Journal of Surface Engineered Materials and Advanced Technology, 2013, 3, 75-83
http://dx.doi.org/10.4236/jsemat.2013.31A011 Published Online February 2013 (http://www.scirp.org/journal/jsemat)
75
Cracking of S235JR Cold-Deformed Steel during
Galvanizing—Developing a Test to Evaluate and Predict
the Effect of the Zinc Alloy Composition
Anne-Lise Cristol1,2, David Balloy1,2, Christophe Niclaeys1,2, Philippe Quaegebeur1,2, Ludovic Néel3
1Univ Lille Nord de France, Lille, France; 2ECLille, Laboratoire de Mécanique de Lille, Villeneuve d’Ascq, France; 3Galvazinc
Association, Issy les Moulineaux, France.
Received October 16th, 2012; revised November 18th, 2012; accepted November 25th, 2012
ABSTRACT
This paper presents a study on the cracking of steel pieces during their galvanization in alloyed liquid zinc. An experi-
mental design was developed to show the effect of the amount of the various alloying elements (Sn, Bi, Pb) on this
phenomenon. The characterization of the effect was obtained by 1) deformation by three-point bending of a piece of
steel with different levels of deflection; 2) galvanizing and 3) observation and measurement of the cracks. A model of
the critical deflection (deflection for crack starting) with the amounts of Sn, Pb, and Bi is presented and the predictions
are described.
Keywords: Galvanizing; Cracking; Steel; Experimental Design
1. Introduction
The impact of atmospheric corrosion on resistance and
aspect of steel structures is well known. The galvaniza-
tion is one of the most usual ways to protect steel. Un-
fortunately, in some situations, steel cracks during hot-
dip galvanizing. This phenomenon has been known for a
long time. However, it has been insufficiently explored,
and liquid metal-induced embrittlement (LME), grain
boundary diffusion, or thermo-mechanical aspects could
be, among other the possibilities, the cause.
LME has been the subject of many papers [1,2]. The
mains studies are about the behavior of the steel in con-
tact with liquid sodium [3-5] or Pb-Bi liquid alloys [6,7].
The case of steel in liquid zinc has only been studied in a
few papers e.g. [8,9]. LME is the reduction in ductility
and fracture stress of metals immerged in certain liquid
metals [1,2,10,11], by reduction of the surface energy
and a decrease of the critical stress intensity factor, KIC
[1,11].
The European FAMEGA program, which ended in
2007, studied the cracking of steel during galvanizing.
Some parameters such as the steel grade, its surface
treatments, the surface stress associated, pickling, flux-
ing, and the zinc alloy composition were studied. The
results show that residual stresses induced by the steel
forming lead to situations conducive to cracking [12,13]
and that immersion in alloys of different compositions,
including tin (Sn), bismuth (Bi), and lead (Pb), gives
different resistance to cracking [14]. The effect of these
elements on the thermal behavior of the bath has also
been highlighted [15]. However, given the complexity
of the phenomenon and the multitude of criteria, the
underlying mechanisms have not yet been clearly dem-
onstrated. Nonetheless, it is known that at least two
conditions must be fulfilled for cracking. Firstly, the
steel must have been strongly plastically deformed;
secondly, it should have been immersed in a liquid me-
tallic alloy [1,2].
In a previous work [16], we developed an experimen-
tal protocol (described in Section 2) to quantify the effect
of the addition of Sn, Bi, and Pb to the galvanization bath
on the cracking of steel specimens. This experimental
work showed that the surface state of the steel influenced
the test sensitivity. For an “as delivered” industrial state,
the difference of the cracking behavior in two baths was
greater than for a polished surface. In the latter case, for a
given plastic deformation, no difference was observed
for the tested compositions. In this protocol the samples
are galvanized in conditions close to the industrial proc-
ess.
This paper presents an experimental design performed
to investigate the effect of the additions of Sn, Pb, and Bi
in a galvanizing bath on the cracking of cold deformed
steel, using our crack sensitivity test.

