Experimental studies regarding wear processes through dry [625439]

Experimental studies regarding wear processes through dry
friction of the superficial layer for an unconventional treated
steel
C P Papadatu
Dunarea de Jos University of Galati, Faculty of Engineering, 47 Domneasca street,
Romania

E-mail: [anonimizat]
Abstract. The aim of the studies on tribomodels regarding the dry friction wear and the
processes of the wear in this case is to determine the wear intensity for a certain type of
tribomodel and for a certain type of material. An Amsler stand wa s used. The experimental
study uses two distinct values of task of loading (Q). The rolls with different diamete rs were
used in order to obtain different sliding degrees (ξ). Studies have been made for the
improvement of the mechanical properties of a Chromium – Molybdenum alloyed steel,
unconventional treated in a magnetic field. The Thermo -magnetic treatment was applied
before a thermo -chemical treatment. The mechanical properties of the material have been
improved, particular ly in the case of a great content o f aluminum and chromium. The hardness
values of the superficial layers which have been obtained after a complex thermo -magnetic
and thermo – chemica l treatments, the superficial layers content and the behavior of the steels
at the wear tests were used as c riterion. Diffractometric analysis and a statistical modeling
completed this study.
1. Introduction
An important quantity of the aluminum in the structure of the steel increases the thermo -magnetic
treatment power and the results are the best. At the same time, the existence of aluminum content in
the structure of the steel causes some hardening problems which are countered by the Chromium
existence.
There were considered different thermo -magnetic treatments as improvement treatments with
cooling i n water in magnetic field applied before ionic nitriding treatment (plasma nitriding) at 530 °
C. This temperature of the thermo -chemical treatment was considered at 530 ̊ C, being specific for
this kind of the improvement steel . The influence of such parameters affecting the nitriding layers‟
thickness, hardness, composition and residual stress was evaluated [1]. In the Literature, taking into
account the nitriding process, at all temperature below 51 0-520 ̊ C substantial quantit y of the “S –
phase” was found to be present, especially in the case of the austenitic stainless steel [2]. In case of
low temperature (100 ̊ C – 510 ̊ C), plasma nitriding produce s the expanded austenite (the S -phase)
with good behavior at friction . Phase γ (Fe 4N) appear at higher temperatures than 500 ̊ C and reduce s
the thickness of the S -phase. In this paper it was consider ed an improvement steel grade alloyed with
Aluminum and Chromium and the treatments temperatures have been chosen for this ca se. The
increasing of the depth of the superficial layers in the case of unconventional treatment applied has
been reported in accordance with the depth of the superficial layer for the same steel which suffered a
classic improvement treatment before a thermo-chemical treatment. The magnetic field modifies the
residual stresses which were obtained by treatment of hardening/tempering. This process depends by
the content of the carbon from the structure of the steel. In all the cases, the cooling in magnetic field

has been made duri ng the improvement treatment of these steels, the residual stresses by hardening
decreases, the residual austenite quantity decreases too and – as a result – the magnetic field has
positive effect on the mechanical properties because the hardness of the st eels and the wear resistance
increase.
If Aluminum and Chromium contents increase in the structure of the steel the residual austenite
quantity decreases more rapidly. The martensitic quantity and the hardness of the steel increases
significantly, mo re than in the case of the steels with approx. the same content of Carbon but with
lower quantity of Aluminum. As a consequence, the magnetic field intensity, the content of the
Carbo n and the content of the Alumin um from the steels have an important infl uence. Because of
these aspects, the tendency of breaking decreases and the probability of the fragile breakage no longer
exists. Magnetostriction determines local oscillations resulting local plastic deformations [3, 5, 8, 14].
Magnetostriction determine s a reduction of the quantity of the residual austenite. Furthermore, this
situation implies a higher hardness of the material and for many applications – good endurance
characteristics .
The control of the ion (plasma) nitrided layer using micro -hardness curves involves the determining
of the micro -hardness from the superficial layer on the depth. Following this influence of the
magnetic field can be seen the effects of the aluminum (1.18%) and chromium (1.38%) – as alloying
elements of the steel – and the influence of the thermo -magnetic treatment on the micro -hardness of
the superficial layers obtained through thermo -chemical treatment applied after thermo -magnetic
treatments. This influence is determined by the increasing of the thickness of the superficial layer.
This superficial layer thermo -magnetic and thermo -chemical treated has higher micro -hardness values
than the superficial layer classical treated.
To complete this study, it was considered a statistical model. It is necessary to prove the causation
between a norma l load ( Q) and the worn -out depth of the layer ( Uh). I resort to statistical methods for
checking the next assumption: I considered that there is a causal relationship between the independent
variable Q and dependent variable Uh. Between these variables there is a direct connection.
Application of analysis models of regression and correlation implies some steps [10].

