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Tackling Flow Stress of Zirconium Alloys

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Abstract

Flow stress during hot deformation is essentially controlled by the chemistry of material, initial microstructure/texture, strain, strain rate, strain path, stress triaxility and the temperature of deformation. A comprehensive literature survey has been performed to realize this fact completely. In the present research, a neural network model under Bayesian framework has been created to correlate the complex relationship between flow stress with its influencing parameters in various grades of zirconium alloys at different deformation conditions. The network has been trained with published experimental database obtained from the different hot deformation experiments of zirconium alloys. Performance of the model has been evaluated; and excellent agreements between experimentally measured and model calculated data are obtained. The analysis permits the estimation of error bars whose magnitude strongly depends on their position in the input space. The model has been employed to different grades of zirconium alloys to confirm that the predictions are reasonably accurate in the context of basic metallurgical/solid mechanics theories and principles. The work has clearly identified the regions of the input space where further experiments should be encouraged and necessary. This model will be useful to design and manufacture the new generation zirconium alloys in future for the nuclear power plant components according to the needs of nuclear engineers/scientists by controlling the alloying elements and other possible conditions. The result shows that neural computation is a very effective tool to model the complex \(\textit{non-linear}\) behaviour of flow stress of different zirconium alloys under any deformation conditions.

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Abbreviations

AI:

Artificial intelligence

AISI:

American iron and steel institute

ABWRS:

Advanced boiling water reactors

ANN:

Artificial neural network

\(\textit{bcc}\) :

Body centered cubic

BNN:

Bayesian neural network

BWR:

Boiling water reactor

CR:

Cold roll

DMM:

Dynamic material model

DNN:

Deep neural network

DRV:

Dynamic recovery

DRX:

Dynamic recrystallization

DSA:

Dynamic strain aging

EBSD:

Electron back-scatter diffraction

EL:

Elongation

\(\epsilon \) :

Strain

FEA:

Finite element analysis

FEM:

Finite element modelling

FG:

Fine grain

FNN:

Fuzzy neural network

\(\textit{fcc}\) :

Face centered cubic

GB:

Grain boundary

GDX:

Geometric dynamic recrystallization

GS:

Grain size

HT:

High temperature

HCS:

High carbon steels

HWR:

Heavy water reactors

hcp:

Hexagonal closed packed

K:

Strain hardening co-efficient

LGSP:

Large grain superplasticity

LPE:

Log predicted error

L:

Size of committee in ANN

LAS:

Low alloy steel

LCS:

Low carbon steel

LT:

Low temperature

LWR:

Light water reactor

MT:

Martensitic transformation

MRA:

Multiple regression analysis

\(\textit{m}\) :

Strain rate sensitivity

\(\textit{n}\) :

Strain hardening exponent

NN:

Neural network

P:

Pressure

PT:

Pressure tube

PWR:

Pressurized water reactor

RA:

Reduction in area

RT:

Room temperature

RX:

Recrystallization

\(\rho \) :

Dislocation density

\(\sigma _\nu \) :

Regularized sum of squared errors

SD:

Standard deviation

SP:

Superplasticity

SB:

Shear bands/slip bands

SR:

Strain rate

SEM:

Scanning electron microscope

SFE:

Stacking fault energy

SSA:

Static strain ageing

\(\tau _{CRSS}\) :

Critical resolved shear stress

\(\textit{tanh}\) :

Hyperbolic tangent

T:

Temperature

\(T_e\) :

Test error

TT:

Transition temperature

TBC:

Thermal barrier coatings

\(\tau \) :

Stress triaxiality

UNS:

Unified numbering system

UTS:

Ultimate tensile strength

YS:

Yield strength

XRD:

X-ray diffraction

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Acknowledgements

I am extremely grateful to Professor Sir H.K.D.H. Bhadeshia, Phase Transformation and Complex Properties Research Group, Department of Materials Science and Metallurgy, University of Cambridge, England, United Kingdom for the provision of Neuromat Neural Network software for the present analysis. I would also like to thank Professor Eugenio Onate (The Editor in Chief–Archives of Computational Methods in Engineering) for the acceptance of the manuscript.

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  1. Mechanical Metallurgy Division, Materials Group, Bhabha Atomic Research Centre (Department of Atomic Energy), Trombay, Mumbai, Maharashtra, 400 085, India

    Arpan Das

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Das, A. Tackling Flow Stress of Zirconium Alloys. Arch Computat Methods Eng 28, 2103–2131 (2021). https://doi.org/10.1007/s11831-020-09451-z

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