Quantifying Processing Map Uncertainties by Modelling the - - PowerPoint PPT Presentation

Quantifying Processing Map Uncertainties by Modelling the Hot-Compression Behaviour of a Zr-2.5Nb Alloy

Christopher S. Daniel1, Patryk Jedrasiak2, Christian J. Peyton1, João Quinta da Fonseca1, Hugh R. Shercliff2, Luke Bradley3, Peter D. Honniball3,

1The University of Manchester, Manchester, UK 2University of Cambridge, Cambridge, UK 3Rolls-Royce plc, Derby, UK

• Zr alloys: Structural Components, Cladding, Pressure Tubing.
• Dual-phase α + β ZrNb alloys offer higher strength and fracture toughness, with

improved corrosion properties – compared to single phase α Zr alloys.

2

Industrial Relevance

Dual-phase α + β ZrNb alloy microstructure; nuclear fuel assembly; Pressurised Water Reactor (PWR) schematic.

α - hcp β - bcc

20 μm

Christopher

Christopher S. Daniel

3

Research Aims

20 μm

α - hcp β - bcc

Banerjee, S. in Encycl. Mater. Sci. Technol. (Cahn, K. H. et al.) 6287–6299 (Elsevier Science Ltd., 2001). doi:10.1016/B0-08-043152-6/01117-7 Mahmood, S. T. Mechanical Testing of Zirconium Alloys. in ZIRAT18 Semin. 1–37 (ANT International, 2014). *Adamson, R. B. et al. Mechanical Testing of Zirconium Alloys - Hydrides (Volume: 1, Section: 11). in ZIRAT18 Semin. 1–33 (ANT International, 2014).

High temperature rolling of ZrNb alloy at Manchester; Dual-phase α + β microstructure and hcp texture; Hydrides in Zr alloy tube.* Fuel assembly buckling.

• Require better understanding, to predict effect of processing parameters
• n manufactured microstructure/texture in Zr-Nb alloys

– as well as in dual-phase α + β Ti alloys.

• High temp. processing → α + β phase interaction → optimise final product.

Christopher

Christopher S. Daniel

• Two-phase slip deformation.

11ത 20 ||LD

4

Dual-Phase Microstructure Evolution

Suri, S., Viswanathan, G. B., Neeraj, T., Hou, D. H. & Mills, M. J. Slip transmission in an α/β titanium alloy. Acta Mater. 47, 1019–1034 (1999).

Christopher

Christopher S. Daniel

• Two-phase slip deformation.
• Dynamic recovery (DRY) and

dynamic recrystallization (DRX)

– nucleation versus growth. 11ത 20 ||LD

5

Dual-Phase Microstructure Evolution

Suri, S., Viswanathan, G. B., Neeraj, T., Hou, D. H. & Mills, M. J. Slip transmission in an α/β titanium alloy. Acta Mater. 47, 1019–1034 (1999). Chakravartty, J. K., Dey, G. K., Banerjee, S. & Prasad, Y. V. R. K. Dynamic recrystallisation of Zr–2·5Nb: processing maps. Mater. Sci. Technol. 12, 705–716 (1996).

Christopher

Christopher S. Daniel

• Two-phase slip deformation.
• Dynamic recovery (DRY) and

dynamic recrystallization (DRX)

– nucleation versus growth.

• Globularisation

– lamellae shearing and β migration. 11ത 20 ||LD

6

Dual-Phase Microstructure Evolution

Suri, S., Viswanathan, G. B., Neeraj, T., Hou, D. H. & Mills, M. J. Slip transmission in an α/β titanium alloy. Acta Mater. 47, 1019–1034 (1999). Chakravartty, J. K., Dey, G. K., Banerjee, S. & Prasad, Y. V. R. K. Dynamic recrystallisation of Zr–2·5Nb: processing maps. Mater. Sci. Technol. 12, 705–716 (1996). Semiatin, S. L., Seetharaman, V. & Weiss, I. Flow behavior and globularization kinetics of Ti–6Al–4V. Mater. Sci. Eng. A 263, 257–271 (1999).

Christopher

Christopher S. Daniel

• Two-phase slip deformation.
• Dynamic recovery (DRY) and

dynamic recrystallization (DRX)

– nucleation versus growth.

• Globularisation

– lamellae shearing and β migration.

• Dynamic transformation

during deformation

– mechanical activation from 11ത 20 ||LD

7

Dual-Phase Microstructure Evolution

TD RD 25 μm

α β β

net flow softening.

Suri, S., Viswanathan, G. B., Neeraj, T., Hou, D. H. & Mills, M. J. Slip transmission in an α/β titanium alloy. Acta Mater. 47, 1019–1034 (1999). Chakravartty, J. K., Dey, G. K., Banerjee, S. & Prasad, Y. V. R. K. Dynamic recrystallisation of Zr–2·5Nb: processing maps. Mater. Sci. Technol. 12, 705–716 (1996). Semiatin, S. L., Seetharaman, V. & Weiss, I. Flow behavior and globularization kinetics of Ti–6Al–4V. Mater. Sci. Eng. A 263, 257–271 (1999). Daymond, M. R. et al. Texture inheritance and variant selection through an hcp–bcc–hcp phase transformation. Acta Mater. 58, 4053–4066 (2010). Guo, B., Semiatin, & Jonas, J. J. Opposing and Driving Forces with Dynamic Transformation of Ti-6Al-4V. Metall. Mater. Trans. A Phys. Metall. Mater. Sci. 49, 1–5 (2018). Daniel, C. S. An Investigation into the Texture Development during Hot-Rolling of Dual-Phase Zirconium Alloys. (The University of Manchester, 2018).