2. Experimental Procedure
For the experimental program, were considered the samples (rollers) from the material which is a
steel grade of improvement for a machine part construction . This material has the following principal
components: 0.38 % C, 1.18 % Al, 1.38 % Cr, 0.17 % Mo, 0. 5 % Mn, 0.058 % Cu, 0.25 % Si, 0.26 %
Ni, 0.026 % P, 0.026 % S. The existence of the Moly bden um content in the composition of the steel
decreases the stiffening phenomenon. The o uter diameter of the rollers has 40 mm and the inner
diameter of the ro llers has 16 mm . [2, 3, 4, 6].
The first stage from the complex program of treatments consists in thermo -magnetic treatments.
The treatment t1 represents a Martensitic hardening process (at 920 °C) and high tempering (at
620°C), a classic treatment of improvement (Magnetic field intensity is H =0). The other treatment, t3,
represents a hardening process (just cooling in water in strong alternative current (A .C.) of magnetic
field) and high tempering process (just the cooling in water in strong A.C. magnetic field). The
treatment t4 represents a hardening process (just cooling in water, in direct current of magnetic field)
and high tempering process (just cooling in water, in D.C. magnetic field).
The second stage from the complex program of the t reatments consists in applying the thermo –
chemical treatment: a plasma (ion) nitriding at 530 °C , after thermo -magnetic treatment , applied at the
different samples from the same steel grade considered . The treatments were considered such as : Tca
= T3‟= t3 + plasma nitriding; Tcc = T4‟= t4 + plasma nitriding, T 1‟= Tclassic .
Micro -hardness (Vickers) was measured on the treated surface layer obtained by thermo -chemical
treatment regimes shown above. Were performed a minimum eight determinations for each case.
The wear tests have been made using an Amsler machine, roller on roller, taking two sliding
degrees (ξ = 10% or, 20% ), testing in time (3 hours) . After each hour of wear tests the external
diameter was measured. It were determined the wear resistance of the rollers through dry friction and
the surface structure evolution for different parameters of testing regimes. Some factors which
influence this kind of wear process are: the contact geometry of the friction couple (roller on roller ),
the technological parameters (surface quality, thermo -chemical treatment ) and the exploitation
conditions ( for example: the thermal solicitation). Wear tests were carried out on an Amsler machine,

using several couples of rollers, each couple correspondi ng to different sliding degrees ξ, defined as
[3, 4, 7, 14]:

ξ = (1 – ν2/ν1) . 100, [%] (1)

where ν1 and ν2 are the peripheral velocities of the rollers in contact, each one having their specific
peripheral velocity . The rollers are in a direct contact (a linear contact) and the friction process
created through a particular combination of angular speeds ( n1, n2) and diameter sizes ( d1, d2) exists .
Index 1 or 2 are added for the roller 1 or 2, respectively, both of the same tested friction couple.
For instance, ξ= 10 % is obtained for a pair of tested rollers having d1= 40 mm, n1=180 rpm and
d2= 40 mm, n2=162 rpm; ξ= 20 % is obtained for a pair of tested rollers having d1= 44 mm, n2=180
rpm and d2=40 mm, n2=62 rpm; the level of the stress is corresponding to a normal load (Q) of 150
daN and the linear contact between roller s is b=10 mm ( represents the width of the rolls) [5,8].

3. Results and discussion
After plasma (ion) nitriding, the white superficial layers had a higher depth in the case of applying
the magnetic field. In figure 1 was presented the evolution of the micro -hardness values (Vickers ,
HV 0.1) in the plasma nitrided layer , depending on the treatments , measure d in depth of the samples (of
the leading rolls of wear) . It has been noted that: HVa – microhardness of the samples treated in
magnetic field (alternative current); HVc – microhardness of the samples treated in magnetic field
(direct current); DGR – The thikness of the white layer ( the superficial layer).

