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Mathematical and chemical description of friction of diffusive phosphorized iron
Wear,
173
51
(1994) 51-57
Mathematical and chemical description of friction of diffusive phosphorized iron Jerzy Now&i Institute of Materials Engineering, Technical Universityof k&Y, Stqfanowskiego 1 St., 90-924 t&B (Poland)
(Received May 11, 1993; accepted November 18, 1993)
Results of tribological tests on Armco iron after gaseous phosphorizing treatment are presented. As a result of the phosphorizing process, the diffusive layers of the iron phosphides Fe,P and Fe-$, with structure defined by selection of the process parameters, have been formed on the iron surface. It has been proved that the presence of the iron phosphides in the surface layer improves the tribological properties of iron. The optim~tion of the gaseous phosphor~ing parameters has been carried out while assuming minimum wear and dry sliding friction coefficient as optimization criteria. A proposed expianation of the dry friction mechanism occurring between the phosphorized surface and the steel surface is given.
1. Introduction Phosphide compounds, and especially the derivatives of phosphoric and phosphorous acids, are considered as very effective lub~cating additives [l]. Phosphors, as an alloy additive, causes an increase of wear resistance of the iron alloys, e.g. sintered iron-phosphorus alloys [2,3]. Tribological investigations of certain steel types treated by diffusive gaseous phosphorizing indicated their increased resistance to frictional wear [4,53. The tests of diffusive phospho~ation of those steel types were conducted in the processes of bore-, silicon- and nitrophosphorization in solid, fluid and gaseous media [6-%J.As an effect of these operations, multicomponent layers were generated. These borided, silicided or nitrided layers contain on the surface a zone of iron phosphides causing an increase in the chemical, thermal and wear resistance. Tests of diffusive gaseous phosphorizing of Armco iron have been made in a flow reactor by using a mixture of phosphorus and pure argon. The surface layer structure obtained has been investigated in more detail in the author’s earlier work [9,10]. Within the diffusive layer, there is an outer thin zone of iron phosphide, Fe,P, with a hardness of 1100 HV 0.05, and underneath a phosphide zone, Fe3P, with a hardness of about 1000 IIV 0.05 (Figs. 1,2). The ratio of FeP phosphide zone thickness to the thickness of the Fe,P phosphide zone is a fnnction of the gaseous phosphorizing process parameters. An excessive increase in the phosphorus concentration within the surface layer ~3-1~8~4/$07.~ (0 1994 Elsevier Sequoia. All rights reserved SSIX 0043-1648(93)06382-E
Fig. 1. Compact phosphorized layer on iron: upper layer, Fe& underneath, Fe3P and a base.
results in the weakening of the bonding between the compounded zone and the base. As a consequence, a gap arises, and between the base and the layer (Fig. 3) is filled by porous FeP phosphide. The gap starts to form during the advanced stage of the layer growth, as result of an increase in the residual stresses and stiffness of the system. This state is a function of the gaseous process parameters. 2. Method of investiga~n The aim of the investigations was to define the relations among the parameters of the gaseous phos-
J. Nowacki I Descn’ption of fiction
of difisive
phosphorized
iron
p.
a)
0.3
b)
0.3
0.4
0.5
d
Fig. 2. X-ray analysis of diffusive phosphorized
0.6
0,7
04
0 ltadl
Oh 0,7 0.8 B lradl iron: (a) surface; (b) below the first layer (Fe*P); (c) below the second layer (Fe#).
phosphorized layers were made on the tribometer AMSLER A 135. Armco iron was used as a base to eliminate the influence of other alloy components on the diffusive layer properties. Standard specimens [ll] of Armco iron after the gaseous phospho~~ng treatment and counter-specimens of steel 0.4% C, 1% Cr after toughening up to 58 HRC were used. Rotary speed of the counter-specimen of 30 rad s-‘, and normal pressure of 294 N were applied over fixed time intervals of 1800 S.