Christopher

Christopher S. Daniel

• Two-phase slip deformation.
• Dynamic recovery (DRY) and

dynamic recrystallization (DRX)

– nucleation versus growth.

• Globularisation

– lamellae shearing and β migration.

• Dynamic transformation

during deformation

– mechanical activation from

• Phase transformation on

heating and cooling.

11ത 20 ||LD

8

Dual-Phase Microstructure Evolution

{110}𝛾|| 0001 𝛽 and < 1ത 11 >𝛾 || < 11ത 20 >𝛽

TD RD 25 μm

α β β

net flow softening.

Suri, S., Viswanathan, G. B., Neeraj, T., Hou, D. H. & Mills, M. J. Slip transmission in an α/β titanium alloy. Acta Mater. 47, 1019–1034 (1999). Chakravartty, J. K., Dey, G. K., Banerjee, S. & Prasad, Y. V. R. K. Dynamic recrystallisation of Zr–2·5Nb: processing maps. Mater. Sci. Technol. 12, 705–716 (1996). Semiatin, S. L., Seetharaman, V. & Weiss, I. Flow behavior and globularization kinetics of Ti–6Al–4V. Mater. Sci. Eng. A 263, 257–271 (1999). Daymond, M. R. et al. Texture inheritance and variant selection through an hcp–bcc–hcp phase transformation. Acta Mater. 58, 4053–4066 (2010). Guo, B., Semiatin, & Jonas, J. J. Opposing and Driving Forces with Dynamic Transformation of Ti-6Al-4V. Metall. Mater. Trans. A Phys. Metall. Mater. Sci. 49, 1–5 (2018). Daniel, C. S. An Investigation into the Texture Development during Hot-Rolling of Dual-Phase Zirconium Alloys. (The University of Manchester, 2018).

Christopher

Christopher S. Daniel

• Two-phase slip deformation.
• Dynamic recovery (DRY) and

dynamic recrystallization (DRX)

– nucleation versus growth.

• Globularisation

– lamellae shearing and β migration.

• Dynamic transformation

during deformation

– mechanical activation from

• Phase transformation on

heating and cooling.

11ത 20 ||LD

9

Dual-Phase Microstructure Evolution

{110}𝛾|| 0001 𝛽 and < 1ത 11 >𝛾 || < 11ത 20 >𝛽

TD RD 25 μm

α β β

net flow softening.

Suri, S., Viswanathan, G. B., Neeraj, T., Hou, D. H. & Mills, M. J. Slip transmission in an α/β titanium alloy. Acta Mater. 47, 1019–1034 (1999). Chakravartty, J. K., Dey, G. K., Banerjee, S. & Prasad, Y. V. R. K. Dynamic recrystallisation of Zr–2·5Nb: processing maps. Mater. Sci. Technol. 12, 705–716 (1996). Semiatin, S. L., Seetharaman, V. & Weiss, I. Flow behavior and globularization kinetics of Ti–6Al–4V. Mater. Sci. Eng. A 263, 257–271 (1999). Daymond, M. R. et al. Texture inheritance and variant selection through an hcp–bcc–hcp phase transformation. Acta Mater. 58, 4053–4066 (2010). Guo, B., Semiatin, & Jonas, J. J. Opposing and Driving Forces with Dynamic Transformation of Ti-6Al-4V. Metall. Mater. Trans. A Phys. Metall. Mater. Sci. 49, 1–5 (2018). Daniel, C. S. An Investigation into the Texture Development during Hot-Rolling of Dual-Phase Zirconium Alloys. (The University of Manchester, 2018).

Christopher

Christopher S. Daniel

Processing Maps → optimise processing parameters (𝑈, ሶ 𝜁) for microstructure breakdown using analysis of stress-strain curves.

10

• Dilatometer, Gleeble, …

Processing Maps

DIL 805 A/D/T Dilatometer. Gleeble 3500.

• Y. V. R. K. Prasad, K. P. Rao, and S. Sasidhara, Hot Working Guide: A Compendium of Processing Maps Second Edition, 2nd Editio. ASM International, 2015.

Chakravartty, J. K., Dey, G. K., Banerjee, S. & Prasad, Y. V. R. K. Dynamic recrystallisation of Zr–2·5Nb: processing maps. Mater. Sci. Technol. 12, 705–716 (1996). Daniel, C. S. An Investigation into the Texture Development during Hot-Rolling of Dual-Phase Zirconium Alloys. (The University of Manchester, 2018).

Christopher

Christopher S. Daniel

11

• Dilatometer, Gleeble, …
• Strain rate sensitivity;

Processing Maps

Temperature

𝑛 = 𝜖(𝑚𝑜𝜏) 𝜖(𝑚𝑜 ሶ 𝜁)

ሶ 𝜁,𝑈

DIL 805 A/D/T Dilatometer. Gleeble 3500.