Figure 1.The evolution of the microhardness (HV0.1) depending by the treatment and the
thickness of the layer .

Figure 2. A comparison between the microhardness of the layer (HV1) obtained by classic
treatment and the microhardness of the layer (HV4) obtained through the unconventional
treatment T4
0.05 0.1 0.15 0.2 0.254006008001000120014001600
DGRH V a, H V cEvolution of the microhardness,depending by treatment and by the thickniss of the layer

HVa
HVc
00.050.10.150.2
910920930940950960820840860880900920940960
GT1[mm]Microhardness values(HV0.1),depending by the thicknes of the nitrided layer(G),T1,T4
HV1[daN/mm2]HV4[daN/mm2]

In the figures 2 and 3 were presented a comparison between the microhardness of the layer
obtained through the classic treatment and the microhardness of the layer obtained by
unconventional treatments (T3 and T4). The study was continued with diffractometric analysis.
In the figures: 4, 5,…,until 11 , were presented the variation of the diffractometric ch aracteristics,
the distribution of the phases from the superficial layers and the internal tensions evolution depending
by duration of the wear process through the dry friction .

Figure 3. A comparison between the microhardness of the layer obtained by classic
Treatment (HV1) and the microhardness of the layer obtained by unconventional treatment
T3 (HV3) , taking into account the thikness of the superficial layer (GT1).

It was observed an improvement of the mechanical properties (hardness) in the superficial layer
because of the distribution of the γ‟-Fe4N phase, especially in the case of the i ncresing of the normal
load (Q ) and for the increasing of the sliding degrees ( ξ). The structural and magnetic properties of
epitaxial γ‟-Fe4N iron nitrides films have been investigated by Costa – Krämer J L, Borsa D M, and
others , in [8], and it was explain ed why this phase is so important . According with [7], the
magnetization properties described are so far are consistent with a single phase of epitaxial film,
having a cubic structure and a positive anisotropy constant, i.e., the [100] directions are easy
magnetization axes. All the magnetic characteristics presented so far are then dict ated by the value of
the anisotropy constant. This value can be estimated from the hysteresis loops obtained applying the
field along a hard magnetization axis, if the value of the saturation magnetization is known [8].

Figure4. Distribution of I Fe4N and I Fe3N in the
superficial nitride d layer depending by the
duration of the wear process , for Q = 75 daN
and ξ =10 % (T1).
Figure 5. Distribution of I Fe4N and I Fe3N in the
superficial nitrided layer depending by the duration
of the wear process, for Q = 150 daN, ξ = 20 %
(T1).
00.050.10.150.2
9109209309409509606008001000120014001600
GT1[mm]Microhardness values(HV0.1),depending by the thicknes of the nitrided layer(G),T1,T3
HV1[daN/mm2]HV3[daN/mm2]
0 0.5 1 1.5 2 2.5 3810121416182022
t[h]IFe3N1[%] IFe4N1[%]The distribution of the phases,depending by duration t[h], after T1

IFe4N1
IFe3N1
0 0.5 1 1.5 2 2.5 3051015202530
t[h]IFe3N1[%] IFe4N1[%]The distribution of the phases,depending by duration t[h], after T1

IFe4N1
IFe3N1

Figure 6. Distribution of I Fe4N and I Fe3N in the
superficial nitrided layer depending by the
duration of the wear process , for Q =150 daN, ξ
= 20 % (T3).
Figure 7. Distribution of I Fe4N and I Fe3N in the
superficial nitrided layer depending by the duration
of the wear process , for Q =150 daN, ξ = 20 %
(T4).

Figure 8. Distribution of BFe4N and B Fe3N in the
superficial nitrided layer depending by the
duration of the wear process, for Q =75 daN ,
ξ =10 % (T1).
Figure 9. Distribution of B Fe4N and B Fe3N in the
superficial nitrided layer depending by the duration
of the wear process , for Q =150 daN, ξ = 20 %
(T1).

