Journal of Mechanical Science and Technology 35 (8) 2021 DOI 10.1007/s12206-021-0710-1
3369
Journal of Mechanical Science and Technology 35 (8) 2021
Original Article
DOI 10.1007/s12206-021-0710-1
Keywords:
· High temperature
· Kocks - Mecking
· Tensile test
· Work hardening
· Zr-2.5Nb
Correspondence to:
Saptarshi Dutta
d.saptarshi@iitg.ac.in
Citation:
Dutta, S., Robi, P. S. (2021). Analysis of
tensile flow and work hardening behavior
of Zr-2.5Nb alloy in the framework of
Kocks - Mecking approach. Journal of
Mechanical Science and Technology 35
(8) (2021) 3369~3374.
http://doi.org/10.1007/s12206-021-0710-1
Received December 9th, 2020
Revised April 20th, 2021
Accepted May 9th, 2021
† Recommended by Editor
Chongdu Cho
Analysis of tensile flow and work
hardening behavior of Zr-2.5Nb alloy in
the framework of Kocks - Mecking
approach
Saptarshi Dutta and P. S. Robi
Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Assam 781039, India
Abstract High-temperature tensile tests were carried out on Zr-2.5Nb alloy in the
temperature range of 298-873 K for both longitudinal and transverse specimen directions.
Kocks-Mecking (K-M) approach was used to analyze the tensile flow and work-hardening
nature of this alloy. The graph of instantaneous work hardening rate (θ = dσ/dε, where true
stress is denoted by σ and true plastic strain by ε) with stress exhibited two-stage strain
hardening behavior at all temperatures. The graph of θ vs σ and the variation in the parameters
of strain hardening displayed three temperature zones, with a plateau region in 473-573 K. A
fairly good correlation was achieved between the strain hardening parameters measured with
the K-M method and the Voce equation at the above-mentioned temperature range.
1. Introduction
Zr-2.5Nb alloys are the primary option for manufacturing pressure tubes (P.T.) in pressurized
heavy water reactors (PHWR) [1-3]. Zirconium alloys have low neutron absorption cross-
section, sufficient creep resistance, outstanding tolerance to corrosion under aqueous condi-
tions and good microstructural and irradiation stability [4-6]. In the case of a hypothesized de-
sign accident such as loss of coolant accident (LOCA), heat from the core is not absorbed by
the primary coolant, resulting in very high temperatures [7, 8]. These adverse conditions may
lead to the sagging and ballooning of the horizontal P.T.s, which may eventually allow radioac-
tivity to leak into the atmosphere. Thus, it is imperative to have a detailed knowledge of the
work hardening behavior of Zr-2.5Nb at elevated temperature.
The approach of Kocks-Mecking (K-M) is being widely used to analyze and model the strain
hardening nature of metals and alloys [9, 10]. This approach offers a sound explanation of the
physical significance of the Voce relationship [9-11]. The Voce relationship, which relates the
true stress (σ) with the plastic part of strain (ε) [12, 13], is given as
( )
( )
exp
⎡ ⎤ −
= − − −
⎢ ⎥
⎢ ⎥
⎣ ⎦
I
S S I
C
ε ε
σ σ σ σ
ε
, (1)
in which saturation stress is denoted by σ
S
, true stress by σ
I
, true plastic strain is given by ε
I
and ε
C
is a constant. Eq. (1) becomes
( ) exp( ) = − −
S S I v
n σ σ σ σ ε , (2)
when
I
ε = 0, with σ
S
, σ
I
and
V
n as the constants where 1/ = −
V C
n ε . The behavior of instan-
taneous work hardening rate ( / = d d θ σ ε ) with flow stress σ, by K-M method exhibits three
stages of strain hardening. Stage I of work hardening is exhibited by single crystals where de-
© The Korean Society of Mechanical
Engineers and Springer-Verlag GmbH
Germany, part of Springer Nature 2021