Cracking of S235JR Cold-Deformed Steel during Galvanizing—Developing a Test to Evaluate and Predict the
Effect of the Zinc Alloy Composition
76
2. Experimental Procedure
2.1. Experimental Design
The chosen experimental design was the Roquemore
311B developed by K. G. Roquemore in 1976 [17,18].
The software that we used for applying the Roquemore
311B is MS Excel. It allows the study of the effects of
three factors xi (with i from 1 to 3) and allows the devel-
opment of a quadratic mathematical model associated
with a response surface y (Equation (1)). The response y
of this experimental design is the minimal deflection that
should be imposed on a steel sample for the appearance
of cracks after galvanizing, here called “critical deflect-
tion.” This cold deformation is performed on a steel sam-
ple using three-point bending.
The field of study is defined by the composition of the
three alloying elements: Sn and Pb from 0 to 1 wt% and
Bi from 0 to 0.1 wt%. The experimental design was asso-
ciated with a mathematical model to estimate the simple
interaction and the quadratic effects of the alloying ele-
ments as well as to provide an idea of the shape of the
response surface in the field of study.
The experimental design contained 11 tests and de-
fined the values taken by the factors xi for each test (Ta-
ble 1).
01122331212
22
13 13232311 1222333
yaax axaxaxx
axxaxxax ax ax
 
 
2
(1)
with
a0 the mean value of the response y; ai the coefficient of
the simple effect of the factor xi; aii the coefficient of the
quadratic effect of the factor xi; aii the coefficient of the
interaction effect of the factors xi and xj.
Table 1. Values of the factors xi in the Roquemore 311B
experimental design.
Test number x1 x
2 x 3
1 0 0 +2.449
2 0 0 −2.449
3 −0.751 −2.106 −1
4 +0.751 −2.106 +1
5 −0.751 +2.106 +1
6 +0.751 +2.106 −1
7 −2.106 −0.751 +1
8 +2.106 −0.751 −1
9 −2.106 +0.751 −1
10 +2.106 +0.751 +1
11 0 0 0
A factor xi is related to a composition wn of one of the
studied elements: x1, x2, and x3 are, respectively, related
to the compositions wSn, wPb, and wBi of the galvanizing
bath in the elements Sn, Pb, and Bi. For each element, a
low and a high composition level (n and n ww

) are de-
fined. They correspond to the maximum and the mini-
mum values of the composition of the elements tested
(Table 2). For all the compositions, the low level n w

is
equal to 0 wt%. The high level n equals 1 wt% for w
Sn
w

and
P
b
w

, and 0.1 wt% for
B
i
Using the values of the factors, the low and high
composition levels and the maximum and minimum val-
ues of the factors, the tested compositions can be calcu-
lated for the 11 tests (Equation (2)) and the experimental
design matrix can be written (Table 3).
w.
0
nn
wwsx
i

 (2)
with
0
2
nn
n
ww
w


 (3)
and
max min
nn
ii
ww
s
x
x




 (4)
Table 2. Low and high levels of element composition Wn
(wt%).
WSn W
Pb W Bi
Low level 0 0 0
High level 1 1 0.1
Table 3. Experimental design matrix with Sn, Pb, and Bi
composition (wt%).
Test number WSn W
Pb W Bi
1 0.500 0.500 0.100
2 0.500 0.500 0.000
3 0.321 0.000 0.039
4 0.678 0.000 0.070
5 0.321 1.000 0.070
6 0.678 1.000 0.039
7 0.000 0.321 0.070
8 1.000 0.321 0.039
9 0.000 0.678 0.039
10 1.000 0.678 0.070
11 0.500 0.500 0.050