Figure 10. Distribution of B Fe4N and B Fe3N in
the superficial nitrided layer depending by the
duration of the wear process , for Q =150 daN,
ξ = 20 % (T3).
Figure 11. Distribution of B Fe4N and B Fe3N in the
superficial nitrided layer depending by the duration
of the wear process, for Q =150 daN, ξ = 20 %
(T4).
0 0.5 1 1.5 2 2.5 31515.51616.51717.518
t[h]IFe3N1[%] IFe4N1[%]The distribution of the phases,depending by duration t[h], after T3

IFe4N1
IFe3N1
0 0.5 1 1.5 2 2.5 356789101112
t[h]IFe3N1[%] IFe4N1[%]The distribution of the phases,depending by duration t[h], after T4

IFe4N1
IFe3N1
0 0.5 1 1.5 2 2.5 32.533.544.55
t[h]BFe3N1[%] BFe4N1[%]The evolution of the internal tensions (II),depending by wear duration t[h], for T1

BFe4N1
BFe3N1
0 0.5 1 1.5 2 2.5 31.522.533.544.55
t[h]BFe3N1[%] BFe4N1[%]The evolution of the internal tensions (II),depending by wear duration t[h],Q=150daN, =20%,T1

BFe4N1
BFe3N1
0 0.5 1 1.5 2 2.5 31.522.533.54
t[h]BFe3N1[%] BFe4N1[%]The evolution of the internal tensions (II),depending by wear duration t[h],Q=150daN, =20%,T3

BFe4N1
BFe3N1
0 0.5 1 1.5 2 2.5 32.72.752.82.852.92.9533.053.13.153.2
t[h]BFe3N1[%] BFe4N1[%]The evolution of the internal tensions (II),depending by wear duration t[h],Q=150daN, =20%,T4

BFe4N1
BFe3N1

In figures:8,…,11, the internal tensions of the phases determine a lower resistance of the Fe 3N
phase during the cyclical fatigue.This fact was determined by machanical oscilations created by the
magnetic field (A.C. current) through the permanently changes of the field lines directions, because of
the magnetostriction existence . This magnetostriction from thermo -magnetic treatment changes the re –
crystallization conditions, the speed of germination. That‟s why the hardness of the superficial
nitrided layers i ncreases. The degree of the Martensitic Tetragonalitate (c/a) is higher in the case of γ‟ –
Fe4N (see figure 12).

Figure12. The evolution of the c/a characteristic, depending by duration, in case
of the treatments: T1 (classic) and T3 (unconventional treatment)

In figures: 13,… ,15, were presented some micro -structural aspects of the superficial nitrided layer,
in case of T1 (classic treatment) and in case s of T3 and T4 (unconventional treatment regimes) ,
considering a Nital attack 2%. From the structural point of view, applying a magnetic field (A.C. or,
D.C.), there is a noticeable finishing grain size, from 9 value until 7 -8 value, This situation will enable
a better diffusion all along the grain boundary, when applying a thermo -chemical diffusion treatment
such as ion nitriding.

Figure 13 . Superficial
layer thickness, in the
case of T1 treatment
(x100).
Figure 1 4. Superficial layer
thickness, in the case of T3
treatment (cooling in A.C. Current
–magnetic field), (x100).
Figure 15 . Superficial layer
thickness, in the case of T4
treatment (cooling in D.C.
Current –magnetic field), (x 200).

It was considered the
evolution of the worn -out layer
depth (Uh) during three hours of
the wear process through dry
friction process and the values
are presented in Table 1 .

Table 1. The worn -out layer
depth evolution
Q
[daN] 75 150 190
Uh
[mm] 0.09 0.14 0.18

Figure16 . Worn-out depth of the superficial layer (Uh) evolution ,
depending by sliding degrees ( ξ =10% or 20%) and normal force
(Q), for the treatment T1 case.
0 0.5 1 1.5 2 2.5 31.61.822.22.42.6
t[h]B211T1[%],B211T3[%]Degree of Martensitic tetragonalitate(B211=c/a),depending by duration t,Q=150daN, =20%T1,3

B211T1
B211T3
60 80100 120140 160180 200
1015200.090.10.110.120.130.140.150.160.170.18
Q[daN] [%]Uh[mm]

In figure16, the worn -out depth (Uh) of the superficial layer increases simultaneously with the
increases of the normal load (the down force , Q).

