1. Influence of the loading path on the deformation mechanisms of magnesium alloys
K. Máthis1, J. Čapek1, B. Clausen2, T. Panzner3
1Charles University in Prague, Department of Physics of Materials, Ke Karlovu 5, Prague, Czech Republic
2Los Alamos National Laboratory, MST-8, NM 87545, Los Alamos, USA
3Paul Scherrer Institute, Laboratory for Neutron Scattering and Imaging, 5232 Villigen PSI, Switzerland

2. Motivation Deformation mechanisms are frequently studied for Mg alloys
a lot of interesting modeling results
the experimental proof of theory is often not available
Our goal
Study of the influence of the loading path on the
twinning evolution
activity of the slip systems
using advanced in-situ experimental methods
Advantage: getting statistically relevant dataset

3. 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

4. Neutron diffraction – uniaxial tests
LANSCE – Los Alamos
Set up
∡ 45° loading direction and incident beam
∡ 90° incident and diffracted beam
Axial and radial planes
Complementary information about the changes in the microstructure

5. Neutron diffraction – biaxial tests
PSI – Villigen
Multi-axial deformation
Proportional (1:1) and non-proportional (2:1) tests
Strain field monitored by digital image correlation (DIC) technique
1 detector
Horizontally: Q || loading dir.
Vertically: Q loading dir.
S. Van Petegem et al., Acta Mater. 2016

6. In-situ neutron diffraction and twinning
Neutron diffraction – in-situ monitoring of twin growth
Tension
Active twinning system {10-12}  change of intensities of peaks {00.2} and {10.0}  estimation for twinned volume

7. In-situ neutron diffraction and twinning
Neutron diffraction – in-situ monitoring of twin growth
Tension
Active twinning system {10-12}  change of intensities of peaks {00.2} and {10.0}  estimation for twinned volume

8. Neutron diffraction – Twin volume estimation
2-bank Rietveld refinement assuming an axisymmetric texture
Development of the axial distribution function for the peak during deformation
J. Čapek et al., Mater. Sci. Eng. A 602 (2014) pp

9. Neutron diffraction – Twin volume estimation
2-bank Rietveld refinement assuming an axisymmetric texture
Development of the axial distribution function for the peak during deformation
J. Čapek et al., Mater. Sci. Eng. A 602 (2014) pp

10. Neutron diffraction – Twin volume estimation
2-bank Rietveld refinement assuming an axisymmetric texture
Development of the axial distribution function for the peak during deformation
J. Čapek et al., Mater. Sci. Eng. A 602 (2014) pp

11. Neutron diffraction – Twin volume estimation
2-bank Rietveld refinement assuming an axisymmetric texture
Development of the axial distribution function for the peak during deformation
J. Čapek et al., Mater. Sci. Eng. A 602 (2014) pp

12. Neutron diffraction – Twin volume estimation
2-bank Rietveld refinement assuming an axisymmetric texture
Development of the axial distribution function for the peak during deformation
J. Čapek et al., Mater. Sci. Eng. A 602 (2014) pp

13. In-situ neutron diffraction & disloc.
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:

14. Source: M.D. Sangid, Acta Mater., 2011
Acoustic emission
Dislocations – detection of avalanche-like motion of large number of dislocations
Twin nucleation – collective motion of several hundred twin dislocations
– well detectable
Twin growth – slow process
– not detectable
Source: M.D. Sangid, Acta Mater., 2011

15. Basic principles of AE measurement
Classical approach
Threshold level
1st level – exclusion of the background noise
2nd level – separating strong signals
Dead-time
The recording of an AE event terminates, when the signal does not cross the threshold during the dead-time

16. Basic principles of AE measurement
Classical approach – hit-based processing
Amplitude, risetime, duration, energy, counts, count rate

17. Basic principles of AE measurement
Classical approach – hit-based processing
Amplitude, risetime, duration, energy, counts, count rate
How to discriminate the twinning and dislocation AE events?
In Mg difficult – concurrent activity of def. mechanisms – overlapping…

18. 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, problem with 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

19. Typical “window” size: 2 ms
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
Typical “window” size: 2 ms

20. Statistical analysis of AE data
Calculation of PSD function – distribution of signals’ power over different freq.

21. 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

22. Statistical analysis of AE data
Output – statistically well separated “CLUSTERS”

23. Statistical analysis of AE data
Output – statistically well separated “CLUSTERS”
Allocation of clusters to deformation mechanisms:
Characteristic features
– twinning – high energy
– dislocation motion – low energy, broader frequency range
Time appearance – e.g. noise at the onset of straining
Supplementary experiments
– neutron diffraction
– digital image correlation etc.
K. Máthis et al.
Int. J. Plast. 72 (2015) pp

24. Statistical analysis of AE data
Output – time evolution of # of elements in particular clusters – information about DYNAMICS of deformation mechanisms

25. Statistical analysis of AE data
Output – time evolution of # of elements in particular clusters – information about DYNAMICS of deformation mechanisms
Basal slip
Twinning
Noise

26. Output: dominant deformation mechanism in a given time range
Statistical analysis of AE data
Output – time evolution of # of elements in particular clusters – information about DYNAMICS of deformation mechanisms
Basal slip
Twinning
Noise
Output: dominant deformation mechanism in a given time range

27. Loading mode dependence
of deformation mechanisms
UNIAXIAL TESTS
Pure Mg, random texture
Tension, compression

28. Experimental – Pure Mg, Mg-Al
Specimen – Mg-Al magnesium alloys
as-cast, random texture
Mg + 1 wt.% Zr – grain size: 100 µm (pure Mg)
Mg + 2 wt.% Al – grain size: 85 µm (Mg2Al)
Pure Mg
Strain rate
210-3 s-1
Testing mode and temperature
Tension, Compression
20ºC
Methods
Acoustic emission, Neutron diffraction
Mg2Al