• Y. V. R. K. Prasad, K. P. Rao, and S. Sasidhara, Hot Working Guide: A Compendium of Processing Maps Second Edition, 2nd Editio. ASM International, 2015.

Chakravartty, J. K., Dey, G. K., Banerjee, S. & Prasad, Y. V. R. K. Dynamic recrystallisation of Zr–2·5Nb: processing maps. Mater. Sci. Technol. 12, 705–716 (1996). Daniel, C. S. An Investigation into the Texture Development during Hot-Rolling of Dual-Phase Zirconium Alloys. (The University of Manchester, 2018).

Christopher

Christopher S. Daniel

log ሶ 𝜁 log 𝜏 Cubic Fit

Driving Force Time

12

• Dilatometer, Gleeble, …
• Strain rate sensitivity;
• High 𝑛 values;

Processing Maps

Temperature

𝑛 = 𝜖(𝑚𝑜𝜏) 𝜖(𝑚𝑜 ሶ 𝜁)

ሶ 𝜁,𝑈

DIL 805 A/D/T Dilatometer. Gleeble 3500.

– Optimise DRX processes. – ‘Breakdown’ of microstructure. – Increased ductility. – Avoid flow instabilities

• Y. V. R. K. Prasad, K. P. Rao, and S. Sasidhara, Hot Working Guide: A Compendium of Processing Maps Second Edition, 2nd Editio. ASM International, 2015.

Chakravartty, J. K., Dey, G. K., Banerjee, S. & Prasad, Y. V. R. K. Dynamic recrystallisation of Zr–2·5Nb: processing maps. Mater. Sci. Technol. 12, 705–716 (1996). Daniel, C. S. An Investigation into the Texture Development during Hot-Rolling of Dual-Phase Zirconium Alloys. (The University of Manchester, 2018).

Christopher

Christopher S. Daniel

log ሶ 𝜁 log 𝜏 Cubic Fit

Driving Force Time

13

• Dilatometer, Gleeble, …
• Strain rate sensitivity;
• High 𝑛 values;

Processing Maps

Temperature

𝑛 = 𝜖(𝑚𝑜𝜏) 𝜖(𝑚𝑜 ሶ 𝜁)

ሶ 𝜁,𝑈

DIL 805 A/D/T Dilatometer. Gleeble 3500.

• Y. V. R. K. Prasad, K. P. Rao, and S. Sasidhara, Hot Working Guide: A Compendium of Processing Maps Second Edition, 2nd Editio. ASM International, 2015.

Chakravartty, J. K., Dey, G. K., Banerjee, S. & Prasad, Y. V. R. K. Dynamic recrystallisation of Zr–2·5Nb: processing maps. Mater. Sci. Technol. 12, 705–716 (1996). Daniel, C. S. An Investigation into the Texture Development during Hot-Rolling of Dual-Phase Zirconium Alloys. (The University of Manchester, 2018).

Christopher

Christopher S. Daniel

– Optimise DRX processes. – ‘Breakdown’ of microstructure. – Increased ductility. – Avoid flow instabilities

14

.21 .29 .40 50 .44 .39 52 45

Chakravartty, J. K. et al. Identification of Safe Hot-Working Conditions in Cast Zr-2.5Nb. Zircon. Nucl. Ind. 17th Vol. 259–281 (2015). Chakravartty, J. K. et al. Dynamic Recrystallization in Zirconium Alloys. J. ASTM Int. 7, 121–149 (2010). Chakravartty, J. K., Dey, G. K., Banerjee, S. & Prasad, Y. V. R. K. Dynamic recrystallisation of Zr–2·5Nb: processing maps. Mater. Sci. Technol. 12, 705–716 (1996). Saxena, K. K. et al. Effect of Temperature and Strain Rate on Deformation Behavior of Zirconium Alloy: Zr-2.5Nb. Procedia Mater. Sci. 6, 278–283 (2014). Chakravartty, J. K., Dey, G. K., Banerjee, S. & Prasad, Y. V. R. K. Characterization of Zr-2.5Nb-0.5Cu using processing maps. J. Nucl. Mater. 218, 247–255 (1995).

Processing Maps – Issues

Christopher

Christopher S. Daniel

15

.21 .29 .40 50 .44 .39 52 45

Chakravartty, J. K. et al. Identification of Safe Hot-Working Conditions in Cast Zr-2.5Nb. Zircon. Nucl. Ind. 17th Vol. 259–281 (2015). Chakravartty, J. K. et al. Dynamic Recrystallization in Zirconium Alloys. J. ASTM Int. 7, 121–149 (2010). Chakravartty, J. K., Dey, G. K., Banerjee, S. & Prasad, Y. V. R. K. Dynamic recrystallisation of Zr–2·5Nb: processing maps. Mater. Sci. Technol. 12, 705–716 (1996). Saxena, K. K. et al. Effect of Temperature and Strain Rate on Deformation Behavior of Zirconium Alloy: Zr-2.5Nb. Procedia Mater. Sci. 6, 278–283 (2014). Chakravartty, J. K., Dey, G. K., Banerjee, S. & Prasad, Y. V. R. K. Characterization of Zr-2.5Nb-0.5Cu using processing maps. J. Nucl. Mater. 218, 247–255 (1995).

