PRISMS – Sept 4‐6 – U of Michigan 

Stress states associated with twin nucleation  and propagation C.N. Tomé , A. Kanjarla, S. Niezgoda, R.A. Lebensohn, J. Wang,  H. Wang*, P. Wu* MST Division, Los Alamos National Laboratory, USA * McMaster University, Hamilton, Canada

“Multiscale Study of the Role of Microstructure in the  Deformation Behavior of Hexagonal Materials”  OBES‐DOE Project FWP 06SCPE401

Twinning and mechanical response of Mg •

The stress-strain response of textured Mg alloys is highly anisotropic

•

(10-12) tensile twinning plays a dominant main role in shaping mechanical response, texture evolution and hardening Tensile & compressive response of pure Mg

Initial rolling  texture

Texture after  10% In‐Plane  Compression

EBSD after 3% IPC

STAGES OF TWINNING and ACTIVATION STRESSES

NUCLEATION

PROPAGATION

GROWTH

 Nucleation, propagation, and growth  have associated different activation mechanisms  are stress-activated stages of twinning  must take place in sequence  Models need to capture the mechanisms and their relation with stress

CRYSTAL PLASTICITY MODELS: elasto‐visco‐plastic (Elasto) Visco Plastic Self Consistent (EVPSC) Polycrystal Model • grain is an ellipsoidal inclusion embedded in an Effective Elasto-Plastic medium • average neighborhood interaction • stress is homogeneous inside grain * Lebensohn & Tome, Acta Metall Mater 41 (1993) 2611 * Wang, Wu, Tome, Huang, J Mech Phys Solids 58 (2010) 594

 grain  medium

ij,j  0

Elasto-Visco-Plastic Fast Fourier Transform (EVP-FFT) Crystal Plasticity Model • stress equilibrium solved locally • interaction with neighbors accounted for • stress inhomogeneous inside grain * Lebensohn, Acta Metall 49 (2001) 2723-37 * Lebensohn, Kanjarla, Eisenlohr, IJP 32-33 (2012) 59-69

Microstructure with 2500 grains (64x64X64 voxels each)

Composite-Grain Twin Model COUPLED dc dt dg

dc dmfp

dt

Proust & Tome, Acta Materialia 55 (2007) 2137

dt

Twins are activated by the resolved stress present at the twin-matrix interface



tw in



p a re n t

dc-dt

dg

Proust, Tome, Jain, Agnew, Int J of Plasticity 25 (2009) 861

Continuity of stress and strain across the twin-matrix interface



parent 13

 

twin 13



parent 23

 

twin 23

 12parent

  12twin

UNCOUPLED Separate treatment of parent and twin as ellipsoidal inclusions. Account for evolving shape with deformation

Mg: study of twin‐parent‐neighborhood interaction in‐bulk/in‐situ using synchrotron X‐ray diffraction (beam size ~200 m) 

Evolution of shear stress parallel to parent-twin interface Discontinuity of stress & strain across twin-matrix interface

dmf p

Average Resolved Shear Stress in the parent

Average Resolved Shear Stress in the twin Aydiner et al, Phys Rev B 80 (2009)

Modeling Twinning & De-Twinning (TDT) with EVPSC code (*)

Parent

Twin propagation  driven by RSS in the parent

ijTWIN

Growth of twin  driven by RSS in the twin

Detwinning  driven by RSS in the parent Secondary detwinning (growth of twin inside twin)  driven by RSS in the twin

ijPARENT * H. Wang, P. Wu, C. Tomé, J. Wang, Mats Sc and Eng A555 (2012)

EVPSC‐TDT model applied to deformation of Mg AZ31  * TDT uses average stress in parent for activating twin propagation and detwinning * TDT uses average stress in twin for activating growth and secondary detwinning * TDT reproduces stress-strain and twin fraction evolution during strain-path changes 400



(b)

In-Plane Tension

300

Using parent stress to drive twin

Tension 200

Compression In-Plane

Compression 100 Experiment (6.4mm) Simulation 0

0

0.05

0.1

0.15



IPC

TTC

0.2

Predictions & Exps: Proust, Tomé, Kaschner, Acta Mater 55 (2007) Predictions:

H. Wang, Wu, Tomé, J. Wang, Mats Sc Eng A555 (2012) 93

Experiments:

Lou, Li, Boger, Agnew, Wagoner, Int J Plasticity 23 (2007)

Using stress in the twin to drive twinning (TDT model)

EVPSC‐TDT model applied to cyclic deformation of Mg AZ31  TDT reproduces stress-strain, texture and twin fraction evolution during cyclic deformation 5%

Twin volume fraction



400

P2

2% 200

P0

P1

P2 P3

P4

P5

1

P6

fpropagation MR

(b)

fgrowth TP

0.5

P0

0

P1 68%

82%

0

fTR retwinning fMP

Experiment Simulation

P3 -400 -0.08

f tw

-0.5

46%

-200

P7 P8

-0.04

0

Retwinning  growth of twin inside twin (driven by twin stress)