4. Statistical model .
It can be said that the linear model of uni -factorial regression can describe with success the
relationship between the two indicators analyzed.
The main problem of any regression model is the determination of the model parameters, operation
which can be performed using the method of least squares. It starts from the regression equation of a
simple linear model:
y = a + bx + u t = 1, (3)

Where: t, u are theoretical values of variable y obtained only function by the values essential factor x
and by the estimators values of the parameters “a” and “b”, respectively, “â” and ” ”.
To prove the causation between a normal load (Q) and the worn -out depth of the superficial layer
(Uh), resort to statistical methods for checking the next assumption: I assume that there is a causal
relationship between the independent variable (Q) and a dependent variable (Uh). Between these
variables there is a direct connection. Application of analysis models of regression and correlation
implies the following steps :
First Step is represented by a correct identification of the variables X and Y. In this case, Q will be
considered the factorial variable X (the cause) and Uh will be the dependent variable y (the efficient
variable). The second Step is represented by a verification of the existence of the connection between
X and Y.
For this method, the graph of the correlation called the correlogram will be used . Based on the
graph of correlation we can say that between the two variables, there is a direct connection. Because
of the tendency towards the concentration is around a straight line, the graph suggests a linear
connection.
The third step is the e stablishment of the mathematical form of the connection: the development of
the regression equation corresponding to this regression model. In the case of regression unifactorial ,
it is considered th at on a resulting characteristic “y” acts the only variable factor “x” and the others
can have a constant and negligible action: y = f(x). Considering that the graphic of the function f (x) is
a straight line, results a linear model of the simple regression [10]. The function of estimation is given
by the expression:
ŷ = a + bx. (4)
Modeling function is given by the following expression:
yxi = a + bx i, (5)
for the linearity of connection and it means an additive interaction scheme of variables, in conditions
by uniform changing with const ant amounts of characteristic “x” [11].
The parameter “a” is the value of the regression function at the point x = 0. This parameter “a” is
the ordinate by origin, meaning the point where the regression right intersects the 0y axis.
The parameter “b” called the regression coefficient, shows the amount with which you can modify
the variable “y”, to change the variable with one unit .
The Method of least squares assumes the minimization of the following function:

The minimum conditi on of this function implies the formation of the system of two equations with
two unknowns:

𝑛𝑎 +𝑏 𝑥𝑖𝑛
𝑖=1= 𝑦𝑖 𝑛
𝑖=1, (7)
𝑎 𝑥𝑖𝑛
𝑖=1+ 𝑏 𝑥𝑖2𝑛
𝑖=1= 𝑥𝑖𝑛
𝑖=1𝑦𝑖, (8)

For this case, n =3.
One can write the equations from the following system of equations :
3a + b (75 + 150 + 190) = 0.09 + 0.14 + 0.18
a (75 + 150 + 190) + b (752 + 1502 + 1902) = 75 . 0.09 + 150 . 0.14 + 190 . 0.18

Finally results are:
b = 0.00076 > 0; a = 0.0315
Because the coefficient “b”, also called regression coefficient, has a positive value, it shows a direct
relation between the two variables. In the graph of correlation the regression coefficient (b) represents
the straight line slope. Replacing the values of “a” and “b” in the regression equation, it was obtained
the new regression equation:
ŷ = 0.00076 x + 0.0315 (9)

or, yxi = 0.00076 x i + 0.0315 (10)

It is estimated that the connection between the two variables (Q and Uh) is the straight line
equation. Using the coefficients “a” and “b” it is calculated the regression equation value of each „x”
characteristic size. These values of the regression equation are also called theoretical values of y
according to x. The operation of replacing of the real terms y with the values of regression equations
(theoretical values) is called adjustment.
To check the accuracy of parameters calculation of a regression function it is used the following
relation:
∑ ŷ = ∑ y (11)

This relation is based on the fact that by calculating the regression equation it is obtained a
redistribution of the degree of factors influence. To emphasize the logical connection between
phenomena is necessary to investigate a large number of individual cases in which deviations (in
either direction) is offset each other [13].
Comparing the real values of y with the adjusted values for resulting feature ŷ, there are small
differences, presented in table 2. It is estimated that the bond between these two variables (Q and Uh)
is represented by the equation of straight line (Figure 17). Using Matlab Program, it was obtained the
correlation graphic corresponding to the equation ( 9),for the values of correlation from table 2 (figure
17).

