Journal of Minerals and Materials Characterization and Engineering, 2012, 11, 1095-1100
Published Online November 2012 (
Mechanical Property Estimation of Similar Weld using Ball
Indentation Technique
Harshit Kumar Khandelwal1*, Kamal Sharma2, Rahul Chhibber3
1Homi Bhabha National Institute, Mumbai, India
2Reactor Safety Division, Bhabha Atomic Research Centre, Mumbai, India
3Indian Institute of Technology Rajasthan, Jodhpur, India
Email: *
Received July 4, 2012; revised August 10, 2012; accepted August 24, 2012
A weld joint is composed of three principal zones viz., base metal, Heat Affected Zone (HAZ), and weld zone. Thus,
the variation in mechanical behavior exists not only among these zones, but also from point to point in each individual
zone. Being destructive in nature, the conventional method of mechanical testing cannot successfully used to estimate
the variation in the mechanical behavior at different zones of the weld joint. Moreover, the conventional method of me-
chanical testing cannot characterize the material using small amount of material. In this respect, Ball Indentation (BI)
methodology was considered to be useful approach, since it can characterize the mechanical properties of a material
using very small amount of material in non destructive manner. The present work is an attempt to characterize the
variation in the mechanical properties among each zone (global variation), and from point to point in each zone (local
variation) of the similar weld joint used in nuclear application using BI approach. For this purpose, the similar weld
joint of two SS-304 LN pipe lines was investigated using BI approach.
Keywords: Ball Indentation; In Situ; Similar Weld Joint; Flow Properties; Pressurized Water Reactor; Reactor Pressure
1. Introduction
1.1. Similar Weld Joint (Weld Joint of SS 304
LN Pipelines)
Pressurized Water Reactor (PWR) is the most widely
used reactor type in the world, in which enriched (about
3.2% U-235) uranium dioxide is utilized as the fuel in
zirconium alloy cans. The fuel is arranged in the arrays
of fuel pins and interspersed with the movable control
rods. The fuel is held in a steel vessel through which wa-
ter at high pressure (at 16 MPa, to suppress boiling) is
pumped to reactor vessel via cold lag pipeline to act as
both a coolant and a moderator. After absorbing the heat
from the core of reactor, high-pressure water is passed to
a steam generator, via hot lag pipeline which raises
steam in the usual way. Both hot lag and cold lag pipe
lines are made of SS 304 LN material and have the simi-
lar weld joint. The chemical composition of SS 304 LN
which was used for the present investigation is shown in
Table 1.
2. Ball Indentation Approach
Ball Indentation (BI) is a non destructive approach to
Table 1. Chemical composition of SS 304 LN material used
for investigation.
C MnNiSiS P Cr N Fe
0.032 8-1210.030.04 18-20 0.1 Balance
determine mechanical behavior of the materials. More
over it utilizes very small amount of material during me-
chanical behavior examination. This technique can be
utilized for the situations where in situ investigation of
mechanical behavior is required. In order to find out the
mechanical properties using BI testing, many theories
and models have been proposed. Tabor [1] proposed an
empirical relationship, which correlates the plastic strain
corresponding to uniaxial loading with plastic indenta-
tion strain corresponding to indentation loading using
spherical indenter. Mayer [2] was the first one, who cor-
related the yield strength of material with the impression
diameter and the mean pressure during indentation load-
ing. Haggag et al. [3-8] developed BI setup to predict the
mechanical behavior of the materials. Later this setup
was utilized for the investigation of flow and fracture be-
havior of different materials by several researchers [9-11].
There exists a good agreement between BI generated
*Corresponding author.
Copyright © 2012 SciRes. JMMCE
flow and fracture properties with those generated through
conventional mechanical testing. H. K. Khandelwal et al.
[12] characterized the flow behavior of reactor pressure
vessel steel SA 508, pressure tube material Zr-2.5Nb and
other nuclear component materials using BI approach.
Kamal Sharma et al. [13] used numerical simulation with
finite element and artificial neural network methodology
to estimate the mechanical properties using BI approach.
Kamal Sharma et al. [14] also applied BI methodology to
estimate the degradation of Zr-2.5Nb alloy. G. Das et al.
[15] utilized BI approach for the study of the effect of
cold work on tensile flow behavior of SS 316 steel. Mok
[16,17] and Duffy [17] worked on BI approach with va-
rious strain rates. Mathew et al. [18] investigated the aging
effect on the mechanical behavior of alloy 625 through
BI approach.