Fig. 3. Phosphorized layer on iron with a gap: upper layer, Fe,P; second iayer, Fe,P; underneath, gap @led with porous FeSP and the base.
phorizing treatment and tribological properties of the iron after that treatment. The investigations of the wear resistance and measurements of the dry sliding friction coefficient of the
The influence of the gaseous phosphorizing parameters - time (3600 s df d 18 000 s), temperature (800 K
J. Nowacki i Description of friction of diffusive phosphotied
iron
TABLE 1. Weight wear m, (mg) and dry friction coefficient b of phosphorized Armco specimens as function of phosphorizing parameters Modified variables
Phosphor&g parameters P (Pa)
t 6) 3600 10800 18000 3600 10800 18000 3600 10800 18000 3600 10800 18000 3600 10800 ‘18000 3600 10800 18000 x00 10800 18000 3600 10800 18000 3600 18000
(by eg. 1)
800 800 800 950 950 950 1100 1100 1100 800 800 800 950 950 950 1100 1100 1100 800 800 800 950 950 950 1100 1100 1100
By introdu~ng
600 600 600
600 600 600 600 600
1800 1800 1800 1800 1800 1800 1800 1800 1800 3000 3000 3000 3000 3000 3000 3000 3000 3000
Experimental values p
$)
2)
-1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1
-1 -1 -1 0 0 0 1 1 1 -1 -1 -1 0 0 0 1 1 1 -1 -1 -1 0 0 0 1 1 1
:a)
Gg)
-1
31 20 17 23 10 9 23 13 11 29 19 1.5 21 9 10 22 11 13 27 18 14 23 10 12 23 12 15
-1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1
0.29 0.28 0.28
0.27 0.27 0.28 0.28 0.29 0.31 0.28 0.27 0.27 0.25 0.25 0.26 0.26 0.27 0.29 0.28 0.28 0.27 0.25 0.25 0.26 0.26 0.26 0.28
new variables tI, T,, pl, where
t,=7200-*x(t-10800) T,=150_‘X(T-950) p,=1200-lx@-1800)
-l<&
(1)
the coordinate system of variables (r, T, p) has been moved to the center of the experiment, which simplified the calculations. One essential target of the investigations was then to define the phosphorizing process parameters at optimum values of m, and p whereby the minimum wear at a given friction coefficient was taken as a criterion. This problem was solved by means of the Fiacco - McCormick optimization procedure [12] with constraints of inequalities:
where r, is a positive constant. The optimization task consisted of successive sequential modifications for corresponding discrete monotonically decreasing values of r,, which resulted in the extreme for r&+0, i.e.
=w”(fl’, T,‘,~1’)
where tl’, TIo, pIo mean the extreme points, so that the region X0 is restricted: G,=t,+l>O,
(5)
G,=T,+l>O,
(6)
G,=pl+l>,O,
(7)
G,=l-t,&O,
(8)
G,=l-T,>O,
(9)
G6=1-~~30,
(10)
G, = p” - EL@,,TI, PI) 2 0
(11)
where p” means the value of the restricted function ct=&, TI, pl), as above. After the friction tests, the following investigations were made: o metallographic 0 gravimetry analysis l X-ray analysis l Auger electron spec~oscopy
3. Results of investigations Based on the measurements, the dependence of wear m, and the coefficient of friction P on the parameters of the gaseous phosphorizing process is defined by the following equations: m,= 10.15 -5.89t, -2.61T, -0.17~~ +5.22&’
+t, TI -k 0.67trpl + 4.39T12 + T,=p12+ 0.72p12
i= 1, 2, .... M
(2)
The modified objective function comprises primitive and penalty functions:
(12)
/L= 0.252 f O.O05t,-O.OOlT, - O.OlOp,+ 0.005t12 + O.O09t,TI +0.002&p, + 0.018T12 + 0.007p,2
Gi(tl, TI,PI)~O
(4)
(13)
From the flat cross-sections of eqns. (12) and (13) which are represented in Figs. 4-9, it results that the specimen wear m, shows a strong dependence on the
54
J. Nowocki I Description of friction of difisive phosphorized iron
032f
I
I 3,s Fig. 7.
‘22
14
l&d
p=f(t) for: 1, T=800 K, p=6m Pa; 2, Pa; 3, T=950 K.,p=1800 Pa; 4, T=%O & T=llOO K, p=600 Pa; 6, T=llOO K, p-R300
Dependence
T=~IJCI~,p-3000 Fig. 4. Dependence m,=f(t) for: 1, T-800 K, ~~600 Pa; 2, T=8# &p=3OOO Pa; 3, T=950 I&p=1800 Pa; 4, T-950 K, p=3ooO Pa; 5, T=llOO K, p=1800 Pa; 6, T=llOO K,p=3OOO Pa.
