Pack boriding of aisi p20 steel. estimation of boron diffusion coefficients in the fe2 b layers and tribological behaviour

Int. J. Surface Science and Engineering, Vol. 11, No. 6, 2017 563
Copyright © 2017 Inderscience Enterprises Ltd.
Pack-boriding of AISI P20 steel: estimation of boron
diffusion coefficients in the Fe2B layers and
tribological behaviour
M. Keddam*
Laboratoire de Technologie des Matériaux,
Faculté de Génie Mécanique et Génie des Procédés,
USTHB, B.P. No. 32, 16111 El-Alia,
Bab-Ezzouar, Algiers, Algeria
Email: keddam@yahoo.fr
*Corresponding author
M. Elias-Espinosa
Instituto Tecnológico y de Estudios Superiores de Monterrey-ITESM,
Campus Santa Fe, Av. Carlos Lazo No. 100,
Del. Álvaro Obregón, CP. 01389, D. F., México
Email: mielias@itesm.mx
M. Ortiz-Domínguez, I. Simón-Marmolejo and
J. Zuno-Silva
Universidad Autónoma del Estado de Hidalgo,
Escuela Superior de Ciudad Sahagún-Ingeniería Mecánica,
Carretera Cd. Sahagún-O tumba s/n,
Zona Industrial CP. 43990, Hidalgo, México
Email: martin_ortiz@uaeh.edu.mx
Email: isaias.simn@gmail.com
Email: zunojorge@gmail.com
Abstract: In the present study, the AISI P20 steel was pack-borided in the
temperature range of 1,123–1,223 K for treatments times between 2 and 8 h. A
new kinetic model based on the integral method was used to estimate the boron
diffusion coefficients in the Fe2B layers. As a result, the activation energy for
boron diffusion in the AISI P20 steel was estimated as 194.3 kJ mol–1
. This
value of energy was compared with the literature results. Furthermore, to
validate experimentally the present model, two additional boriding conditions
were used. The morphology of cross-sections of borided samples was examined
by scanning electron microscopy. The formation of a single boride layer was
confirmed by x-ray diffraction analysis. The Daimler-Benz Rockwell-C
indentation technique was used to evaluate the cohesion of boride layers on the
surface of AISI P20 steel. Finally, the scratch and pin-on-disc tests for wear
resistance were carried out by means of a LG Motion Ltd and a CSM
tribometer respectively under dry sliding conditions.
Keywords: incubation time; diffusion model; activation energy; growth
kinetics; cohesion, wear.

564 M. Keddam et al.
Reference to this paper should be made as follows: Keddam, M.,
Elias-Espinosa, M., Ortiz-Domínguez, M., Simón-Marmolejo I. and
Zuno-Silva, J. (2017) ‘Pack-boriding of AISI P20 steel: estimation of
boron diffusion coefficients in the Fe2B layers and tribological behaviour’,
Int. J. Surface Science and Engineering, Vol. 11, No. 6, pp.563–585.
Biographical notes: M. Keddam is a Full Professor in the Department of
Materials Science at USTHB, Algiers, Algeria. He received his PhD in
Metallurgy from the Ecole Nationale Polytechnique, Algiers in 2004. He has
published over 70 publications in the field of thermochemical treatments and
modelling of the mass transfer phenomena.
M. Elias Espinosa received his PhD in Mechanical Engineering from the
Escuela Superior de Ingeniería Mecánica y Eléctrica-Zacatenco, Instituto
Politécnico Nacional, México – 2013. He has published over 15 publications in
the field of boriding and nitriding process. His scientific interests include
materials, mechanical design, and wear. Since 2001, he is a Full Professor in
the Instituto Tecnológico y de Estudios Superiores de Monterrey in México.
M. Ortiz Domínguez is a Research Professor at the Escuela Superior de Ciudad
Sahagún-UAEH. He received his PhD in Mechanical Engineering from the
Escuela Superior de Ingeniería Mecánica y Eléctrica-Zacatenco, Instituto
Politécnico Nacional, México – 2013. He has published over 55 publications in
the field of boriding process and classical electrodynamics. He is a member of
the National System of Researchers of the National Council of Science and
Technology at México.
I. Simón-Marmolejo received his MS in Industrial Engineering from the
Institute of Basic Sciences and Engineering of the Universidad Autónoma del
Estado de Hidalgo (UAEH) at Pachuca, Hidalgo, México, in 2009. To date he
is studying a doctorate in advanced manufacturing at the Centro de Tecnología
Avanzada, CIATEQ A.C. Currently, he is a Professor of the Escuela Superior
de Ciudad Sahagún-UAEH. His current research interests are towards the
engineering of productive systems. A publication of interest was his book Un
primer paso a la simulación con FlexSim, published in 2016 by FlexSim
Software Products, Inc.
J. Zuno-Silva studied his PhD on Materials at the University of Sheffield,
UK – 2009. The main research topics are: high strength steels (cast steels, cast
iron, mechanical properties), heat treatment (high hardness coating, forged, hot
deformation), high resolution microscopy and wear analysis of coating and heat
treated steels. Currently, he is in charge as Director and Leader of the Research
Group of the Escuela Superior de Ciudad Sahagún-UAEH, developing projects
research on advanced high strength steels in collaboration with international
automotive industries.
1 Introduction
The boriding process is a surface treatment in which the boron atoms are diffused into the
surface of steel parts to obtain a wear resistant boride layer (Sinha, 1991).
The boride layer may consist of either a single phase layer (FeB) or a double phase
layer (FeB + Fe2B) depending on the boron activity in the boriding agent. The iron
borides are known to be very hard and resistant to corrosion. The boriding treatment

