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, 121 16 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

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

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

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

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

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

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

Neutron diffraction – Twin volume estimation 2-bank Rietveld refinement assuming an axisymmetric texture Development of the axial distribution function for the 00.2 peak during deformation J. Čapek et al., Mater. Sci. Eng. A 602 (2014) pp. 25-32

Neutron diffraction – Twin volume estimation 2-bank Rietveld refinement assuming an axisymmetric texture Development of the axial distribution function for the 00.2 peak during deformation J. Čapek et al., Mater. Sci. Eng. A 602 (2014) pp. 25-32

Neutron diffraction – Twin volume estimation 2-bank Rietveld refinement assuming an axisymmetric texture Development of the axial distribution function for the 00.2 peak during deformation J. Čapek et al., Mater. Sci. Eng. A 602 (2014) pp. 25-32

Neutron diffraction – Twin volume estimation 2-bank Rietveld refinement assuming an axisymmetric texture Development of the axial distribution function for the 00.2 peak during deformation J. Čapek et al., Mater. Sci. Eng. A 602 (2014) pp. 25-32

Neutron diffraction – Twin volume estimation 2-bank Rietveld refinement assuming an axisymmetric texture Development of the axial distribution function for the 00.2 peak during deformation J. Čapek et al., Mater. Sci. Eng. A 602 (2014) pp. 25-32

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:

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

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

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

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…

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

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

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

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

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

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. 127-150.

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

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 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

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

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

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: 10.1016/j.ijplas.2015.05.009 Good agreement of experimental and theoretical data

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

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

Twinning - EPSC simulations + AE TWIN NUCLEATION K. Máthis et al - Int. J. Plast.. (2015) DOI: 10.1016/j.ijplas.2015.05.009 Larger number of twin variants nucleated in tension – good agreement with the AE data (ASK analysis)

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: 10.1016/j.ijplas.2015.05.009

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

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

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)

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)

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

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: 10.1016/j.ijplas.2015.05.009

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: 10.1016/j.ijplas.2015.05.009

DISLOCATION ACTIVITY

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

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

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

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

EPSC modeling vs. ASK analysis of AE data

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

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

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

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

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

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

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

Digital image correlation Higher deformation in the 2:1 mode

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

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