Cracking of S235JR Cold-Deformed Steel during Galvanizing—Developing a Test to Evaluate and Predict the
Effect of the Zinc Alloy Composition
77
The mean value and the sampling interval of the ele-
ment composition.
2.2. Three-Point Bending Cold Deformation
The steel is a commercial hot rolled steel (EN 10025 -2
S235JR/AISI A36-04b/Y.S. = 235 MPa; A% = 21) of
which the composition is given in Table 4. In agreement
with the low carbon content, this steel is essentially con-
stituted by ferrite grains with an average size of ap-
proximately 30 µm (Figure 1). The specimens with a
100 × 20 × 10 mm3 shape were extracted transversally in
relation to the rolling direction from the 100 × 10 × 6000
mm3 plate. The surface of the sample was left unchanged.
Recent works [19,20] show that the cracking of steel
depends on the rate of strain and there exists a critical
stress leading to failure depending on the temperature of
the liquid zinc.
In this study, the tests were performed according to the
industrial treatment of pieces i.e. deformed at room tem-
perature before galvanizing in liquid alloy at 450˚C. The
cold deformation (at room temperature) was performed
on steel samples using three-point bending on a 100-kN
MTS electromechanical tensile machine equipped with a
three-point bend bench (Figure 2). The bench had the
following configuration: the two 25 mm diameter sup-
ports were 70 mm apart and the punch was 10 mm in
diameter. The displacement of the punch was controlled
at a rate of 50 mm/min.
For each test planned by the experimental design,
various deflections from 12 to 32 mm were performed
with three samples for each deflection.
Table 4. Composition of the steel (wt%).
C Mn P S Si Cu Ni Cr
0.043 0.546 0.007 0.021 0.133 0.315 0.090 0.113
Figure 1. Micrograph of the steel.
(
a
)
(b)
Figure 2. (a) MTS electromechanical tensile machine; (b)
Three-point bend bench.
2.3. Galvanizing Process
After the three-point bending deformation, the samples
were submitted to galvanizing (Figure 3).
The 11 baths planned in the experimental design were
successively tested. The galvanizing baths were prepared
for a total mass of 10 kg with respect to the compositions
defined in Table 3 and with an addition of 0.004 wt% of
Al and 0.05 wt% of Ni and a saturation of Fe. Before
galvanizing, the composition of the bath was checked
using a LECO GDOES 850A spectrometer. Slight dif-
ferences between the planned and performed composi-
tions can appear. These differences were taken into ac-
count to correct the value of the factors that will be used
to develop the mathematical model.
Before the anticorrosion treatment by galvanizing, the
deformed steel samples underwent a preparation process
composed of cleaning, pickling, and fluxing. The sam-
ples were cleaned for 30 min in a 2% Lerabilt®, pro-
vided by Stockmeier, (35% phosphoric acid + 20% sul-
furic acid) in demineralized water and rinsed in water 2
min (30 s of immersion and 30 s of emersion ×2). They
were then pickled 15 min in a bath composed of 150 g/L
HCl + 60 g/L of Fe (427 g/L FeCl2·4H2O) + 0.2% Lera-