IiD t fsl
P=~CJI)O Pa; 5, Pa.
0,30 q 0,28
1
800
900
TM3
1000
w0f.l
Fig. 8. Dependence F=~(T) for: 1, t -3.6 t-18.0x1@ s, p=600 Pa; 3, t=l0.8Xld t-3.6x1@ s, p=3000 Pa; 5, t=lS.Oxld t-18.0~10~ s, p=3000 Pa.
T[Kl Fig. 5. Dependence m,=f(T) for: 1, t=3.6~ t=10,8xld s, p=600 Pa; 3, t=3.6xl@ t=18.0xld s, p=1800 Pa; 5, t=10.8xld t=18.0xld s, p=3000 Pa.
30%
'i
ld s, p=600 Pa; 2, s, p=1800 Pa; 4, s, p=3OOO Pa; 6,
X
lo3 s, p = 600 Pa; 2, s, p=l800 Pa; 4, s, p=3000 Pa; 6,
0321’
I I
600
Ii00
l&o
2400
3000
p Ipa Fig. 9. Dependence p=f(p) for: 1, t=3.6~ ld s, T=800 K, 2, t=3.6x1O%,T=950K,3,f=l0.8xlds,T=8OOK,4,t=10.8xld s, T=llOO Ic; 5, t=18.0 xld s, T=950 K; 6, t=18.0xld s, T=llOO K.
p CRJl Fig. 6. Dependence m, =f(p) for: 1, t = 3.6 x Id s, T= 800 K, 2, t=3.6xld s, T-1100 K, 3, t=10_8xld s, T=SOO K; 4, r=18.0xld s, T==800 K; 5, r=18.0 xld s, T=950 K; 6, t=l8.Oxl@ s, T=llOO K.
parameters of the gaseous phospho~zi~g trea~ent, especially on the process time and temperature. Furthermore, the minimum of wear can be observed in intervals: 11000 s~t~15000 s and 950 K~T~1050 K. From the metallographic investigations f10,13] it results that the wear decreases together with the increase
55
J. Nowacld I Desctiption of friction of dij‘&sive phosphorized iron
extensive spalling after friction tests, which causes the increase of the wear (Figs. 10-12). As the result of qualitative investigations of chemical constitution of the phosphorized layer surface, before and after friction tests, carried out on Auger’s spectrometer, an increase of the oxygen concentration has been shown in the surface layer, which suggests the assumption of oxidizing of the layer during the friction time (Fig. 13). The estimated depth of the raised oxygen concentration in the surface layer valued (7.530) x 10e5 mm; was too small to be investigated by means of Xray tests. The investigations made on the powdered
Fig. 10. Cracked the friction test.
phosphorized
layer on iron with a gap after
Fe
Fig. 11. Surface of the compact phosphorized the friction test.
Fig. 12. Surface of the phosphorized after the friction test.
layer on iron after
layer on iron with a gap
of the layer thickness, up to the state when the process of gap creation between the layer and the base starts. The layers with the gap show a grid of cracking and
’ Ar c
200
O FeFe
400
600
Fe
800
lOO(
E IaVl Fig. 13. Auger electron spectroscopy of the compact phosphorired layer on iron after the friction test. Duration of etching by argonions: 1, non-etched; 2, 3 min; 3, 7 min; 4, 10 min.
56
J. Nowacki I Description of friction of di@sive phosphorized iron
The optimal parameters of the phosphorizing process determined as the result of calculations, and the tribological properties of iron corresponding to them, are compared to the tribological properties of non-phosphorized iron in Table 2.