Pack-boriding of AISI P20 steel: estimation of boron diffusion coefficients 565
requires temperatures ranging from 800 to 1050°C with a treatment time varying from
0.5 to 12 h.
Boriding can be performed with boron in different states such as powder, paste,
liquid, gas and plasma (Nait Abdellah, 2012a; Campos et al., 2003; Kaouka et al., 2014;
Kulka et al., 2013; Chegroune et al., 2016; Keddam et al., 2017).
The widespread used method is pack-boriding because of its technical advantages and
cost-effectiveness (Meric et al., 2000; Vipin and Sundararajan, 2002). Generally, the
commercial mixture of powders is composed of B4C as a boron source, KBF4 as an
activator and silicon carbide (SiC) as a diluent for controlling the activity of active boron
in the boriding medium (Keddam et al., 2015).
From a kinetic point of view, some diffusion models regarding the growth kinetics of
Fe2B layers on different substrates (Campos-Silva et al., 2009, 2010, 2011; Campos-Silva
and Ortiz-Dominguez, 2010; Keddam and Chegroune, 2010; Ortiz-Domínguez et al.,
2011, 2014a; 2014b, 2015a, 2017; Nait Abdellah et al., 2013; Kouba et al., 2015;
Flores-Rentería et al., 2015; Zuno-Silva et al., 2015; Gómez-Vargas et al., 2017) were
published in the literature by considering the effect of boride incubation times. For
instance, (Ortiz-Domínguez et al., 2017) have investigated the growth kinetics of Fe2B
layers on AISI 9840 steel in the temperature range of 1,123–1,273 K by means a kinetic
model that assumes a nonlinear boron concentration profile with the presence of a
constant boride incubation time. In their diffusion model, they have introduced a non-
dimensional kinetic parameter to estimate the boron diffusion coefficients in Fe2B. In
addition, (Campos-Silva and Ortiz-Dominguez, 2010) have applied a kinetic model for
estimating the growth of Fe2B layers on AISI 1018 steel. Their model takes into
consideration the difference in specific volume between the substtrate and the Fe2B
phase. Likewise, Kouba et al. (2015) have numerically analysed the growth of Fe2B
layers on Armco iron by using a sharp interface approach. In their model, the boron
diffusion coefficient in the substrate was taken into account. The boron flux imposed at
the material surface was used as a fitting parameter to experimentally reproduce the
boride incubation time required to get a compact Fe2B layer on Armco iron.
In the present study, a new diffusion model based on the integral method was
suggested to estimate the boron diffusion coefficients in the Fe2B layers on the AISI P20
steel’s substrate in the temperature range of 1,123–1,223 K. An analytic solution was
obtained that gives the expression of boron diffusion coefficient as a function of
parabolic growth constant and the upper and lower boron concentrations in Fe2B and
taking into account the presence of boride incubation times.
Basing on our experimental results, the value of activation energy for boron diffusion
was estimated for AISI P20 steel and compared with the literature data.
This kinetic approach was inspired from the work of Leon Cazares et al. (2014) who
has modelled the growth kinetics of plasma nitrided pure iron. Recently, the authors
(Hernández et al., 2017) have also developed a kinetic approach, by using the heat
balance integral method and a front tracking finite difference scheme, to analyse the
growth kinetics of compound layer on nitrided pure iron for a cylindrical geometry.
The objective of the present work was to investigate the boriding kinetics of AISI P20
steel and mechanical behaviour in terms of cohesion test and wear resistance. The formed
boride layers on AISI P20 steel were characterised by SEM and x-ray diffraction (XRD).
The Daimler-Benz Rockwell-C indentation technique was used to assess the cohesion
resistance of boride layers on the AISI P20 steel’s substrate for two boriding conditions.