Cracking of S235JR Cold-Deformed Steel during Galvanizing—Developing a Test to Evaluate and Predict the
Effect of the Zinc Alloy Composition
78
Figure 3. Galvanizing bath.
pas BP®, provided by Stockmeier, (corrosion inhibitor:
ethynylcarbinol alkoxylate 15% and but-2-yne-1,4-diol
5%) in demineralized water and rinsed 2 min as previ-
ously. Finally, they were prefluxed for 5 min in a bath of
ZnCl2 (220 g/L) - NH4Cl (200 g/L) in demineralized wa-
ter and dried at 110˚C for a minimal duration of 10 min.
The anticorrosion treatment was conducted by immer-
sion of the steel samples in the liquid zinc alloy bath at
450˚C ± 2˚C (temperature controlled using a K-type
thermocouple). The samples were immerged at a rate of
0.3 m/min, kept 3 min in the bath, and emerged at 0.3
m/min.
2.4. Definition of Critical Deflection
After the anticorrosion process, the samples were pre-
pared for observation of the cracks. First, the samples
were cut to extract the central part where the punch was
located during the three-point bending test and then this
central part was cut into two pieces (Figure 4). Each
piece was embedded and then polished to a 6 µm grade.
The presence of cracks was identified using an optical
microscope (Olympus PMG3: Figure 5).
If cracks appeared, their length was measured. For
each deflection of each bath composition tested, the total
length of cracks (TLC) was calculated as the sum of the
crack lengths measured on the two pieces of the three
tested samples divided by 2.
For the 11 bath compositions, the TLC versus the im-
posed deflection could be plotted over time (Figure 6(a)).
The curves were fitted using a third-order polynomial
law and the value of the deflection at TLC = 0, called
critical deflection, was determined (Figure 6(b)). This
critical deflection value was the response that will be
used in the experimental design.
3. Results
3.1. Response Surface
The values of factors xi in the Roquemore 311B experi-
1 2
3
Face observed
observed faces
Figure 4. Preparation of the samples for observation of
cracks.
Figure 5. Optical microscope (Olympus MPG3).
0
2
4
6
8
10
12
10 12 14 16 18 20 22 24 26 28
3 -p oi n t be n d ing d e flection (m m)
Total lenght cracks (mm)
b)
Total len
g
th of cracks
(
mm
)
(a)
0
2
4
6
8
10
12
10 1214 1618 2022 24 2628
3-point bending deflection (mm )
T
o
t
a
l
l
eng
ht
crac
k
s
(
mm
)
Critical deflection
= 15.05 mm
T o tal len
g
th of cracks
(
mm
)
(b)
Figure 6. Total length of cracks at various deflections for
bath no. (a) Raw results; (b) With the fitted 3rd-order poly-
nomial law to determine the critical deflection.

Cracking of S235JR Cold-Deformed Steel during Galvanizing—Developing a Test to Evaluate and Predict the
Effect of the Zinc Alloy Composition
79
mental design must be modified to take into account the
effective compositions of the anticorrosion bath. The
compositions measured before galvanizing are reported
in Table 5 . The modified values of the factors are calcu-
lated using Equation (2) and presented in Table 6.
The results of the tests in terms of TLC (Table 7) were
used to determine the experimental design response y.
Crack lengths range between 0.05 and 1.60 mm, and
their number range from 0 to 8 for each level deflection.
When the chemistry of the bath leads to a low level of
cracking, few cracks with length < 0.8 mm are observed.
Conversely, when the level of cracking is high the aver-
age length of cracks is 1.2 mm and their number rises up
to 8.
Table 5. Composition of the baths (wt%).
Test
number Sn Pb Bi Al Ni Fe Zn
1 0.458 0.423 0.089 0.0035 0.0401 0.022998.964
2 0.430 0.420 <0.001 0.0044 0.0410 0.0460 99.058
3 0.307 0.005 0.038 0.0043 0.0501 0.011299.584
4 0.691 0.005 0.077 0.0039 0.0458 0.019699.158
5 0.340 0.926 0.056 0.0028 0.0437 0.026898.605
6 0.768 1.000 0.045 0.0031 0.0574 0.019598.107
7 0.014 0.342 0.090 0.0049 0.0586 0.048799.442
8 1.020 0.362 0.036 0.0043 0.0567 0.024698.496
9 0.014 0.667 0.045 0.0045 0.0575 0.024499.188
10 0.957 0.594 0.069 0.0032 0.0493 0.019698.308
11 0.500 0.433 0.045 0.0045 0.0474 0.061498.909
Table 6. Modified values of factors xi.
Test number X1 X
2 X3
1 −0.177 −0.324 1.912
2 −0.295 −0.337 −2.451
3 −0.813 −2.086 −0.588
4 0.805 −2.086 1.324
5 −0.674 1.795 0.294
6 1.129 2.107 −0.245
7 −2.048 −0.666 1.961
8 2.191 −0.582 −0.686
9 −2.048 0.707 −0.245
10 1.926 0.396 0.931
11 0.000 −0.282 −0.245
Table 7. Total length of crack in mm.
Test
number 12 14 16 18 20 22
1 0 1.5254.882 6.779 8.7127.387
2 0 0 2.765 6.775 7.29710.150
3 0 0 0.925 3.8005.125
4 0 0 5.875 6.6756.850
5 0 0 2.087 5.012 5.7877.200
6 0 0.7124.885 7.260 9.0377.687
7 0 0 0 0.175 0 1.627
8 0 0.5507.000 7.540 9.7759.850
9 0 0 0 0
10 0 0 2.700 7.120 9.79510.107
11 0 0 4.212 5.875 8.2128.487
Test
number 22 24 26 28 30 32
1 7.387
2 10.150
3 5.125 6.6007.025
4 6.850
5 7.200 7.65510.405
6 7.687
7 1.627 0.2752.785 2.060
8 9.850
9 0 1.235 0 2.820 1 3.785
10 10.107
11 8.487
For each bath, the TLC values versus the three-point
bending imposed deflection were plotted. Figure 3(a)
shows an example of the results obtained for bath no. 5.
No crack is observed for 12 and 14 mm deflections. The
cracking phenomenon appears at a 16 mm deflection
with a 2.1 mm TLC. The TLC reached 10.4 mm for the
last deflection of 26 mm. To determine response y, some
points were deleted from the curve: the points for TLC
equals 0 and the points obtained for the last deflection if
they presented stabilization behavior. For bath No. 5,
points at 12 and 14 mm deflection were deleted. The last
point obtained for a 26 mm deflection was retained since
it did not show stabilization. The as-obtained curves were
fitted using a third or second-order polynomial law ac-
cording to the best convergence of points for y = 0. The
response was determined as the value of the three-point