29. Loading mode dep. - EPSC simulations
EPSC model – Voce empirical hardening law
Model parameters in MPa t0 t1 q0 q1
Basal 4 2
200
125
Prismatic 19 8
250
100
Pyramidal 75 60
300
150
Twinning
K. Máthis et al - Int. J. Plast.. (2015)
DOI: /j.ijplas
Good agreement
of experimental and theoretical data

30. We will discuss the {𝟏𝟎 𝟏 2} 𝟏𝟎 𝟏𝟏 extension twinning

31. Twinning - EPSC simulations + AE
TWIN NUCLEATION
K. Máthis et al - Int. J. Plast.. (2015)
EPSC - Larger number of twin variants nucleated in tension

32. Twinning - EPSC simulations + AE
TWIN NUCLEATION
K. Máthis et al - Int. J. Plast.. (2015)
DOI: /j.ijplas
Larger number of twin variants nucleated in tension
– good agreement with the AE data (ASK analysis)

33. Twinning - EPSC simulations + ND
TWIN GROWTH
Larger twinned volume in compression
– good agreement with the ND data
K. Máthis et al - Int. J. Plast.. (2015)
DOI: /j.ijplas

34. Loading mode dependence of twinning
This part worked out in cooperation with Matthew Barnett
EBSD – 1% strain
Loading direction
T1, C1 – ideally oriented for twinning – more variants in tension
T2, C2 – lower Schmid factor for twinning – less variants in tension

35. Loading mode dependence of twinning
Tension
Larger fraction of grains with SF > 0
BUT only 10% has SF > 0.4
Compression
25% of grains SF > 0.4
More grains with high SF

36. Loading mode dependence of twinning
Tension
Larger fraction of grains with SF > 0
BUT only 10% has SF > 0.4
Compression
25% of grains SF > 0.4
More grains with high SF
High SF – one or two variants
nucleated in compression
Up to six in tension 
Higher number of twins in
tension (cf. AE)

37. Loading mode dependence of twinning
Tension
Larger fraction of grains with SF > 0
BUT only 10% has SF > 0.4
Compression
25% of grains SF > 0.4
More grains with high SF
High SF – one or two variants
nucleated in compression
Up to six in tension 
Higher number of twins in
tension (cf. AE)

38. Loading mode dependence of twinning
Tension
Larger fraction of grains with SF > 0
BUT only 10% has SF > 0.4
Compression
25% of grains SF > 0.4
More grains with high SF
High SF twins tends to be
thicker (more effective load
transfer to twinning plane) 
Larger twinned volume in
compression

39. Loading mode dep. - EPSC simulations + ND
2nd order pyramidal (<c+a>) slip
More <c+a>-slip in compression
– predicted by EPSC
K. Máthis et al - Int. J. Plast.. (2015)
DOI: /j.ijplas

40. Loading mode dep. - EPSC simulations + ND
2nd order pyramidal (<c+a>) slip
More <c+a>-slip in compression
– measured by ND!!
K. Máthis et al - Int. J. Plast.. (2015)
DOI: /j.ijplas

41. DISLOCATION ACTIVITY

42. Dislocations - EPSC simulations + AE
Common features – straining starts with basal slip,
prismatic slip around yield point

43. Dislocations - EPSC simulations + AE
Common features – straining starts with basal slip,
prismatic slip around yield point
AE shows similar behavior

44. Dislocations - EPSC simulations + CMWP
Differences – less pronounced prismatic slip in compression cf. ND

45. Dislocations - EPSC simulations + CMWP
Differences – <c+a>-slip only in compression (exhausting of twinning)
CMWP
EPSC

46. EPSC modeling
vs.
ASK analysis of AE data

47. EPSC vs. AE
REMARK
EPSC
Information about the relative activity of particular deformation mechanisms at a given stress level – concurrent activity included
ASK analysis of AE data
At a given time window (stress) only one AE source can be dominant
If one source is dominant in several consecutive time window – the contributions of others decrease to zero!
Comparison shown for pure Mg

48. EPSC vs. AE BASAL SLIP – activation of at low stresses;
decreasing activity above ~50 MPa

49. EPSC vs. AE
NON-BASAL SLIP – dominant role at higher (>60 MPa) stresses

50. EPSC vs. AE TWINNING – onset of twinning at low applied stresses
decreasing activity with increasing stress

51. Loading mode dep. - Conclusions
More nucleated twins in tension
BUT!!
Larger twinned volume in compression
due to fast growth of twin variants with high Schmid-factor for twinning

52. Loading mode dep. - Conclusions
More nucleated twins in tension
BUT!!
Larger twinned volume in compression
due to fast growth of twin variants with high Schmid-factor for twinning
More 2nd pyramidal slip (<c+a>) in compression
exhausted twinning due to fast growth – need for a further mechanism

53. Loading mode dependence
of deformation mechanisms
BIAXIAL TESTS
Pure Mg, random texture
1:1, 2:1 mode
Preliminary results

54. Digital image correlation
Higher deformation in the 2:1 mode

55. Acoustic emission and ND
Higher AE activity for 1:1 – more
nucleated twins
Intensity variation larger for 2:1 –
larger twinned volume
More grains involved in twinning for 1:1 BUT restricted growth – it will act against the macroscopic deformation

56. Acknowledgement The Czech Grant Agency, Grant Nr. 16-12075S
Daria Drozdenko – EBSD
Matthew Barnett – SF dependence of twinning