Processing Maps – Issues

Christopher

Christopher S. Daniel

700℃ 900℃

1 −1 −2 −3

Temperature Log (strain rate, s−1)

800℃

16

.21 .29 .40 50 .44 .39 52 45

Chakravartty, J. K. et al. Identification of Safe Hot-Working Conditions in Cast Zr-2.5Nb. Zircon. Nucl. Ind. 17th Vol. 259–281 (2015). Chakravartty, J. K. et al. Dynamic Recrystallization in Zirconium Alloys. J. ASTM Int. 7, 121–149 (2010). Chakravartty, J. K., Dey, G. K., Banerjee, S. & Prasad, Y. V. R. K. Dynamic recrystallisation of Zr–2·5Nb: processing maps. Mater. Sci. Technol. 12, 705–716 (1996). Saxena, K. K. et al. Effect of Temperature and Strain Rate on Deformation Behavior of Zirconium Alloy: Zr-2.5Nb. Procedia Mater. Sci. 6, 278–283 (2014). Chakravartty, J. K., Dey, G. K., Banerjee, S. & Prasad, Y. V. R. K. Characterization of Zr-2.5Nb-0.5Cu using processing maps. J. Nucl. Mater. 218, 247–255 (1995).

Processing Maps – Issues

Christopher

Christopher S. Daniel

700℃ 900℃

1 −1 −2 −3

Temperature Log (strain rate, s−1)

800℃

Aim → Quantify experimental uncertainty of processing maps, to see if they justify any idealised processing regimes in Zr-2.5Nb.

17

Experimental Methodology

R1 R2

{0002} {1120}

Forged Zr-2.5Nb alloy, α laths and

• utline of large prior-β grains.*

100 μm 1 mm R1 R2 CD

DIL 805 A/D/T quenching and deformation dilatometer

• Material

Forged Zr-2.5Nb. Cylinder – 10 mm height, 5 mm diameter.

• Compression Dilatometer

*Optical polarised light micrographs taken with Zeiss Axio Scope.A1

Christopher

Christopher S. Daniel

18

Experimental Methodology

2.5 mm R2 CD R1 R2 R1 CD

R2

• Material

Forged Zr-2.5Nb. Cylinder – 10 mm height, 5 mm diameter.

• Compression Dilatometer

α-phase EBSD orientation map of forged Zr-2.5Nb at 5 μm step size. DIL 805 A/D/T quenching and deformation dilatometer

*Using CamScan MX2000 FEG-SEM, with Channel 5 software analysis.

Christopher

Christopher S. Daniel

19

Experimental Methodology

2.5 mm R2 CD R1 R2 R1 CD

R2

• Material

Forged Zr-2.5Nb. Cylinder – 10 mm height, 5 mm diameter.

• Compression Dilatometer
• 9 x Temperatures

650ºC → 850ºC (25°C increment)

β-phase EBSD orientation map of forged Zr-2.5Nb at 5 μm step size.*

*High temperature β reconstruction software based on the Burgers relationship, {110}𝛾|| 0001 𝛽 and < 1ത 11 >𝛾 || < 11ത 20 >𝛽, by P. S. Davies, University of Sheffield, 2009. β approach curve determined using length changes on DIL 805 A/D/T dilatometer in quenching mode.

DIL 805 A/D/T quenching and deformation dilatometer

Christopher

Christopher S. Daniel

20

Experimental Methodology

2.5 mm R2 CD R1 R2 R1 CD

R2

• Material

Forged Zr-2.5Nb. Cylinder – 10 mm height, 5 mm diameter.

• Compression Dilatometer
• 9 x Temperatures

650ºC → 850ºC (25°C increment)

• 8 x Strain Rates

10−2.5 → 10+1 s−1 (10+0.5 s−1 increment)

• 50% Height Reduction

𝜁true = 0.693

β-phase EBSD orientation map of forged Zr-2.5Nb at 5 μm step size.* DIL 805 A/D/T quenching and deformation dilatometer

*High temperature β reconstruction software based on the Burgers relationship, {110}𝛾|| 0001 𝛽 and < 1ത 11 >𝛾 || < 11ത 20 >𝛽, by P. S. Davies, University of Sheffield, 2009. β approach curve determined using length changes on DIL 805 A/D/T dilatometer in quenching mode.

Christopher

Christopher S. Daniel

21

10

.

10 10

.

10 10

.

10 10

.

10

Strain Rate, s

‘Notional’ True Stress-Strain Curves

𝜏𝑢𝑠𝑣𝑓 = 𝐺 𝜌𝐸2 𝜁true = ln 𝐼 𝐼0 𝐼0𝐸0 = 𝐼𝐸

• ‘Apparent’ flow softening.
• Repeatability ~ 5% – 10%.
• Uncertainty greatest at low
• temp. and high strain rates.

~ 5 MPa

Data analysed using a Python script in the Jupyter Notebook application.

Christopher

Christopher S. Daniel

22

10

.

10 10

.

10 10

.

10 10

.