Cracking of S235JR Cold-Deformed Steel during Galvanizing—Developing a Test to Evaluate and Predict the
Effect of the Zinc Alloy Composition
80
bending deflection at TLC equals 0 with the fitted curve.
Figure 3(b) presents the fitted curve for bath No. 5. The
response obtained for this bath was 15.05 mm. The ex-
perimental design matrix was completed with the re-
sponse values (Table 8).
Using this matrix, the mathematical model associated
with the experimental design can be developed as written
in Equation (1). In this equation, the model is expressed as
a function of the xi factor values. As the value of the study
is the influence of adding alloying elements, this model
was rewritten to be expressed as a function of the wn
elements composition values (Equation (5)) using the
relation between xi and wn presented in Equation (2).
0
222
SnSn PbPb BiBi
SnPbSn PbSnBi Sn BiPbBi PbBi
SnSn SnPbPb PbBiBiBi
yb bwbwbw
bwwbww bww
bwb wbw
 

 
(5)
with
b0 the mean value of the response y; bn the coefficient of
the simple effect of the element composition wn; bnn the
coefficient of the quadratic effect of the factor wn; bnmthe
coefficient of the interaction effect of the factors wn and
wm.
The mathematical model obtained for the experimental
design is presented in Equation (6).
22 2
25.99 36.111.3810.33
3.16141.88103.25
19.583.62201.80
Sn PbBi
Sn PbSn BiPb Bi
Sn PbBi
ywww
wwww ww
ww w
 
 