In addition, the sample borided at 1,148 K for 8 h was subjected to the scratch and pin-
on-disc tests by using a LG Motion Ltd and a CSM tribometer, under dry sliding
conditions (in ambient air at room temperature). Finally, coefficient of friction and wear
behaviour were compared with the unborided AISI P20 steel.
2 The diffusion model
The diffusion model was applied to investigate the growth kinetics of Fe2B layer grown
on the AISIP20 steel’s substrate which is saturated with boron atoms. Schematic boron
concentration – profile through the Fe2B layer is shown in Figure 1.
Figure 1 Schematic boron concentration profile through the Fe2b layer
The f(x, t) function represents the distribution of boron concentration in the substrate
before the nucleation of Fe2B phase. 2
0 ( )Fe B
t T is the incubation time required to form a
continuous and compact layer of Fe2B. 2Fe B
upC denotes the upper limit of boron content in
Fe2B (= 9 wt.%), 2Fe B
lowC is the lower limit of boron content in Fe2B (= 8.83 wt.%) and the
point x(t) = u represents the Fe2B layer thickness. A small homogeneity range of about 1

at % was reported for the Fe2B layer (Brakman et al., 1989). The term B
adsC denotes the
adsorbed boron concentration in the boride layer during the boriding treatment (Yu et al.,
2005). C0 is the boron solubility in the matrix which is very low (≈0 wt. %) (Krukovich
et al., 2016; Okamoto, 2004; Nait Abdellah, 2012b).
The assumptions considered during the formulation of diffusion model can be found
elsewhere (Elias-Espinosa et al., 2015).
The initial and boundary conditions for the diffusion problem are given by:
2 00, 0, with [ ( ), 0] 0Fe Bt x C x t t C= > = = ≈ (1)
Boundary conditions:
( )2 2
2 00 0, for 8.83 wt.%Fe B Fe B B
Fe B up adsC x t t t t C C⎡ ⎤= = = = >⎣ ⎦ (2)
2
2 [ ( ) ( ), ] for 8.83 wt.%Fe B B
Fe B low adsC x t t u t t t C C= = = = < (3)
The boron concentration profile along the Fe2B layer is described by the Second Fick’s
law as follows:
2 2
2
2
2
[ , ] [ , ]Fe B Fe B
Fe B
C x t C x t
D
x t
∂ ∂
=
∂ ∂
(4)
where the boron diffusion coefficient is only dependent on the boriding temperature. It is
possible to obtain the expression of boron-concentration profile through the Fe2B layer
using the Goodman’s method (Goodman, 1964).
2
2
2
[ , ] ( )( ( ) ) ( )( ( ) ) for 0Fe B
Fe B lowC x t C a t u t x b t u t x x u= + − + − ≤ ≤ (5)
The three time-dependent unknowns a(t), b(t) and u(t) must satisfy the boundary
conditions given by equations (2) and (3). It is noticed that the two parameters a(t) and
b(t) must be positive because of a decreasing nature of the boron – concentration profile.
By applying the boundary condition on the surface, equation (6) was obtained:
( )2 22
( ) ( ) ( ) ( ) Fe B Fe B
up lowa t u t b t u t C C+ = − (6)
By integrating equation (4) between 0 and u(t) and applying the Leibniz rule, the ordinary
differential equation (ODE) given by equation (7) was obtained :
2
2 3
2( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) 2 ( ) ( )
2 3
Fe B
u t da t du t u t db t du t
a t u t b t u t D b t u t
dt dt dt dt
+ + + = (7)
The mass balance equation at the (Fe2B/substrate) interface is given by equation (8):
2
2
[ , ]Fe B
Fe B
x u x u
C x tdx
W D
dt x= =
∂
= −
∂
(8)
with
( )
( )
2 2
2
0
2
Fe B Fe B
up low Fe B
low
C C
W C C
⎡ ⎤−
= + −⎢ ⎥
⎣ ⎦
At the (Fe2B/substrate) interface, the boron concentration remains constant and
Equation (8) rewritten in the following manner:

2
2
2
2
[ , ]
[ , ]
[ , ]
Fe B
Fe Bx u
Fe B
Fe B x u
x u
C x t
t C x t
W D
C x t x
x
=
=
=
⎛ ⎞∂
⎜ ⎟
∂ ∂⎜ ⎟− = −
⎜ ⎟∂ ∂
⎜ ⎟
∂⎝ ⎠
(9)
Substituting equation (4) into equation (9) and after derivation with respect to the
diffusion distance x(t), equation (10) was obtained:
( )2 2 2
( ) ( )Fe B Fe B
up lowC C b t a t+ = (10)
Equations (6), (7) and (10) represent a set of differential algebraic equations (DAE) in
a(t), b(t) and u(t) subjected to the initial conditions of this diffusion problem. To
determine the expression of boron diffusion coefficient in the Fe2B layers, an analytic
solution exists for this diffusion problem by setting:
2
1/2
0( ) ( )Fe B
u t k t t T⎡ ⎤= −⎣ ⎦ (11)
( )
( )
a t
u t
=
α
(12)
and
2
( )
( )
b t
u t
=
β
(13)
where u(t) is the Fe2B layer thickness, 2
0 ( )Fe B
t T the associated incubation time and k the
parabolic growth constant at the (Fe2B/substrate) interface. It is noticed that that the use
of equation (11) is acceptable from a practical point of view since it has been observed in
many experiments. The two unknowns α and β have to be identified for solving this
diffusion problem. After substitution of equations (11), (12) and (13) into the DAE
system and derivation, the expression of boron diffusion coefficient was obtained as
follows:
2
2
Fe BD ηk= (14)
with
2 2 2 2
2 2 2 2
1 1
1 1 4
16 12
Fe B Fe B Fe B Fe B
up uplow low
Fe B Fe B Fe B Fe B
up uplow low
C C C C
η
C C C C
⎡ ⎤⎛ ⎞⎛ ⎞ ⎛ ⎞+ −⎛ ⎞ ⎛ ⎞⎢ ⎥⎜ ⎟= + + +⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎢ ⎥− + ⎝ ⎠⎝ ⎠⎝ ⎠ ⎝ ⎠⎝ ⎠⎣ ⎦
along with the expressions of a(t) and b(t) given by equations (15) and (16):
2
1/2
0
( )
( )Fe B
α
a t
k t t T
=
⎡ ⎤−⎣ ⎦
(15)
22
0
( )
( )Fe B
b t
k t t T
=
⎡ ⎤−⎣ ⎦
β
(16)

with
2 2 2 2
2 2
( )
1 1 4
2
Fe B Fe B Fe B Fe B
up uplow low
Fe B Fe B
up low
C C C C
C C
⎡ ⎤⎛ ⎞+ −
⎢ ⎥= − + + ⎜ ⎟⎜ ⎟+⎢ ⎥⎝ ⎠⎣ ⎦
α
and 2 2
2
( )Fe B Fe B
up lowC C
=
+
α
β
3 Experimental details
3.1 The material and the boriding treatment
The material that was borided was AISI P20 steel. It had a nominal chemical composition
of 0.25–0.40% C, 0.20–0.80% Si, 0.60–1.50% Mn, 1.40–2.00% Cr, 0.30–1.20% Mo,
0.030% P and 0.050% S. The samples had a cubic shape with dimensions of 10 mm × 10
mm × 10 mm. Prior to the boriding process, the specimens were polished, ultrasonically
cleaned in an alcohol solution and deionised water for 15 min at room temperature, and
dried and stored under clean-room conditions. The samples were embedded in a closed,
cylindrical case in contact with a mixture of powders consisting of 20% B4C as the donor,
10% KBF4 as an activator, and 70% SiC as the diluent. The powder-pack boriding
process was carried out in a conventional furnace under a pure argon atmosphere in the
temperature range of 1,123–1,223 K. Four treatment times (2, 4, 6 and 8 h) were selected
for each temperature. Once the boriding treatment was finished the container was
removed from the furnace and slowly cooled to room temperature.
3.2 Experimental techniques
The borided and etched samples were cross-sectioned for microstructural investigations
using a LECO VC-50 cutting precision machine and the cross-sections of formed boride
layers were observed by SEM (JEOL JSM 6300 LV). For a kinetic study, the boride layer
thickness was automatically measured with the aid of MSQ PLUS software. To ensure
the reproducibility of the measured layers, 50 measurements were taken from different
sections of the borided samples to estimate the Fe2B layer thickness; defined as an
average value of the long boride teeth (Campos-Silva et al., 2013, 2010). The boride
formed on the surface of borided sample was identified by means of XRD equipment
(Equinox 2000) using CoKα radiation at λ = 0.179 nm. The Daimler-Benz Rockwell-C
technique, using an indenter tester, was performed to get qualitative information on the
cohesive strength of the boride layers to the substrate. The well-known Rockwell-C
indentation test is prescribed by the VDI 3198 norm, as a destructive quality test of
coated compounds (Vidakis et al., 2003; Taktak, 2007).
The principle of this method was reported in the reference work (Taktak, 2007). A
load of 1,471 N was applied to cause coating damage adjacent to the boundary of the
indentation. Three indentations were made for each borided sample to assess the cohesion
test. The indentation craters were examined by SEM.

Figure 2 Principle of the VDI 3198 indentation test
Source: Taktak (2007)
Figure 3 Schematic diagram of typical pin-on-disc test device
Note: 1 – elastic arm; 2 – weight (1 N, 2 N, 5 N and 10 N); 3 – friction force sensor;
4 – pin, ball holders; 5 – wear track; 6 – rotating disc or cap for liquid testing.
During the cohesion test, a conical diamond indenter penetrated into the surface of an
investigated layer, thus inducing massive plastic deformation to the substrate and fracture
of the boride layer. The damage of the boride layer was compared with the cohesion
strength quality maps HF1–HF6 displayed in Figure 2. In general, the cohesion strength
HF1–HF4 are defined as sufficient cohesion, whereas HF5 and HF6 represent insufficient
cohesion (Vidakis et al., 2003; Taktak, 2007). The pin-on-disc tests were carried out in
dry sliding conditions at ambient temperature using a CSM tribometer shown in Figure 3
with a relative humidity of 40%. Before the tests, the samples were cleaned with acetone
in order to remove contaminants from the surface. The tested samples had a disc shape