10

Strain Rate, s

𝜏𝑢𝑠𝑣𝑓 = 𝐺 𝜌𝐸2 𝜁true = ln 𝐼 𝐼0 𝐼0𝐸0 = 𝐼𝐸

• ‘Apparent’ flow softening.
• Repeatability ~ 5% – 10%.
• Uncertainty greatest at low
• temp. and high strain rates.

~ 5 MPa

Data analysed using a Python script in the Jupyter Notebook application.

‘Notional’ True Stress-Strain Curves

Christopher

Christopher S. Daniel

23 650℃ 675℃ 700℃ 725℃ 750℃ 775℃ 800℃ 825℃ 850℃

Temperature m

Zr-2.5Nb Processing Map

𝑛 = 𝜖(𝑚𝑜𝜏) 𝜖(𝑚𝑜 ሶ 𝜁)

ሶ 𝜁,𝑈

Christopher

Christopher S. Daniel

24 650℃ 675℃ 700℃ 725℃ 750℃ 775℃ 800℃ 825℃ 850℃

Temperature m

𝑛 = 𝜖(𝑚𝑜𝜏) 𝜖(𝑚𝑜 ሶ 𝜁)

ሶ 𝜁,𝑈

Christopher

Christopher S. Daniel 700℃ 750℃ 800℃ 850℃

Temperature

25°C

Zr-2.5Nb Processing Map – Fewer Points

m

25 650℃ 675℃ 700℃ 725℃ 750℃ 775℃ 800℃ 825℃ 850℃

Temperature m

𝑛 = 𝜖(𝑚𝑜𝜏) 𝜖(𝑚𝑜 ሶ 𝜁)

ሶ 𝜁,𝑈

Christopher

Christopher S. Daniel 700℃ 750℃ 800℃ 850℃

Temperature

25°C

Zr-2.5Nb Processing Map – Fewer Points

m

Overfitting of data in 1000s of papers

– 4 or 5 points is too few to constrain cubic fit.

Chakravartty, J. K. et al. Identification of Safe Hot-Working Conditions in Cast Zr-2.5Nb. Zircon. Nucl. Ind. 17th Vol. 259–281 (2015). Chakravartty, J. K. et al. Dynamic Recrystallization in Zirconium Alloys. J. ASTM Int. 7, 121–149 (2010). Chakravartty, J. K., Dey, G. K., Banerjee, S. & Prasad, Y. V. R. K. Dynamic recrystallisation of Zr–2·5Nb: processing maps. Mater. Sci. Technol. 12, 705–716 (1996). Saxena, K. K. et al. Effect of Temperature and Strain Rate on Deformation Behavior of Zirconium Alloy: Zr-2.5Nb. Procedia Mater. Sci. 6, 278–283 (2014).

26

m m m m m m

Random ±𝟔 𝐍𝐐𝐛 Noise

• Random noise normally distributed over ±5 MPa range.
• Same general trend with strain rate.
• Peaks in 𝑛 change → consistent with variation seen in literature.

Christopher

Christopher S. Daniel

27

Optical Images – Sample Centre

R1 CD R1 CD

700°C, 10+0 s−1 800°C, 10+0 s−1 850°C, 10+0 s−1 700°C, 10−2.5 s−1 800°C, 10−2.5 s−1 850°C, 10−2.5 s−1

20 μm 20 μm

𝑛 = −0.20 𝑛 = 0.08 𝑛 = 0.12 𝑛 = 0.06 𝑛 = 0.30 𝑛 = 0.20

Optical polarised light micrographs taken with Zeiss Axio Scope.A1

Christopher

Christopher S. Daniel

28

Optical Images – Stage Scan

R1 CD 1 mm R1 CD 1 mm

700°C, 10+0 s−1 800°C, 10+0 s−1 850°C, 10+0 s−1 700°C, 10−2.5 s−1 800°C, 10−2.5 s−1 850°C, 10−2.5 s−1

• Flow localisation/barrelling increases at higher temperatures/lower strain rates.
• Sliding at prior-β grain boundaries.

Optical polarised light micrographs taken with Zeiss Axio Imager.M2m in stage scan mode.

Christopher

Christopher S. Daniel

29

α-Phase Orientation Map

R1 CD 1 mm R1 CD

700°C, 10+0 s−1 800°C, 10+0 s−1 850°C, 10+0 s−1

1 mm

700°C, 10−2.5 s−1 800°C, 10−2.5 s−1 850°C, 10−2.5 s−1

R2

Optical polarised light micrographs taken with Zeiss Axio Imager.M2m in stage scan mode. EBSD maps taken using TESCAN MIRA3 FEG-SEM, with Channel 5 software analysis.

Christopher

Christopher S. Daniel

30

R1 CD 1 mm R1 CD

700°C, 10+0 s−1 800°C, 10+0 s−1 850°C, 10+0 s−1 700°C, 10−2.5 s−1

1 mm R2

R1 R2

{0002} {1120}

R1 R2

{0002} {1120}

R1 R2 CD

α-Phase Orientation Map

Optical polarised light micrographs taken with Zeiss Axio Imager.M2m in stage scan mode. EBSD maps taken using TESCAN MIRA3 FEG-SEM, with Channel 5 software analysis.

Christopher

Christopher S. Daniel

31

m

Barrelling

Maximum/Average Cross-Section Area

• Non-uniform temperature gradient and friction

→ barrelling

• Barrelling correlates with

artefacts in processing map.