(6)
According to the dimensional equation, the parameters
unit is the same as y: mm. We assess the precision of y
value +/− 1 mm.
Using this model, the surface response can be drawn to
Table 8. Complete matrix of the experimental design.
Test number x1 x2 x3 y
1 −0.177 −0.324 1.912 13.37
2 −0.295 −0.337 −2.451 14.75
3 −0.813 −2.086 −0.588 17.65
4 0.805 −2.086 1.324 15.95
5 −0.674 1.795 0.294 15.05
6 1.129 2.107 −0.245 13.75
7 −2.048 −0.666 1.961 20
8 2.191 −0.582 −0.686 13.8
9 −2.048 0.707 −0.245 22.2
10 1.926 0.396 0.931 15.2
11 0.000 −0.282 −0.245 14
study the simple interaction and quadratic effects of the
alloying elements.
3.2. Analysis of the Results of the Mathematical
Model
The ai coefficient of the mathematical model should rep-
resent the simple and combined effects of the alloying
elements. However, this model allows the prediction of
the critical deflection (CD) as a function of the chemical
composition of the bath alloy, but the parameters ai result
only from a mathematical treatment of the results and are
not representative of a physical phenomenon. Moreover,
from the ai coefficients it is not possible to conclude on
the behavior of the CD with the contents of the alloying
elements. However, it is possible to present the results in
terms of CD vs. the chemical composition.
3.2.1. Effect of Pb and Bi with Constant Sn wt%
Figure 7 presents a two-dimensional representation of
the CD for the iso Sn contents (0, 0.5 and 1 wt%). When
the zinc alloy wt% Sn equals 0, the CD varied from 30
mm (less sensitive to cracking) to 14.9 mm (more sensi-
tive to cracking). In the corner near (0.1 wt% Bi and 1
wt% Pb), the CD is the lowest (14.85 mm). In the corner
near (0 wt% Bi and 1 wt% Pb), the CD is the highest
( 28.23 mm).
Also, when there was no Sn in the galvanizing bath,
addition of lead slightly decreased the sensitivity to
cracking. Without Pb, the addition of Bi slightly in-
creased the sensitivity to cracking. When the two ele-
ments were added simultaneously, there was a more sig-
nificant decrease in CD.
When the Sn content rose to 0.5 wt%, the CD de-
creased. The Bi + Pb-rich corner was still the zone where
the CD was the lowest, with a value calculated for 1 wt%
Pb and 0.1 wt% Bi equal to 10.6 mm. Here, the central
area was trough-shaped, with a CD lower at the center
than in the corners, which were rich only in Bi or in Pb.
For example, for (0.05 wt% Bi, 0.5 wt% Pb) CD = 13.95
mm, for (0.1 wt% Bi , 0 wt% Pb) CD = 17.04 mm, and
for (0 wt% Bi , 1% Pb) CD = 16.79 mm.
When the Sn content rose to 1 wt%, the area with the
lowest CD was displaced to the corner (0 wt%Bi, 0 wt%
Pb). The CD increased with the Bi and the Pb content,
and the CD is maximal in the corner (0.1 wt% Bi , 0 wt%
Pb).
3.2.2. Effect of Sn and Bi with Constant Pb wt%
Figure 8 shows a two-dimensional representation of the
CD for iso Pb contents (0, 0.5 and 1 wt%). Without Pb
and Bi in the galvanizing bath, the CD increased with the
Sn content. This means that cracking will appear for a
less damaged steel when the Sn content increases. Be-

Cracking of S235JR Cold-Deformed Steel during Galvanizing—Developing a Test to Evaluate and Predict the
Effect of the Zinc Alloy Composition
81
(a)
(b)
(c)
Figure 7. Two-dimensional representations of the critical
deflection with constant w t% Sn content: (a) 0%; (b) 0.5; (c)
1%.
tween 0 and 0.06 wt% Bi, the CD demonstrated the same
behavior when the Sn content rose. For %Bi higher than
0.06 wt%, the CD vs % Sn presents a minimal value. The
corners (0.1 wt% Bi, 1 wt% Sn) with CD = 20.66 mm
and (0.1 wt% Bi, 0 wt% Sn) with CD = 22.90 mm were
less sensitive to cracking than the central position (0.06
wt% Bi, 0.6 wt% Sn) CD = 15.31 mm. Adding Bi in-
creased the CD (beneficial effect) when the Sn content
was high, whereas it decreased the CD when Sn content
was low.
When Pb content increased to 0.5 wt%, the positions
of the areas with the highest CD (0 wt% Bi, 0 wt% Sn)
(a)
(b)
(c)
Figure 8. Two-dimensional representations of the critical
deflection with constant wt% Pb content: (a) 0%; (b) 0.5%;
(c) 1%.
and (0.1 wt% Bi, 1 wt% Sn) and those with the lowest
CD (0 wt% Bi, 1 wt% Sn) remained more or less the
same, with a central trough of a lower CD.
With 1 wt% Pb, the more at-risk area shifted upwards
(0.1 wt% Bi, 0.6 wt% Sn), and in these conditions, the
lower the Sn and Bi contents, the higher the CD. Thus,
cracking sensitivity is lower.
3.2.3. Effect of Pb and Sn with Constant Bi wt%
Figure 9 shows a two-dimensional representation of the
CD for iso Bi contents (0, 0.05 and 0.1 wt%). Without Pb
and Bi in the galvanizing bath, the CD decreased

