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Sine Hyperbolic Models and Their Applicability Towards Creep Deformation Behaviour of 9% Chromium Steels

Technical Paper
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Abstract

Two different variants of creep models have been developed. In Model-I, sine hyperbolic kinetic law defining primary and secondary creep deformation has been added to tertiary creep rate for complete description of creep strain–time trajectories. In Model-II, evolution of damages such as subgrain growth, forest dislocation density, internal stress and precipitate coarsening have been coupled into the sine hyperbolic creep rate relation in the framework of phenomenological based approach for describing three stages of creep deformation. Applicability as well as implications of both the models has been examined for creep deformation of P9 steel for 150 MPa at 793 K.

Keywords

Kinetic creep law Additive formalism Microstructure based model Creep strain–time prediction 

List of symbols

\(\dot{\varepsilon }_{p}\)

Primary creep rate

k

Boltzmann constant

\(\dot{\varepsilon }_{s}\)

Secondary creep rate

R

Gas constant

\(\dot{\varepsilon }_{tr}\)

Tertiary creep rate

G

Shear modulus

\(\dot{\varepsilon }\)

Generalized creep rate

εc

Rate constant for internal stress evolution

\(\dot{\varepsilon }_{IAS}\)

Creep rate for initial applied stress

C,Ω

Constant related to tertiary creep rate

\(\dot{\varepsilon }_{ref}\)

Reference creep rate

M

Taylor factor

\(\dot{\varepsilon }_{0}\)

Initial strain rate

\(\rho_{m}\)

Mobile dislocation density

Q

Activation energy

\(\rho_{f}\)

Forest dislocation density

σ

Applied stress

\(\rho_{f,0}\)

Initial forest dislocation density

σi

Internal stress

λw

Width of subgrain

σi0

Initial internal stress

λw,0

Initial width of subgrain

σis

Saturation stress

Kp

Rate constant for precipitate coarsening

σe

Effective stress (σ − σi)

f

Volume fraction of precipitate

σes

Effective stress at saturation (σ − σis)

r

Radius of precipitate

σi,Max

Maximum achievable internal stress

r0

Mean initial precipitate radius

T

Temperature

β

Dislocation annihilation parameter

t

Time

n

Constant associated with dislocation annihilation

b

Burgers vector

νD

Debye frequency

h

Material constant associated with internal stress evolution

LS

Least-square error

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Copyright information

© The Indian Institute of Metals - IIM 2017

Authors and Affiliations

  1. 1.Deformation and Damage Modeling Section, Mechanical Metallurgy Division, Indira Gandhi Centre for Atomic ResearchHBNIKalpakkamIndia

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