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
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
AE in cast polycrystalline magnesium Specimen – polycrystalline magnesium as-cast, random texture Mg + 1.00 wt.% Zr – grain size: 110 µm Strain rate 210-3 s-1 Testing temperature 20ºC Methods EPSC, AE, EBSD, neutron diffraction
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
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
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
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 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 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 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 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 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 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.
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
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:
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>)
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
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
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
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
Twinning – EPSC model Two important findings: Higher NUMBER of nucleated twins IN TENSION Larger TWINNED VOLUME in COMPRESSION
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
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
Dislocation slip – ND CMWP Dislocation density – ND line profile analysis Higher values from 4% of applies strain in compression REASON?
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)
Dislocation slip – EPSC model EPSC conclusions – Common features for both tension and compression: Dominancy and early onset of the basal slip
Dislocation slip – EPSC model EPSC conclusions – Common features for both tension and compression: Dominancy and early onset of the basal slip – AE proof - OK
Dislocation slip – EPSC model EPSC conclusions – Common features for both tension and compression: Macroscopic yield – intensive prismatic <a> slip
Dislocation slip – EPSC model EPSC conclusions – Common features for both tension and compression: Macroscopic yield – intensive prismatic <a> slip – AE proof - OK
Dislocation slip – EPSC model EPSC conclusions – Different features of tension and compression: <c+a> slip – Tension – negligible, Compression – remarkable NO AE evidence
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
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
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
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