with a diameter of 25.4 mm and a thickness of 10 mm. All tests were then conducted for
a total sliding distance of 500 m with a sliding speed of 0.08 m/s and the covered radial
distance was of 14 mm under a normal load 5 N. The CSM tribometer was used to
determine the magnitude of friction coefficient and wear as two surfaces rub together. In
one measurement method a pin or a sphere is loaded onto the test sample with a precisely
known force. The pin is mounted on a stiff lever, designed as a frictionless force
transducer. The friction coefficient is determined during the test by measuring the
deflection of the elastic arm. Diamond-made indenter with a 10 mm-diameter
hemispheric, commonly employed, were used to slide against the surface of the pack-
borided AISI P20 steel. Before the scratch wear tests, the samples with a rectangular
shape of dimensions: 12 mm × 7 mm × 7 mm were cleaned with acetone in order to
remove the contaminants from the surface. The scratch wear test consists in scratching
the sample surface by using a LG Motion Ltd (scratch) with a single-pass under
increasing normal load at a rate of 10 N mm–1
of covered distance. Applied loads were
between 0 and 90 N. This permitted determination of the critical load (Lc) corresponding
to the apparition of the layer damage. The scratch wear tests were carried out in dry
sliding conditions (at ambient conditions without lubrication) using a LG Motion Ltd.
(see Figure 4). This technique of characterisation involves generating a controlled scratch
with a sharp tip on a selected area. The tip material [commonly diamond or hard metal
(WC)] is drawn across the borided surface under constant, incremental or progressive
load. At a certain critical load, the boride layer will start to fail. The critical loads are very
precisely detected by means of an acoustic sensor attached to the load arm but can also be
confirmed and collated with observations from a built-in optical microscope. The critical
load data is used to quantify the adhesive properties of different boride layer-substrate
combinations.
Figure 4 Schematic diagram of typical scratch test device
Note: 1 – Rockwell-C indenter; 2 – weight (1 N, 2 N, 5 N, 10 N…, 90 N); 3 – trail
obtained; 4 – tangent force; 5– horizontal displacement of the borided sample
(x(t)); 6 – substrate; 7 – borided surface.

Figure 5 SEM micrographs of the cross-sections of AISI P20 steels borided for 2 h at different
temperatures, (a) 1,123 K, (b) 1,148 K, (c) 1,173 K, (d) 1,198 K and (e) 1,223 K

4 Results and discussions
4.1 Microstructural observations of boride layers
Figure 5 shows the cross-sectional views of boride layers formed on the surfaces of AISI
P20 steel borided during 2 h at increasing temperatures. The saw-tooth morphology of
boride layers is seen in all the SEM images with the formation of a single phase layer.
The boride needles grow in the [001] crystallographic direction that minimises the growth
stress (Ramdan et al., 2010; Brakman et al., 1989) since the atom density of boron is
maximum along this direction (Gómez-Vargas et al., 2017). It is noticed that the
thickness of Fe2B layer increased with the boriding temperature since the diffusion
phenomenon of boron atoms into the substrate is a thermally activated process. The value
of Fe2B layer thickness ranged from 20.3 ± 2.93 µm to 67.07 ± 6.36 µm between 1123
and 1223 K for 2 h.
4.2 XRD analysis
Figure 6 shows the XRD pattern recorded on the surface of borided AISI P20 steel at a
temperature of 1,223 K for 8 h. The crystallographic nature of iron boride formed at the
surface of AISI P20 steel was confirmed by XRD analysis. The diffraction peaks
displayed in Figure 6 indicated the formation of Fe2B layer on the surface of AISI P20
steel. The growth of Fe2B layers is a controlled diffusion process with a highly
anisotropic nature (Ortiz-Domínguez et al., 2014a).
Figure 6 XRD patterns obtained at the surface of the borided AISI P20 steel at 1,223 K for 8 h