Cracking of S235JR Cold-Deformed Steel during Galvanizing—Developing a Test to Evaluate and Predict the
Effect of the Zinc Alloy Composition
82
(a)
(b)
(c)
Figure 9. Two-dimensional representations of the critical
deflection with constant w t% Bi content: (a) 0%; (b) 0.05%;
(c) 0.1%.
drastically with the increase of Sn from 25.9 mm for 0
wt% Sn to 9.65 mm for 1 wt%. This means that the sen-
sitivity for cracking is higher when the Sn content in-
creases. When the Pb content increased, without Sn, the
CD increased (less cracking). In the presence of Sn, the
CD was higher when Pb was added. This shows the
beneficial effect of the addition of Pb.
For Bi wt% = 0.05, the cracking sensitivity was glob-
ally better. The lowest level was around 15 mm. The
adverse effect on CD of an increase of Sn content re-
mains, but the beneficial effect of Pb disappears.
When 0.1 wt% Bi was added to the bath, the most
critical area is displaced to the center and the top of the
graph. In these conditions, the addition of Pb decreased
CD, which means that cracking sensitivity increases. The
first addition of Sn—between 0 and 0.5 wt% Sn—de-
creased CD, but with a second addition—between 0.5
and 1 wt% Sn—the CD increased.
3.2.4. Discussion o n the Mathematica l Model
The results of this study are in agreement with the study
[21]. The Table 9 presents a comparison between the
results of [21] and the results of the same bath composi-
tions calculated with the mathematical model presented
in this paper.
When the chemical bath composition leads to a low
strain to failure (εf) according to [21], as for the bath
named a2, the CD calculated with the model proposed is
low. For compositions a0 and a1, the evolutions of εf and
CD are correlated.
The model obtained with the experimental design
shows the best precision when the compositions within
the area defined by the experimental compositions tested.
Outside the area defined, results may be less reliable. The
further we depart from this experimental data, less reli-
able the results will be.
4. Conclusions
This paper presents a study on the measurement of the
sensitivity to cracking of steel parts during their galvani-
zation in alloyed liquid zinc, to improve corrosion resis-
tance.
Using a protocol defined in a previous work [16] to
measure the number and length of cracks formed on steel
during the anticorrosion process, an experimental design
was carried out to study the effect of the chemical com-
position of the zinc alloy on steel cracking. The influence
of Sn, Pb, and Bi contents was studied. A model to pre-
dict the critical deflection y, i.e. the minimum deflection
to observe cracks on steel after galvanization, versus the
amounts of Sn (wSn), Pb (wPb), and Bi (wBi) is proposed:
22 2
25.99 36.111.3810.33
3.16141.88103.25
19.583.62201.80
Sn PbBi
Sn PbSn BiPb Bi
Sn PbBi
ywww
wwww ww
ww w


 

The coefficients do not have a physical signification,
but result from a mathematical treatment of numerical
data. As a consequence, it is not possible to draw a con-
Table 9. Comparison between [21] and this study.
Bath [21]wt% Snwt% Pb wt% Bi εf (%) CD (mm)
a0 1.20 0.00 0.10 10 18
a1 0.00 0.70 0.00 31 >22
a2 1.00 1.10 0.05 6 16

Cracking of S235JR Cold-Deformed Steel during Galvanizing—Developing a Test to Evaluate and Predict the
Effect of the Zinc Alloy Composition
83
clusion concerning the effect of only one element re-
garding its coefficients. Indeed, this work highlights the
fact that the interaction of these 3 elements has a strong
impact on the behavior of the room temperature de-
formed steel during anticorrosion treatment. This model
allows the drawing of 2D diagrams showing the variation
of y versus two of the three elements and with the third
fixed. As examples, these tendencies are commented on.
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