• FE Modelling Aim – predict ‘true’ stress-strain

behaviour by correcting for deformation inhomogeneity

Compression sample shapes – a) initial, b) idealised and c) barrelled.

Christopher

Christopher S. Daniel

32

FE Modelling

• 100°C temperature gradient (worst case). Friction 𝜈 = 0.5.
• Convergence/mesh size and friction/temperature sensitivity

study using Zener-Holloman.#

• Look-up table from second order surface fit;*

𝜏 = 𝑔 𝑈, ሶ 𝜁 at discrete 𝜁

• 2 × 2 matrix to limit uncertainty.

– 700℃ → 800℃ and 10−2 s−1 → 10+0.5 s−1

Example of surface fit to stress against (a) temperature and (b) log( ሶ 𝜁) at 0.05 strain.

𝛽𝜁 = 0.034 − 0.328𝜁 + 1.545𝜁2 − 3.542𝜁3 + 3.844𝜁4 − 1.584𝜁5 𝜃𝜁 = 6.40 − 18.78𝜁 + 72.54𝜁2 − 102.45𝜁3 + 49.11𝜁4 𝑅𝜁 = 140.5 − 108.6𝜁 + 263.6𝜁2 − 229.7𝜁3 ln 𝐵𝜁 = 31.03 − 73.82𝜁 + 373.36𝜁2 − 926.93𝜁3 + 1147.23𝜁4 − 572.62𝜁5 *Empirical 𝜏-𝜁 curve fitting is of limited value, such as a 5th order polynomial fit…

# sinh

𝜏 𝜏0 𝑜

=

ሶ 𝜁 ሶ 𝜁0 exp 𝑅 𝑆𝑈

← 4 adjustable parameters.

Christopher

Christopher S. Daniel

FE mesh of 1600 elements, along with temp. and friction constraints.

33

FE Modelling – Offset Correction

Constitutive material response

Christopher

Christopher S. Daniel

34

FE Modelling – Offset Correction

Constitutive material response FE analysis

Christopher

Christopher S. Daniel

35

FE Modelling – Offset Correction

Constitutive material response FE analysis FE analysis

• utput

Christopher

Christopher S. Daniel

36

FE Modelling – Offset Correction

Constitutive material response FE analysis FE analysis

• utput

Offset Evaluate at discrete strains

Christopher

Christopher S. Daniel

37

FE Modelling – Offset Correction

Constitutive material response FE analysis FE analysis

• utput

Offset Evaluate at discrete strains

Christopher

Christopher S. Daniel

38

FE Modelling – Offset Correction

Constitutive material response FE analysis FE analysis

• utput

Offset Validate corrected constitutive data Evaluate at discrete strains

Christopher

Christopher S. Daniel

39

FE Modelling – Offset Correction

• Correction ∆𝜏(𝑈, ሶ

𝜁) varies with strain → affects flow softening.

Initial input to FE model and resulting output. Corrected input response and resulting corrected output.

Christopher

Christopher S. Daniel

40

FE Modelling – Offset Correction

• Correction ∆𝜏(𝑈, ሶ

𝜁) varies with strain → affects flow softening.

Initial input to FE model and resulting output. Corrected input response and resulting corrected output.

Christopher

Christopher S. Daniel

41 650℃ 675℃ 700℃ 725℃ 750℃ 775℃ 800℃

Temperature m

FE Modelling – Processing Map

Maximum/Average Cross-Section Area

• There is only an

increase in 𝑛 at higher temperatures and lower strain rates. 𝑛 = 𝜖(𝑚𝑜𝜏) 𝜖(𝑚𝑜 ሶ 𝜁)

ሶ 𝜁,𝑈

Experimental FE Model

Convergence limit 2 × 2 matrix

Christopher

Christopher S. Daniel

42

FE Modelling – Deformation Inhomogeneity

R1 CD 1 mm R1 CD 1 mm

700°C, 10+0 s−1 800°C, 10+0 s−1 850°C, 10+0 s−1 700°C, 10−2.5 s−1 800°C, 10−2.5 s−1 850°C, 10−2.5 s−1 Christopher

Christopher S. Daniel

1 mm R1 CD 1 mm R1 CD

43

FE Modelling – Deformation Inhomogeneity

800°C, 10+0 s−1 800°C, 10−2.5 s−1 ~ 4 × ~ 5 × ~ 4 × Christopher

Christopher S. Daniel

Temperature Strain Strain Rate ~ 6 ×

44

α EBSD Maps – Sample Centre

100 μm R1 CD R2

𝟐𝟏+𝟏 𝐭−𝟐, 𝟗𝟏𝟏℃ 𝟐𝟏−𝟑.𝟔 𝐭−𝟐, 𝟗𝟏𝟏℃

𝑈 = 800℃, ሶ 𝜁 = 10+0 s−1, 𝜁 = 0.7 𝑈 = 800℃, ሶ 𝜁 = 10−2.5 s−1, 𝜁 = 0.7

R2 R2

Christopher

Christopher S. Daniel

45

100 μm R1 CD R2

𝟐𝟏+𝟏 𝐭−𝟐, 𝟗𝟏𝟏℃ 𝟐𝟏−𝟑.𝟔 𝐭−𝟐, 𝟗𝟏𝟏℃

𝑈 = 800℃, ሶ 𝜁 = 10+0 s−1, 𝜁 = 0.7 𝑈 = 800℃, ሶ 𝜁 = 10+0.6 s−1, 𝜁 = 2.8 𝑈 = 800℃, ሶ 𝜁 = 10−2.5 s−1, 𝜁 = 0.7 𝑈 = 800℃, ሶ 𝜁 = 10−1.8 s−1, 𝜁 = 4.0