4. Conclusions The increase of the wear resistance of iron subjected to the diffusion gaseous phosphorizing process is restricted by the hardness and anti-adhesion properties of the phosphides Fe,P and Fe,P as well as the good di~sional connection of the layer to the base. The gap generated between the layer and the base during the advanced stage of phosphorization causes a decrease in wear resistance. Based on the results of investigations, the following mechanism of the sliding dry friction of phosphorized
8(rod)
(b)
Fig. 14. Diffractogram of powdered extracted phosphorized layer (a) before the heat test, (b) after heating at a temperature of 630 K for 1800 s in air. TABLE 2. Optimal parameters of the gaseous phosphorizing process for which the wear and the friction coefficient achieve the minimum in comparison to non phosphorized iron Time t
Temperature
(s)
TK)
Partial pressure of phosphorus P 0%
950 11770 Non phosphorized
2508 Armco iron
Weight of wear m, (WI
Coefficient of friction p
9.51 74
0.25 0.43
extracted phosphor~ed layer confirmed indirectly the possibilities of its oxidation during friction. As the result of the gravimetric analysis of powdered formulations, the possibility of oxidation of the phosphorized layer at a temperature above 550 K was revealed. The speed of this process was increasing with the increase of the temperature. The specimen surface temperature defined on the basis of the martensite hardness changed during the time of the friction process of the counter-specimen, and was estimated to be 580-653 K. This temperature was higher than the temperature of the layer start oxidation process defined by the method of gravimetric analysis. As the result of X-ray examinations, the presence of iron phosphate Fe,PO, in the powdered extracted phosphorized layers held at a temperature of 630 K in an air atmosphere was identified (Fig. 14), which confirmed the friction temperature as the cause of the oxidation process of the phosphorized layer.
Fig. 15. Scheme of the friction process of the phosphorized compact layer: 1, oxidization on product film; 2, zone of phosphide F,P; 3, zone of phosphide Fe& 4, base.
IN
Fig. 16. Scheme of the friction process of phosphorized layer with the gap filled with porous phosphide Fe,P: 1, oxidization product film; 2, zone of phosphide Fe& 3, zone of phosphide Fe& 4, gap filled with porous Fe,P; 5, base. Visible cracks in the layer.
.I. Nowacki 1 Descrtption of friction of di@sive phosphotized
iron
57
the hairline cracking of a layer with a gap is its local deformation during friction. Acknowledgment The author gratefully acknowledges the help of Dr S. Strzelecki, Technical University, in the translation from Polish to English and in tracing graphs. 0
40
t3l2co
400
600
I [ml
References
Fig. 17. Dependence of the friction coefficient /.Lon the friction path I in the rubbing test. Phosphorization parameters: t = 10 800 s, T= 950 K, p = 1800 Pa.
layers (Figs. 15,16) has been proposed. The layer which is generated as the result of the phosphorizing process in an atmosphere of pure argon and gaseous phosphorus is characterized by significant chemical cleanness, and the process of oxidation at ambient temperature and atmosphere does not occur because of the chemical resistance of the layer. Trace quantities of absorbed elements oxygen, sulphur and carbon can be observed on the layer surface only. These elements have some influence on the wear and friction coefficients at the first phase of the friction process. At this stage, seizure of the friction pair does not occur and the value of the friction coefficient is moderate because plastic deformations around the contact region of the layer with high hardness are not large and the adhesive joints are small. The process of oxidation of the friction pair starts with the increase of the layer surface temperature as a result of the friction heat. Iron phosphate Fe,PO,, a product of phosphide oxidation, is forming on the surface of the phosphorized layer. This process causes the decrease of the friction coefficient. The unstable relationship of the friction coefficient to the parameters of the phosphorizing process, its decrease with the increase of the friction path and then its stabilization at a constant level (Fig. 17) is the result of the forming of the iron phosphide, Fe,PO,, film. In the case of a layer with a gap, cracking and crumbling of the phosphide zone occurs during the friction. The reason for
5
6
7
8
9 10 11 12
13