BI approach is based on multiple indentations at a par-
ticular location on the component using a spherical in-
denter in order to determine mechanical behavior at that
location. During multiple indentations, work piece is sub-
jected to several loading and unloading cycles at the in-
dentation location and data from each of these cycles
yield a point on the flow curve. In order to carry out BI
testing, a computer controlled BI setup is mounted over
the component whose mechanical properties to be inves-
tigated. The computer allows the indenter of BI machine
to touch the work piece surface. During indentation, se-
veral loading and unloading cycles perform at a particu-
lar location on the work piece surface. The indentation
prfile during each loading and unloading cycle of BI tes-
ting is shown in Figure 1. Figure 2 shows the cyclic
nature of load vs displacement during BI testing. Total
depth of indentation (ht), plastic depth of indentation (hp),
and applied indentation load (P) are measured during each
loading cycle. The cycles of indentation continues up to
the point when the total depth of indentation reaches the
value corresponding to the half of ball indenter diameter.
For each loading and unloading cycle, the value of
plastic indentation diameter (dp) and total indentation
diameter (dt) from ht and hp, can be find using Equation
(1) and Equation (2) respectively. In Equation (1), the
value of dp can be calculated using regression analysis.
Figure 1. Indentation geometry during BI testing [18].
Figure 2. Load vs Displacement profile during BI Testing.
12 PPP
d 2.7350.25d
EE hh
dh 
h (2)
Tabor [1] correlated the indentation hardness and strain
corresponding to a spherical indenter with plastic strain
during uniaxial loading. He established the relation
(Equation 1.3) between true plastic strain (εp) corre-
sponding to uniaxial tensile test and the indentation strain
(dp/D) corresponding to ball indentation test [1].
0.2 D
 (3)
In Equation (3), D and dp are ball indenter diameter
and plastic indentation diameter respectively. The plastic
depth (hp) corresponding to a cycle, during BI testing is
converted to corresponding plastic indentation diameter
dp, using Equation (1). The maximum strain that can be
measured during BI test is 20%, when dp = D. In the pre-
sent work, maximum strain value lies between 10 to 12 %.
P is the maximum measured load corresponding to a cy-
cle in BI loading. Under load P, the mean normal pres-
sure (Sm) acting on the material is given by 4P/πdp
Equation (4) and Equation (5) correlates the uniaxial
flow stress (σ) with the mean normal pressure.
In Equation (4) and Equation (5), δ is constraint factor
which can be found out using Equation (6).
2.87 m
The parameter αm in Equation (6) depends mainly on
Copyright © 2012 SciRes. JMMCE
the strain rate sensitivity and work hardening characteris-
tic of the material being tested. αm varies from 0.9 to 1.25
for different materials. αm has the value of 1.0 for low
strain rate sensitive materials [20].
The flow portion of the true stress vs true plastic strain
curves can be represented using power law relationship
as given in Equation (7) [20].
 (7)
In Equation (7) n, K, σ, and εp represent strain harden-
ing exponent, strength coefficient, true stress and true
plastic strain respectively. The values of strength coeffi-
cient (K) and strain hardening exponent (n) can be de-
termined using regression analysis of the data fitted to
Equation (7). For the case when
p = n, Equation (8) pro-
vides the expression for true ultimate tensile strength-
Thus engineering ultimate tensile strength is given
by Equation (9),
Yield strength of specimen is not equal to the value of
stress corresponding to first cycle during BI testing, since
the minimum attainable ball indentation strains for a no-
minal size indenter are about 20 times larger than the
strain corresponding to yield stress. Hence, the strain cor-
responding to yield stress is too small to measure directly
from indentation test. Therefore, a different approach is
adopted for the estimation of yield strength of the ma-
terial [19].
Mayer [2] was the first one who established an em-
pirical relationship between the mean pressure and the
impression diameter during indentation (Equation 1.10).
Data points from all loading cycles (maximum value of
dt/D = 1.0) are fit by regression analysis to the relation-
ship of Equation (10).
 (10)
In Equation (10), m and A are Meyer’s exponent (m)
and yield parameter respectively. Parameter “m” gener-
ally has a value between 2 to 2.5. The value of dt can be
determined from total depth of indentation using the
Equation (2).
The yield strength (σy) is proportional to the Meyer’s
hardness (4P/pd2), where d is the final impression di-
ameter, and is given by Equation (11).
 (11)
In Equation (11), parameter βm is a constant for a
given class of material. The value of βm for each class of
material is determined from the yield strength obtained
using standard tensile tests.
3. Experimentation
The mechanical behavior of similar weld joint was char-
acterized using a weld joint of two SS 304 LN pipelines.
This weld joint comprised of three principal zones viz.,
two zones of SS 304 LN base metal and a weld zone,
lying in between the two base metal zones. This investi-
gation was carried out in order to study the gradients in
the mechanical behavior of subzones of the similar weld
joint viz., Weld, HAZ and base metal zone. In order to
study the gradients in mechanical behavior at these sub-
zones, BI experiments were performed along the three
principal zones of weld joint. The BI testing was per-
formed using load control condition. For this purpose, BI
machine was installed over the weld jointed pipelines
and BI experiments were performed at these zones of the
weld joint at 0.5 KN/min. loading rate. The maximum
load during each of the experiments was kept 1.5 KN.