R2 R2

Christopher

Christopher S. Daniel

α EBSD Maps – Sample Centre

46

100 μm R1 CD R2

R1 R2

{0002} {1120}

R1 R2

{0002} {1120} R1 R2 CD

𝟐𝟏+𝟏 𝐭−𝟐, 𝟗𝟏𝟏℃ 𝟐𝟏−𝟑.𝟔 𝐭−𝟐, 𝟗𝟏𝟏℃ ሶ 𝜁 = 10+0.6 s−1, 𝜁 = 2.8 ሶ 𝜁 = 10−1.8 s−1, 𝜁 = 4.0

R2 R2

Christopher

Christopher S. Daniel

α EBSD Maps – Sample Centre

47

Poster

Christopher

Christopher S. Daniel

• Texture development of the α and β phases

during hot-rolling of a Zr-2.5Nb alloy.

• 700, 725, 750, 775, 800, 825, 850, 900°C.
• 50%, 75%, 87.5% rolling reduction.

48

Conclusions

• Hot-compression dilatometer matrix

– 9x temperatures, 8x strain rates (each repeated) – to avoid overfitting.

Christopher

Christopher S. Daniel

49

Conclusions

• Hot-compression dilatometer matrix

– 9x temperatures, 8x strain rates (each repeated) – to avoid overfitting.

• Processing map variation

– Peaks in 𝑛 depend on number of data-points. – Adding ±5 MPa random noise produces different maps.

Christopher

Christopher S. Daniel

50

Conclusions

Christopher

Christopher S. Daniel

• Hot-compression dilatometer matrix

– 9x temperatures, 8x strain rates (each repeated) – to avoid overfitting.

• Processing map variation

– Peaks in 𝑛 depend on number of data-points. – Adding ±5 MPa random noise produces different maps.

• Sample variability

– Inhomogeneous deformation due to temperature and friction → barrelling. – Large β-grain size.

51

Conclusions

m

Christopher

Christopher S. Daniel

• Hot-compression dilatometer matrix

– 9x temperatures, 8x strain rates (each repeated) – to avoid overfitting.

• Processing map variation

– Peaks in 𝑛 depend on number of data-points. – Adding ±5 MPa random noise produces different maps.

• Sample variability

– Inhomogeneous deformation due to temperature and friction → barrelling. – Large β-grain size.

• FE Modelling

– Correct constitutive data using offset ∆𝜏(𝑈, ሶ 𝜁). – Predict temperature, stress and strain (rate) inhomogeneity. – Only increase in 𝑛 with higher 𝑈 and lower ሶ 𝜁.

52

Conclusions

• Hot-compression dilatometer matrix

– 9x temperatures, 8x strain rates (each repeated) – to avoid overfitting.

• Processing map variation

– Peaks in 𝑛 depend on number of data-points. – Adding ±5 MPa random noise produces different maps.

• Sample variability

– Inhomogeneous deformation due to temperature and friction → barrelling. – Large β-grain size.

• FE Modelling

– Correct constitutive data using offset ∆𝜏(𝑈, ሶ 𝜁). – Predict temperature, stress and strain (rate) inhomogeneity. – Only increase in 𝑛 with higher 𝑈 and lower ሶ 𝜁.

Processing maps strongly affected by experimental uncertainty. Deformation inhomogeneity → scatter and artefacts. Microstructural examinations can be misleading if strain (rate) distribution is not accounted for.

m

Christopher

Christopher S. Daniel

53

Acknowledgements

• Patryk Jedrasiak, Christian J. Peyton, João Quinta da Fonseca,

Hugh R. Shercliff, Luke Bradley, Peter D. Honniball.

• Email: christopher.daniel@manchester.ac.uk
• Profile: https://lightform.org.uk/people/dr-christopher-stuart-daniel

The University of Manchester.

54

Conclusions

• Hot-compression dilatometer matrix

– 9x temperatures, 8x strain rates (each repeated) – to avoid overfitting.

• Processing map variation

– Peaks in 𝑛 depend on number of data-points. – Adding ±5 MPa random noise produces different maps.

• Sample variability

– Inhomogeneous deformation due to temperature and friction → barrelling. – Large β-grain size.

• FE Modelling

– Correct constitutive data using offset ∆𝜏(𝑈, ሶ 𝜁). – Predict temperature, stress and strain (rate) inhomogeneity. – Only increase in 𝑛 with higher 𝑈 and lower ሶ 𝜁.