0.04



-1

detwinning

-0.03

0.0

0.03

0.0

-0.03

0.0



0.03

0.0

0.08

parent

twin * B Morrow et al, Metall Mater Trans (2013)

EVPSC‐TDT model applied to cyclic deformation of Mg AZ31 

TDT reproduces stress-strain, texture and twin fraction evolution during cyclic deformation



400

400



5%

P2

2%

6% P3

200

200

P0

0

P1 68%

82%

P0

41%

-200

P2

72% Experiment Simulation

P3 -400 -0.08

0

46%

-200

P1 3%

44%

-0.04

0

0.04



0.08

-400 -0.08

-0.04

0

0.04

Predictions:

H. Wang, Wu, J. Wang, Tomé, Int J Plasticity, in press (2012)

Experiments:

Lou, Li, Boger, Agnew, Wagoner, Int J Plasticity 23 (2007)



0.08

TWIN PROPAGATION & INTERACTIONS grain boundary

twin 2

What are the stresses associated with the interaction between a twin and a grain boundary or another twin boundary?

What can we learn from local Crystal Plasticity simulations of such interaction?

twin 1

Local elasto-plastic FFT calculation of stresses inside twin, parent, and surrounding orientation •

Simulation of twin nucleation induced by macroscopic compression (40 Mpa) of a grain included between two grains

•

Basal, prism and pyramidal slip  CRSS of 3.3 / 36 / 86 MPa

•

Twin is introduced as a shear transformation (S=0.13) imposed in 2000 small increments while stress is held constant at 40 MPa Buffer

(0º,0º,0º)

(75º,62º,60º) Grain 2

Parent grain

Grain 2

40 MPa

Distribution of the resolved shear stress on the twin plane at the end of the twin-transformation process PARENT

TWIN Max: -9.01

Max: 16.45

Min: -67.74

Min: -64.33

Inversion of resolved shear stress inside twin (-67 to -10MPa)

Stress inversion in parent in the vicinity of the twin (~ -10 MPa)

NEIGHBOR Max: 26.24

Min: -11.04

Stress reaction at boundary (from -11 to 26 MPa)

Resolved shear stress on twin interface at the end of twintransformation process and after increase in the applied stress 50

60 MPa

CASE‐1 25

Upon further increase in the stress

0

T‐RSS (MPa)

RSSparent

‐25

RSStwin

At the end of the transformation process

‐50

‐75

‐100 600

500

400

300

200

100

0

Distance from the twin tip (voxel)

40 MPa RSS is favorable to twin growth at the center but reverses near GB !!  may this be the cause of lenticular twin shape ?

Effect of neighbor orientation on resolved shear stress on twin interface Back stress varies between 10 and 27 MPa depending on plastic accommodation in neighbor grain

40

20

0

T‐RSS (MPa)

0

case 1 case 2

‐20

‐20

T‐RSS (MPa)

case 3 case 4 case 1

‐40

‐40

case 5

case 2

case 6

case 3 case 4

‐60

60 MPa

‐60

case 5

600

40 MPa

case 6

500

400

300

200

100

Distance from the twin tip (voxel)

‐80 600

500

400

300

200

100

0

Distance from the twin tip (voxel)

RSS is favorable to twin growth at the center but reverses near GB !!  does it lead to lenticular twin shape ??

0

Evolution of tensile twins in Mg

Cycled Mg single crystal Qin Yu & Yan-Yao Jiang, U of Nevada Reno (private communication)

 Tensile twins in Mg adopt an increasing lenticular shape as strain increases

Twins in Cobalt Wang, Liu, Tome, Mao, Gong, Mats Research Letters (2013)

 HR-TEM reveals serrated twin boundaries

Effect of neighbor on resolved shear stress on twin interface • • •

Backs-tress on twin is independent of grain orientation Resolved applied stress increases with Schmid factor of twin Twins in best oriented grains experience a larger RSS and are likely to grow more and be thicker 40

T‐RSS (MPa)

20 0

c a s e 1

‐20

25 m

‐40 ‐60 600

• •

400

200

0

Distance from the twin tip (voxel

For small grains the profile of RSS is likely to be mostly negative and show no plateau As a consequence, it is less likely for small grains to twin, which may lead to a Hall-Petch effect

Beyerlein et al - Mg twin statistics – Phil Mag (2010)

Serrations and apparent twin curvature

Mg-8%Al M. Gharghouri (PhD) Mc Master U (1996)

Pure Mg H. El Kadiri et al Acta Mater (2013)

 Tensile twins are not usually straight or seemingly parallel to (1 0 -1 2)  At the nano-scale, they show serrated features

HR‐TEM of flat twin‐matrix boundary reveals BP serrations matrix Basal-Prism serrations

matrix

{101̅2}

twin

Plane Traces (matrix) prism {101̅2} twin

basal

5 nm

Tensile twins in pure Mg single crystal Morrow, Cerreta, Tome (unpublished) S6P02 – monotonic tension, low 