In our study, Kayali (2015) identified the metallic borides (MnB) besides the iron borides
(FeB and Fe2B) by XRD analysis when using Ekabor 2 on the pack-borided AISI P20
steel. (Uslu et al., 2007) also showed by XRD studies the existence of metallic borides
(MnB and CrB) inside the double boride layers (FeB and Fe2B) at the surfaces of
pack-borided AISI P20 steel. However, only the iron boride (Fe2B) was detected at the
surface of borided AISI P20 steel when using a mixture of powders consisting of (20%
B4C, 10% KBF4 and 70% SiC). In our case, the metallic borides such as MnB and CrB
were not formed in the Fe2B layers of AISI P20 steel because of the difference in the
boron activity in the used boriding agent.
Figure 7 SEM micrographs showing indentation of VDI cohesion tests at the surfaces of borided
AISI P20 steels, (a) at 1,123 K for 2 h and (b) at 1,223 K for 8 h
4.3 Rockwell-C cohesion test
To evaluate the cohesion of the boride layers to the substrate, the cohesion tests were
applied on the two pack-borided samples (at 1,123 K for 2 h and 1,223 K for 8 h).
Figure 7 shows the SEM images of the indentation craters generated on the two borided
samples. Figure 7(a) revealed an existence of radial cracks at the perimeter of indentation

crater with delamination. The adhesion strength quality of boride layer obtained at 1,123
K for 2 h conforms to H4 category.
Figure 7(b) showed the presence of a small quantity of spots with flaking caused by
delamination. The adhesion strength quality of boride layer, obtained at 1,223 K during 8
h, is representative of HF3 category. It is concluded that the two boride layers formed (at
1,123 K for 2 h and 1,223 K for 8 h) had sufficient cohesion. According to the literature
data, the cohesion of boride layers depends on the boriding parameters and on the
chemical composition of steels. An investigation carried out by the authors (Taktak and
Tasgetiren, 2006) showed that the cohesion of boride layers obtained on the surfaces of
AISI H13 and AISI 304 steels are affected by the change in the boriding temperature.
Thus, the adhesion of boride layers on both steels decreased with a prolonged time and
increased temperature. In addition, the results of cohesion tests are in good concordance
with the results of fracture toughness obtained on both borided steels (AISI H13 and AISI
304).
4.4 Tribological characterisation
4.4.1 Result of the pin-on-disc test
The frictional behaviour was investigated by means of the pin-on-disc test. Figure 8
compares between the frictional behaviour of the borided surface, obtained at 1,148 K
during 8 h, and the untreated surface using a diamond indenter during sliding under dry
conditions.
Figure 8 Evolution of friction coefficient as a function of the sliding distance using a diamond
indenter against the borided surface of AISI P20 steel at 1,148 K for 8 h and the
unborided substrate

It is seen that that the borided sample exhibits a friction coefficient lower than that of the
unborided substrate. The average friction coefficient for the unborided sample was
between 0.6 and 0.7 whereas the borided sample has a value of friction coefficient
ranging from 0.35 to 0.45. These results agree with those reported in other works on
different tested materials (Gómez-Vargas et al., 2017; Ortiz-Domínguez et al., 2015b;
Elias-Espinosa et al., 2015). It is seen that the measured values of friction coefficient
depend strongly on the boriding parameters (time and temperature) and on the chemical
composition of substrates. For example, Ortiz-Domínguez et al. (2015b) have measured
the value of friction coefficient on the borided AISI D2 steel (treated at 1,273 K for 2 h)
and that of the unborided sample. They have found a value of average friction coefficient
ranged from 0.245 to 0.263 for the borided sample, while the corresponding value of
friction coefficient was between 0.292 and 0.363 for the unborided AISI D2 steel. It is
demonstrated that the presence of a hard layer of Fe2B diminished the value of friction
coefficient and thus improved the tribological behaviour.
Figure 9 SEM micrographs of wear scar at the surfaces of AISI P20 steel, (a) unborided surface
and (b) borided surface at 1,148 K for 8 h

4.4.2 Results of wear scratch test
The wear scratch test was carried out to compare the wear behaviour of borided sample
and untreated sample. Figure 9 gives the SEM micrographs of the unborided and borided
surfaces. The borided samples were treated at 1,148 K for 8 h. Figure 9(a) reveals the
presence of scratching lines and some areas undergoing a plastic deformation. Figure 9(b)
shows the existence of cracks, wear debris resulting from an intense plastic deformation
produced during the application of scratch test on the unborided sample. Such behaviour
was also reported in the works by Gómez-Vargas et al. (2017), Ortiz-Domínguez et al.
(2015b) and Elias-Espinosa et al. (2015) on the pack-borided steels. It is concluded that
the presence of a hard single boride layer (Fe2B) was responsible of improving the wear
resistance of borided AISI P20 steel during the scratch test.
Figure 10 SEM micrographs of wear scar on surfaces of AISI P20 steels, (a) borided surface at
1,123 K for 2 h and (b) borided surface at 1,223 K for 8 h
Figure 10 shows the wear scar on the SEM micrographs of the borided surfaces (treated
at 1,123 K for 2 h and 1,223 K for 8 h) after the scratch tests. Cracks that propagate in
depth along the scratch trails can be observed. They have either a curvilinear form [see
Figure 10(a)] or a mosaic [see Figure 10(b)]. The same situation was also observed for