Processing maps strongly affected by experimental uncertainty. Deformation inhomogeneity → scatter and artefacts. Microstructural examinations can be misleading if strain (rate) distribution is not accounted for.

m

Christopher

Christopher S. Daniel

56

Processing Maps – Issues

700℃ 900℃

1 −1 −2 −3

Temperature Log (strain rate, s−1)

800℃

• Fundamental criticisms identified#

Efficiency; 𝜃 =

𝐾 𝐾𝑛𝑏𝑦 = 2𝑛 𝑛+1

Instability;

𝜖 ln( Τ

𝑛 𝑛+1)

𝜖 ln ሶ 𝜁

+ 𝑛 < 0

1 mm

α α + β

• Overfitting of

data in 1000s

• f papers

– 4 or 5 points is too few to constrain cubic fit.

• Sample

barrelling.

• Large β-grain

size – up to 6 mm

diameter.*

• α-β deformation

mechanisms.

Daniel, C. S. An Investigation into the Texture Development during Hot-Rolling of Dual-Phase Zirconium Alloys. (The University of Manchester, 2018). *Chakravartty, J. K. et al. Identification of Safe Hot-Working Conditions in Cast Zr-2.5Nb. Zircon. Nucl. Ind. 17th Vol. 259–281 (2015).

#Montheillet, F., Jonas, J. J. & Neale, K. W. A critical evaluation of the dissipator power co-content approach. Metall. Mater. Trans. A 27, 232–235 (1996). #Ghosh, S. Interpretation of microstructural evolution using dynamic materials modeling. Metall. Mater. Trans. A 31, 2973–2974 (2000). #Ghosh, S. Interpretation of flow instability using dynamic material modeling. Metall. Mater. Trans. A 33, 1569–1572 (2002).

Christopher

Christopher S. Daniel

57 650℃ 675℃ 700℃ 725℃ 750℃ 775℃ 800℃ 825℃ 850℃

Temperature m

700℃ 750℃ 800℃ 850℃ 900℃ 950℃ 1000℃

Temperature

Zr-2.5Nb Processing Map

m

Chakravartty et al.*

Temperature corrected.

𝑛 = 𝜖(𝑚𝑜𝜏) 𝜖(𝑚𝑜 ሶ 𝜁)

ሶ 𝜁,𝑈

*Chakravartty, J. K. et al. Identification of Safe Hot-Working Conditions in Cast Zr-2.5Nb. Zircon. Nucl. Ind. 17th Vol. 259–281 (2015).

Christopher

Christopher S. Daniel

58

FE Modelling

• 100°C temperature gradient (worst case). Friction 𝜈 = 0.5.
• Convergence/mesh size and friction/temperature sensitivity

study using Zener-Holloman; sinh

𝜏 𝜏0 𝑜

=

ሶ 𝜁 ሶ 𝜁0 exp 𝑅 𝑆𝑈

← 4 adjustable parameters.

FE mesh of 1600 elements, along with temp. and friction constraints.

Christopher

Christopher S. Daniel

59

FE Modelling – Look-Up Table

• Empirical 𝜏-𝜁 curve fitting of limited value.*
• Look-up table from second order surface fit;

𝜏 = 𝑔 𝑈, ሶ 𝜁

• 2 × 2 matrix to limit uncertainty.

– 700℃ → 800℃ and 10−2 s−1 → 10+0.5 s−1

Example of surface fit to stress against temperature and log( ሶ 𝜁) at 0.05 strain.

𝛽𝜁 = 0.034 − 0.328𝜁 + 1.545𝜁2 − 3.542𝜁3 + 3.844𝜁4 − 1.584𝜁5 𝜃𝜁 = 6.40 − 18.78𝜁 + 72.54𝜁2 − 102.45𝜁3 + 49.11𝜁4 𝑅𝜁 = 140.5 − 108.6𝜁 + 263.6𝜁2 − 229.7𝜁3 ln 𝐵𝜁 = 31.03 − 73.82𝜁 + 373.36𝜁2 − 926.93𝜁3 + 1147.23𝜁4 − 572.62𝜁5 *For example, is a 5th order polynomial really capturing the strain dependence…???

Christopher

Christopher S. Daniel

60

α-Phase Pole Figures

R1 CD 1 mm R1 CD

700°C, 10+0 s−1 800°C, 10+0 s−1 850°C, 10+0 s−1 700°C, 10−2.5 s−1 800°C, 10−2.5 s−1 850°C, 10−2.5 s−1

1 mm R2

R1 R2

{0002} {1120}

R1 R2

{0002} {1120}

R1 R2

{0002} {1120}

R1 R2

{0002} {1120}

R1 R2

{0002} {1120}

R1 R2 CD

Optical polarised light micrographs taken with Zeiss Axio Imager.M2m in stage scan mode. EBSD maps taken using TESCAN MIRA3 FEG-SEM, with Channel 5 software analysis.

Christopher

Christopher S. Daniel

61

100 μm R1 CD R2

R1 R2

{0002} {1120}

R1 R2

{0002} {1120} R1 R2 CD

R1 R2

{110} {111}

R1 R2

{110} {111}

𝟐𝟏+𝟏 𝐭−𝟐, 𝟗𝟏𝟏℃ 𝟐𝟏−𝟑.𝟔 𝐭−𝟐, 𝟗𝟏𝟏℃

R2 R2

α and β Phase EBSD Maps

Christopher

Christopher S. Daniel