HR‐TEM of flat twin‐matrix boundary reveals BP serrations twin

prism basal

basal

6.6 nm

prism

4.6 nm

prism 3.3 nm

basal Tensile twins in Mg Morrow, Cerreta, Tome (unpublished)

matrix

(10‐12) twin serrations minimize twin boundary energy

 MD predicts that a symmetric tilt boundary close to the tensile twin orientation relation decomposes into (10-12) boundaries and basalprism (BP) boundaries 120 mJ/m2

170 mJ/m2

Kinetics of serrated boundary climb  The twin dislocation decomposes into a climb and glide components  Both components ‘move’ along serration and recombine again at the bottom  In the process the twin growths by one prism lattice parameter

prism

basal

5.55 A° 5.21 A°

Unit cell prism separation is 5.55 A°

Unit cell basal separation is 5.21 A°

BP

bclimb btwin

B  P transformation introduces a 0.34 A° misfit bclimb= 0.33 A° provides the required plane misfit

bglide

Climb of serrations as the mechanism controlling twin growth ?  a RSS may activate twin growth but, since it provides a stress component normal to the BP boundary…  … could it be the normal stress to the BP boundary (which activates climb) the one that actually controls twin growth ?  Implications on rate and temperature sensitivity of twinning ??

TWINNING

DE-TWINNING

A twin nucleation mechanism at tilt boundaries (Mg) Gliding dislocations driven by applied shear react with grain boundary dislocations to nucleate a tensile twin

* J. Wang, I.J. Beyerlein, Mod Sim Mats Sci Eng 20 (2012)

Atomic shuffle and sliding as the mechanisms of twin nucleation Initial configuration

B

transformation of prism planes into basal planes via shuffle

B BP

B B

TB Twin boundary migration via twinning dislocations

TB

grain boundary sliding along the BasalPrism (BP) plane

Twin Boundary (TB) formation via shuffle

BP

Summary

 twin propagation induces back-stresses as twin interacts with grain boundaries  the back stresses may block twin growth and lead to serrated boundaries  the stress activating twin growth is the stress at the twinparent interface … which is close to the average stress in the twin  relevant to modeling growth, de-twinning and fatigue behavior  twin interfaces present basal-prism (BP) serrations … which may be the controlling mechanism of twin growth

Optical and scanning microscopy of cycled Mg crystal (Courtesy of Qin Yu and Yanyao Jiang, U. of Nevada, Reno)

Twin-Twin reactions originate c-type dislocations and basalbasal boundaries which seem to pin twins when strain is reversed

 10 1 1    10 11  2 000 1 

 10 1 1     101 1   2 10 10 

MD simulations of dislocation reactions at tilt boundaries (Mg)

=28.16o

(11-20) tilt boundaries exhibit GB dislocation configurations

A pile-up of 4 basal dislocations reacts at the GB and creates a stable twin nucleus

Twin nucleation is driven by local stress and dislocation reactions at grain boundaries

* J. Wang, I.J. Beyerlein, Mod Sim Mats Sci Eng 20 (2012)

Zr: stress fluctuations at GBs calculated using FFT

RVE

Distribution of 11 stress fluctuations at GBs

The tail of the distribution is what drives twin nucleation

* 100 Representative Volume Elements with 500 grains each were used in the simulations * Gaussians were fit to the distribution of each stress component ij at the boundaries * In VPSC, a stochastic stress fluctuation ij is added to the average stress in the grain (ij ) to decide if twin variant will propagate twin res ij ij ij



Niezgoda et al, JOM 65 (2013)

 m    



Implementing stress fluctuations at boundaries in VPSC 100 %

Twin volume  fraction

Twin fraction for each variant vs maximum Schmid factor Twin Number Fraction

Frequency of twins vs Schmid factor

Fraction of  twin‐ nucleated grains Twins nucleate earlier but twin propagation lags behind, and so does twin fraction evolution

The distribution of twin variants is consistent with experimental measurements

0.40 0.35 0.30 0.25 0.20

V6 V5 V4 V3 V2 V1

Magnesium

 Only ~40% of twins correspond to  the best oriented  variant (black bars)  Twins with very low Schmid factors  are observed, mainly associated with   unfavorable variants

0.15 0.10 0.05 0.00 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 Schmid Factor

Stochastic modeling of nucleation at grain boundaries (Zr) Basal pole evolution during In-Plane compression at 76K In-Plane Compression at Macroscopic 76K, 150K, response 300K

is consistent with twin variant selection driven by statistical stress fluctuations at grain boundaries 4%

9%

14%

19% Niezgoda et al, JOM 65 (2013)

experimental

predicted

Twinning in HCP Magnesium MD simulations of symmetrically tilted grain boundaries Atomic structures of STGBs are similar in colored domains

Optical and scanning microscopy of cycled Mg crystal Courtesy of Qin Yu and Yanyao Jiang, U. of Nevada, Reno 40 cycles

Relevance of twin-twin pinning to fatigue is that microstructure builds up and hardening is affected

Twin boundaries may accumulate dislocations and retwinning may be more energetically favorable than de-twinning

400 cycles

1600 cycles