The arrangement of installed BI setup over similar weld
joint of two SS 304-LN pipelines is shown in Figure 3.
The indent points generated after BI experiments on
similar weld joint are shown in Figure 4.
SS 304 Pipe
SS 304 Pipe
Weld Zone BI Setup
Figure 3. BI setup installed on weld jointed SS 304 LN pipe-
Figure 4. Final indentation points after BI experiments.
Copyright © 2012 SciRes. JMMCE
4. Results
4.1. Comparison of Different Zones of Similar
Weld Joint
4.1.1. Load vs Displacement Curves
The three subzones of similar weld joint showed vari-
ation in slopes of BI generated load vs displacement
curves. Here, heat affected zone shows higher slope of
load vs displacement curve in comparison to the base
metal zone. Weld zone showed the least slope among the
three subzones. The comparison of load vs displacement
curves at each of the three zones of similar weld joint (i.e .
SS 304 LN, HAZ of SS 304 LN and Weld) is shown in
Figure 5.
4.1.2. Flow Behavior
Each of the three subzones shows clear variation in the
flow properties. Figure 6 shows the true stress vs true
plastic strain patterns for each of these subzones.
4.2. Global Comparison
After carried out the analysis of BI generated true stress
vs true plastic strain curves for three zones of similar
Figure 5. Comparison of load vs displacement curves at
three zones of similar weld joint.
Figure 6. Comparison of true stress vs true plastic strain
curves at three zones of similar weld joint.
weld joint, mechanical properties (strength coefficient,
strain hardening exponent, yield strength and ultimate
tensile strength) were determined. The average strength
coefficient at heat affected zone was found to be higher
than base metal zone. The highest average strength coef-
ficient was found in base metal zone and least average
strength coefficient was found in the weld zone. The
highest value of strain hardening exponent was found in
base metal while least was for heat affected zone. The
average values of yield strength and ultimate tensile
strength of heat affected zones was higher than the re-
spective base metal zones. The highest yield strength and
ultimate tensile strength was found in case of heat af-
fected zone. However, the difference between average
ultimate tensile strength for SS 304-LN base metal and
its heat affected zone was not significant. The base metal
shows least yield strength and weld zone shows least
value of ultimate tensile strength was found in weld zone.
Table 2 shows the local variation of mean values and
standard deviation values of all the BI experiments at
three zones of similar weld joint.
4.3. Local Variation of BI Generated YS & UTS
along Similar Weld Joint
The local variation shows that the heat affected zone had
higher yield strength than its base metal zone. This pat-
tern was also present in case of bimetallic weld joint (for
SA 508 class-2 and SS 304-LN) tested in both loading
rates viz. 0.5 KN/min. and 1.5 KN/min [12]. The ulti-
mate tensile strength for both base metal and its heat af-
fected zone was found to be almost similar. The local
variations of yield strength and ultimate tensile strength
along the three zones of similar weld joint of SS 304-LN
pipelines are shown in Figures 7 and 8 respectively.
5. Conclusions
After carried out the mechanical behavior investigation
Table 2. Comparison of mean and standard deviation va-
lues of BI generated mechanical properties at three zones of
similar weld joint.
Position SS 304
Weld Zone SS 304 HAZ SS 304 Base
Metal Zone
Properties Mean SD Mean SD Mean SD
Coefficient (MPa)1455.454 1529 306.8 1592142
Strain Hardening
Exponent 0.07 0.28 0.03
Yield Strength
(MPa) 556.815.4747.1 68.9 338.0 6.50
UTS (MPa) 785.089.68843.0 85.2 842.735.34
Copyright © 2012 SciRes. JMMCE
Figure 7. Variation of yield strength at three zones of simi-
lar weld joint.
Figure 8. Variation of BI generated ultimate tensile strength
at different zones of similar weld joint.
using BI approach in different sub zones of similar weld
joint (SS 304 LN base metal, HAZ, and weld zone) fol-
lowing points were concluded:
Yield strength of the heat affected zone SS 304-LN
was found to be higher than that of respective base
metal and weld zone.
Heat affected zone and base metal zone shows almost
similar Ultimate tensile strength. However it was
higher than that of weld zone.
Each subzone of weld joint shows significant differ-
rence in mechanical behavior with respect to each
other. Moreover, the variation of mechanical proper-
ties was found to be negligible throughout within
some zones.
The BI approach was found to be extremely useful in
the situations where it is required to conduct non destruc-
tive mechanical behavior examination, in situ inspection,
and structural integrity assessment of structural compo-
nents. Moreover, this approach is useful in the situations
where less amount of material is available for mechanical
behavior evaluation.
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