Table 2. Adjusted values
x ŷ
75 0.0885
150 0.1455
190 0.1759

Table 3. Values compared
ŷ y- ŷ
0.0824 0.09-0.0885=0.0015
0.170 -0.0055
0.216 0.0041

Figure 17. Representation of the equation: ŷ = 0.00076 x + 0.0315

The fourth Step represents the characterization of the connection intensity between the se two
variables using the correlation coefficient "r x, y" and the correlation report [10, 11, 13].
ӯ=1
𝑛∗ 𝑥𝑖 𝑦𝑖 𝑛
𝑖=1 (12)
60 80 100 120 140 160 180 2000.080.090.10.110.120.130.140.150.160.170.18
X

The above relation, for covariance coefficient , can be written [10, 11, 13]:

M x ∙ y = n−1 xin
i=1yi, (13)
For n =3, ӯ = M(x y) = 61.95/3 = 20.65
The simple correlation coefficient “r” can be written [13] :

2
22
2

 







 
nt
nt
nt
ntn nt
nt tt
y yn x xny x yxn
r
(14)

r = (3 . 61.95 – 415 . 0.41) / 204501/2 . 0.01231/2 =15.70/15.85 = 0.99 > 0

In this case, r x,y = 0.99 > 0
This result indicates the correlation, a direct connection between these two variables (Q and
Uh).Theoretically, if the value is closed by 1, we have a very strong connection between the variables.
In this case, it can be talk about a relative deterministi c connection because r x,y = 0.99 and the
following relation: 0.95 ≤ r ≤ 1 was demonstrated . For the interpretation of nonzero values for
coefficients of correlation, an explanation graphics is much more suggestive in mathematical
statistics. The value of the correlation coefficient is in the dependency pairs (x i, y i) with the
distribution of values in a rectangular XOY references.
Regarding t he geometric configuration of the corresponding distribution points, the distinction is
made between the followi ng cases:
a). The points are alignment along a line: it can be a right ascending line (r xy=1), or it can be a right
line downward (r xy = -1). These situations indicate a dependence relation between the two variables.
b) The points are dispersed random, the cloud of the points hasn‟t orientation. The two variables are
independent or uncorrelated (r xy = 0).
It is calculated the simple ratio of correlation (Rx,y) taking into account the multiple ratio of
correlation according to [10,11,12,13].
It is find that Rx,y is approximately equal with the simple coefficient of the correlation “r”. To
confirm the linearity of the connection, the following relation must be met:

｜rx,y ｜= R x,y (15)
In this case,
｜rx,y ｜= R x,y = 0.99

It was confirmed statistically the direct linear connection between these two variables : Q and Uh .
The correlation is positive because the graph of the correlation is linear ascending and is strong
enough because the points are close. It is a linear correlation. Testing suitability of the model is the
formula for the correl ation coefficient obtained (0.95 ≤ r ≤ 1).

5. Conclusion s
The first research direction was to increase the mechanical characteristics (hardness) of the steel
through thermo -magnetic treatment in order to applying the thermo -chemical diffusion treatment
under thermo -magnetic treatment temperature. Another line of the research was to study the influence
of the thermo -magnetic treatment on the superficial layer thermo -chemically treated.
The originality consists of applying the thermochemical diffusion treatment after thermo -magnetic
basic treatment, with the mention that the thermo -chemical treatment temperature is lower than the
temperature of thermo -magnetic treatment. This condition has been mentioned in orde r to not modify
the properties of the material after the thermo -magnetic treatment during the thermo -chemical one.

A mathematical model has been made to confirm the connection between some characteristics of
the material according with the parameters of treatments.
A statistical model from Economics which demonstrated the causal relation between the normal
loading (Q) and the depth of the worn -out nitrided layer (Uh) after three hours of wear process, has
been proposed in this study.
During this work , a correlat ion, a regression line through the linear model of uni -factorial
regression using the least squares approx. method has been prop osed. It was demonstrated that a direct
connection between these two variable exists .
In the cases presented up, it can be talk about a relative deterministic connection because r x,y =
0.99 and the following relation: 0.95 ≤ r ≤ 1 was demonstrated.

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