the pack-borided AISI O1 steels for two boriding conditions (1,123 K for 4 h and 1,273 K
for 4 h) (Elias-Espinosa et al., 2015) and for the borided AISI 1025 steels at (1,123 K for
8 h and 1,273 K for 8 h) (Gómez-Vargas et al., 2017).
Accordingly, this type of cracks is characteristic of a Hertzian fracture on brittle
solids when a blunted indenter is used. These cracks propagate in depth in a semi-conical
shape and start at flaws near the contact surface where high-tension stresses develop
(Allaoui et al., 2006; Lawn, 1998).
4.5 Estimation of activation energy for boron diffusion
The kinetic data in terms of the evolution of square of boride layer thickness versus time
was used to estimate the boron diffusion coefficient in the Fe2B layers formed on the
AISI P20 steel by applying equation (14). Figure 11 gives the time dependence of square
of Fe2B layer thickness for increasing temperatures.
Figure 11 Square of boride layer thickness versus the boriding time at different temperatures
Table 1 provides the experimental values of parabolic growth constants at the
(Fe2B/substrate) interface along with the corresponding boride incubation times deduced
from Figure 11. It is noticed that the boride incubation time is nearly constant and do not
vary with the boriding temperature. Figure 12 describes the evolution of the boron

diffusion coefficients through the Fe2B layers as a function of boriding temperature
according to Arrhenius relationship.
The expression of boron diffusion coefficient in the Fe2B layer can be readily
obtained using a linear fitting in the temperature range of 1,123–1,223 K:
2
1
3 194.3
2.1 10 expFe B
kJmol
D
RT
−
− ⎛ ⎞−
= × ⎜ ⎟
⎝ ⎠
(17)
where R = 8.314 J mol–1
K–1
and T the absolute temperature in Kelvin.
Table 1 The experimental values of parabolic growth constants at the (Fe2B/substrate)
interface along with the corresponding boride incubation times
T(K) Experimental parabolic growth constant k(µm·s–0.5
) Incubation boride time 2
0 ( )Fe B
t T (s)
1123 0.3808 1,961.0
1148 0.4638 1,961.0
1173 0.5925 1,961.0
1198 0.7102 1,961.1
1223 0.8917 1,960.9
Figure 12 The temperature dependence of boron diffusion coefficient in the Fe2B layer

Table 2 Comparison of activation energy for boron diffusion of AISI P20 steel with other
borided materials
Material
Boron activation
energy(kJ mol–1
)
Method of
calculation
References
Armco iron 157.5 (Fe2B) Masse balance
equation
Elias-Espinosa et al.
(2014)
AISI 1026 steel 178.4 (Fe2B) Masse balance
equation
Flores-Rentería et al.
(2015)
AISI 1045 steel 180 (Fe2B) Masse balance
equation
Zuno-Silva et al. (2015)
AISI 1018 steel 167 (Fe2B) Masse balance
equation
Campos-Silva and
Ortiz-Dominguez (2010)
equation
Ortiz-Domínguez et al.
(2015a)
equation
(2017)
AISI D2 steel 201.5 (Fe2B) Masse balance
equation
(2014b)
AISI D2 steel 201.5 (Fe2B) Masse balance
equation
(2015b)
Gray cast iron 184.2 (Fe2B) Masse balance
equation
(2014a)
Nodular cast iron 212.28 (FeB + Fe2B) Parabolic growth law Azouani et al. (2017)
AISI P20 steel 200 (FeB + Fe2B) Parabolic growth law Uslu et al. (2007)
AISI P20 steel 256.485 (FeB + Fe2B) Parabolic growth law Kayali (2015)
(conventional heating)
213.9335 (FeB + Fe2B)
(microwave heating)
AISI P20 steel 194.3 (Fe2B) Integral masse
balance equation
This work
Table 2 compares the value of boron activation energy for AISI P20 steel with the values
found in the literature for some borided materials (Armco iron, steels and cast irons)
(Campos-Silva and Ortiz-Dominguez, 2010; Elias-Espinosa et al., 2014;
Ortiz-Domínguez et al., 2014a, 2014, 2015a, 2015b, 2017; Flores-Rentería et al., 2015;
Zuno-Silva et al., 2015; Kayali, 2015; Azouani et al., 2017; Uslu et al., 2007). It is
concluded that the reported values of boron activation energy depended on various
factors such as: (the method of calculation, the nature of boriding agent and the chemical
composition of the substrate (effect of alloying elements). The value of boron activation
energy found in this work, (i.e., 194.3 kJ mol–1
) was interpreted for the borided AISI P20
steel, as the amount of energy for the movement of boron atoms in the easiest path
direction [001] along the boride layer that minimises the growth stresses. This value of
energy is required to overcome the energetic barrier to allow the boron diffusion inside
the metal substrate. Thus, the diffusion phenomenon of boron atoms can occur along the
grains boundaries and also in volume to form the Fe2B layer on the steel’s substrate. The

