (time interval)  calculation of the power spectral density (PSD) for  windows  characteristic values of PSD used for clustering

12. Statistical analysis of AE data
New method– adaptive sequential k-means (ASK) analysis
Pomponi, Vinogradov, Mech. Syst. Sig Proc., November 2013
Analysis of streaming data – definition of analysis window (time interval)  calculation of the power spectral density (PSD) for  windows  characteristic values of PSD used for clustering

13. Statistical analysis of AE data
Advantages – high time resolution (~ms); without bias - natural cluster forming; concurrent AE sources do not influence the result; separation of sources with similar origin (e.g.. basal vs. non-basal slip)
Noise
Twinning
Basal disl.
Non-basal disl.

14. Statistical analysis of AE data
Advantages – high time resolution (~ms); without bias - natural cluster forming; concurrent AE sources do not influence the result; separation of sources with similar origin (e.g.. basal vs. non-basal slip)
Noise
Twinning
Basal disl.
Non-basal disl.
Output: dominant deformation mechanism in a given time range

15. In-situ neutron diffraction and dislocations
Diffraction peak line broadening caused by anisotropic strain field of dislocations
Convolutional multiple whole profile (CMWP) analysis
Mean crystallite size <x>area
Dislocation density 
Parameters q1 & q2 - used for calculation of fraction of disl. in different slip systems
Disl. contrast factor:

16. In-situ neutron diffraction and dislocations
Diffraction peak line broadening caused by anisotropic strain field of dislocations
Convolutional multiple whole profile (CMWP) analysis
Mean crystallite size <x>area
Dislocation density 
Parameters q1 & q2 - used for calculation of fraction of disl. in different slip systems
Disl. contrast factor:
Output: fraction (density) of particular dislocation types
(e.g. basal <a>, pyramidal <c+a>)

17. EPSC simulations EPSC model – Eshelby’s inclusion approach:
Interaction of a grain (inclusion having a particular orientation) with the surrounding polycrystal (homogenuous equivalent medium)
Accommodation of the applied stress by elastic and plastic deformation at grain level – governed by Schmid-law
Evolution of CRSS with the accumulated plastic strain :
Voce-law
𝜏= 𝜏 0 + 𝜏 1 + 𝜃 1 Γ 1− exp − 𝜃 0 Γ 𝜏 1
Model parameters in MPa t0 t1 q0 q1
Basal 5 2
100
Prismatic 35 50
Pyramidal
130 60
Twinning 7

18. Output: activity of particular deformation mechanisms
EPSC simulations
EPSC model – Eshelby’s inclusion approach:
Interaction of a grain (inclusion having a particular orientation) with the surrounding polycrystal (homogenuous equivalent medium)
Accommodation of the applied stress by elastic and plastic deformation at grain level – governed by Schmid-law
Evolution of CRSS with the accumulated plastic strain :
Voce-law
Output: activity of particular deformation mechanisms
𝜏= 𝜏 0 + 𝜏 1 + 𝜃 1 Γ 1− exp − 𝜃 0 Γ 𝜏 1
Model parameters in MPa t0 t1 q0 q1
Basal 5 2
100
Prismatic 35 50
Pyramidal
130 60
Twinning 7

19. Loading mode dependence of the deformation mechanisms
Two main mechanisms considered:
Twinning – only (10-12) tensile twins were studied!
Dislocation slip
The following steps were performed:
EPSC – theoretical hints
AE & ND – experimental proof

20. Twinning – EPSC model Initial parameters
Model parameters in MPa t0 t1 q0 q1
Basal 5 2
100
Prismatic 35 50
Pyramidal
130 60
Twinning 7
Tension
Good agreement between the experimental and calculated data
Compression

21. Twinning – EPSC model Two important findings:
Higher NUMBER of nucleated twins IN TENSION
Larger TWINNED VOLUME in COMPRESSION

22. Loading mode dependence of AE – ASK analysis
Significant dependence on the loading mode:
Tension – continuous twin nucleation during the deformation
Compression – twin nucleation only at the beginning
# of events - Tension
EPSC
# of events - Compression

23. Loading mode dependence of the deformation mechanisms
Two main mechanisms considered:
Twinning – only (10-12) tensile twins were studied!
Dislocation slip
The following steps were performed:
EPSC – theoretical hints
AE & ND – experimental proof

24. Dislocation slip – ND CMWP
Dislocation density – ND line profile analysis
Higher values from 4% of applies strain in compression
REASON?

25. Dislocation slip – EPSC model
EPSC conclusions – Common features for both tension and compression:
Dominancy and early onset of the basal slip
Macroscopic yield only after activation of prismatic <a> slip
In compression activation of 2nd order pyramidal at higher stresses (exhaustion of twinning)

26. Dislocation slip – EPSC model
EPSC conclusions – Common features for both tension and compression:
Dominancy and early onset of the basal slip

27. Dislocation slip – EPSC model
EPSC conclusions – Common features for both tension and compression:
Dominancy and early onset of the basal slip – AE proof - OK

28. Dislocation slip – EPSC model
EPSC conclusions – Common features for both tension and compression:
Macroscopic yield – intensive prismatic <a> slip

29. Dislocation slip – EPSC model
EPSC conclusions – Common features for both tension and compression:
Macroscopic yield – intensive prismatic <a> slip – AE proof - OK

30. Dislocation slip – EPSC model
EPSC conclusions – Different features of tension and compression:
<c+a> slip – Tension – negligible, Compression – remarkable
NO AE evidence

31. Dislocation slip EPSC conclusions vs. CMWP findings:
Tension and compression – Basal <a>/Prismatic <a> decreases above macroscopic yield
Tension - <a>/<c+a> constant; Compression - <a>/<c+a> decreases

32. Dislocation slip EPSC conclusions vs. CMWP findings:
Tension and compression – Basal <a>/Prismatic <a> decreases above macroscopic yield
Tension - <a>/<c+a> constant; Compression - <a>/<c+a> decreases

33. Dislocation slip - compression
Why is the dislocation density higher and the <c+a>-slip more active?
Consequences of the rapid twin growth:
“Dislocation transmutation” after crossing the twin boundary – increasing hardening, lower probability of the annihilation
Fully twinned grains (or terminated twin growth) – favorable conditions for the <c+a>-slip

34. Conclusions Common features for both tension and compression
Early onset of basal <a>-slip (microplasticity)
Massive prismatic <a>-slip above the macroscopic yield point
Different behavior
Higher dislocation density in compression above 2% strain
More intensive <c+a>-slip in compression
General remark – combination of AE and ND methods can proof the validity of EPSC calculations (qualitatively!!!)
Acknowledgement
The authors are grateful for financial support of the Czech Science Foundation, Grant P204/12/1360