estimated value of activation energy for boron diffusion for AISI P20 steel was very
comparable to that reported by Uslu et al. (2007). Furthermore, Kayali (2015)
investigated the effect of heating method on the boriding kinetics of AISI P20 steel by
comparing between the heating in the conventional furnace and in the micro-wave
furnace. He showed that the obtained value of activation energy for boron diffusion is
lower in the micro-wave furnace due to the increase in the thermal activation.
4.6 Validation of the diffusion model
The present model was validated experimentally by comparing the experimental values
of Fe2B layers thicknesses with the predicted values. Figure 13 shows the SEM
micrographs of the cross-sections of the samples borided at 1,233 K and 1,243 K for 1.5
h and 2 h, respectively.
Figure 13 SEM micrographs of the boride layers formed at the surface of AISI P20 steel for two
boriding conditions, (a) 1,233 K for 1.5 h, (b) 1,243 K for 2 h
The expression relating the Fe2B layer thickness to the boriding parameters (time and
temperature) is given by equation (18):
2
2 0 ( )
( )
Fe B
Fe BD t t T
u t
η
⎡ ⎤−⎣ ⎦= (18)
with h = 13.3175
The predicted values of boride layers thicknesses [using equation (18)] are in good
agreement with the experimental results as shown in Table 3, for an upper boron content
in the Fe2B phase equal to 9 wt.%. Accordingly, for industrial applications for this kind
of steel, knowledge of the variables that control the boriding treatment is of great
importance for obtaining the optimum value of Fe2B layer thickness. From a practical
viewpoint, thin boride layers are used to make protection against adhesive wear, whereas
thick boride layers are intended to combat abrasive wear.
The optimum value of boride layer thickness ranges from 50 and 250 µm for low
carbon steels and low-alloy steels, whereas the corresponding value of boride layer
thickness are between 25 and 76 µm for high – alloy steels (Flores-Rentería et al., 2015).

Table 3 Comparison between the experimental values of Fe2B layers’ thicknesses (obtained
for two boriding conditions) and the predicted values using the integral method for an
upper boron content in the Fe2B phase equal to 9 wt.%
Boriding
conditions
Experimental Fe2B layer thickness
(µm)
Simulated Fe2B layer thickness(µm)
by the integral method equation (18)
1,233 K for 1.5 h 61.24 ± 8.67 56.38 µm
1,243 K for 3 h 103.67 ±12.24 97.56 µm
5 Conclusions
In the present work, the AISI P20 steel was pack-borided in the mixture of powders
composed of (20% B4C, 10% KBF4 and 70% SiC) for 2–8 h in the temperature range of
1123–1223 K. The following conclusions can be drawn as follows:
1 A single boride layer (Fe2B), identified by XRD analysis, was formed at the surface
of pack-borided AISI P20 steel with a boride incubation time independent on the
boriding temperature.
2 A new diffusion model based on the integral method was suggested to estimate the
boron diffusion coefficients in the Fe2B layers, basing on our experimental data. This
model was validated experimentally for two different boriding conditions (at 1,233 K
and 1,243 K for 1.5 h and 2 h, respectively).
3 As a main result, the value of activation energy for boron diffusion was found to be
equal to 194.3 kJ mol–1
for AISI P20 steel. The obtained value of activation energy
for boron diffusion can be interpreted as an amount of energy required to stimulate
the boron diffusion through the Fe2B layer in the preferred crystallographic direction
[001].
4 The experimental boride layers’ thicknesses are in good agreement with the values
estimated from the diffusion model based on the integral method for an upper boron
content of 9 wt.% in Fe2B.
5 The interfacial cohesion of the formed boride layers on AISI P20 steel (at 11,23 K
for 2 h and 1,223 K for 8 h, respectively), were related to HF4 and HF3 categories
according to the VDI 3198 norm.
6 The average friction coefficient value for the borided surface was reduced compared
with that of unborided surface. It is concluded that the boriding treatment improved
the tribological properties of pack-borided AISI P20 steel.
7 The characteristic wear mechanism for the non-treated surface was plastic
deformation, wear debris and scratching lines, whereas for the borided surface some
scratching lines were visible.

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List of symbols
u(t) Boride layer thickness (µm)
a(t) and b(t) Time-dependent parameters
k Parabolic growth constant of the Fe2B layer (µms–0.5
)
t Treatment time (s)
2
0 ( )Fe B
t T Boride incubation time (s)
2Fe B
upC Upper limit of boron content in Fe2B (= 9 wt.%)
2Fe B
lowC Lower limit of boron content in Fe2B (= 8.83wt. %)
Cads Adsorbed boron concentration in the boride layer (wt. %)
C0 Boron solubility in the matrix (≈ 0 wt. %)
2
[ , ]Fe BC x t Boron concentration profile in the Fe2B layer (wt.%)
2Fe BD Diffusion coefficient of boron in the Fe2B phase (m2
s –1
).

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