M. Hebda and A. Wachal, Tribology, WNT, Warsaw, 1980 (in Polish). I.W. Manukan, Antifriction properties of sintered materials based on iron, Sintered Metallurgy, 11 (1977) 81. J. Nowacki, Properties of sintered iron-phosphor materials, Iniynieria Materiabwa, 3(32) (1986) 73-77 (in Polish). J. Nowacki and Z. Has, Method of heat-chemical treatment of steel and cast iron machine parts, Pal. Pat. RP 125719, February 21, 1986 (in Polish). J. Nowacki and W. Kamidski, A mathematical description of the chemical reaction in the gas-solid system, Proc. 4th Conf on Applied Chemistty, Unit Operations and Processes, Hungarian Academy of Science Veszprem, Hungary, Vol. 1, Hungarian Chemical Society, Veszprem, 1983, p. 15. A. Wustenfeld, Verfahren zur Eindiffusion der Elemente Bor, Silizium und Phosphor in Metalobertlache, insbesondere in der Obertlichen von Eisen und Stahl (Process for diffusion of the elements boron, slicon and phosphorus into metal surfaces, especially the surfaces of iron and steel), Ger. Pat. 2429948, 1976. J. Nowacki, Schichtwachstum und Eigenschaften von Eisenphosphidschichten (Film growth and properties of iron phosphide films), Harterei-Technische Mitteiiungen, 2(44) (1989) 107-112. J. Nowacki, The structure and properties of phospho-nitrided layers, J. Metal. Club, University of Strathclyde, Glasgow, Vol. 27, 1992, pp. 72-80. J. Nowacki, Gaseous phosphorizing of steel 40H, Sci. .I. Tech. Univ. Ed&, Mechanics, 70 (1986) 111-127 (in Polish). J. Nowacki, A mathematical model of the chemical reaction in the Fe-P system, Muter. Sci., 9(2) (1983) 133-140. Polish Standard PN-67/M-04305: Defining of Wear Resistance on the AMSLER Machine, (in Polish). A.V. Fiacco and G.P. McCormick, Nonlinear Programming- Unconstrained Minimization Techniques, Wiley, New York, 1968. J. Nowacki, Einflul3 von Phosphorbeimengungen zu Nitrieratmospharen auf Aufbau und Eigenschaften von Nitrierschichten (Influence of phosphorus impurities in nitriding atmosphere on the formation and properties of nitride films), Hiirterei-Technische Mitteilungen, 1(46) (1988) 47-51.
173
51
(1994) 51-57
Mathematical and chemical description of friction of diffusive phosphorized iron Jerzy Now&i Institute of Materials Engineering, Technical Universityof k&Y, Stqfanowskiego 1 St., 90-924 t&B (Poland)
(Received May 11, 1993; accepted November 18, 1993)
Results of tribological tests on Armco iron after gaseous phosphorizing treatment are presented. As a result of the phosphorizing process, the diffusive layers of the iron phosphides Fe,P and Fe-$, with structure defined by selection of the process parameters, have been formed on the iron surface. It has been proved that the presence of the iron phosphides in the surface layer improves the tribological properties of iron. The optim~tion of the gaseous phosphor~ing parameters has been carried out while assuming minimum wear and dry sliding friction coefficient as optimization criteria. A proposed expianation of the dry friction mechanism occurring between the phosphorized surface and the steel surface is given.
1. Introduction Phosphide compounds, and especially the derivatives of phosphoric and phosphorous acids, are considered as very effective lub~cating additives [l]. Phosphors, as an alloy additive, causes an increase of wear resistance of the iron alloys, e.g. sintered iron-phosphorus alloys [2,3]. Tribological investigations of certain steel types treated by diffusive gaseous phosphorizing indicated their increased resistance to frictional wear [4,53. The tests of diffusive phospho~ation of those steel types were conducted in the processes of bore-, silicon- and nitrophosphorization in solid, fluid and gaseous media [6-%J.As an effect of these operations, multicomponent layers were generated. These borided, silicided or nitrided layers contain on the surface a zone of iron phosphides causing an increase in the chemical, thermal and wear resistance. Tests of diffusive gaseous phosphorizing of Armco iron have been made in a flow reactor by using a mixture of phosphorus and pure argon. The surface layer structure obtained has been investigated in more detail in the author’s earlier work [9,10]. Within the diffusive layer, there is an outer thin zone of iron phosphide, Fe,P, with a hardness of 1100 HV 0.05, and underneath a phosphide zone, Fe3P, with a hardness of about 1000 IIV 0.05 (Figs. 1,2). The ratio of FeP phosphide zone thickness to the thickness of the Fe,P phosphide zone is a fnnction of the gaseous phosphorizing process parameters. An excessive increase in the phosphorus concentration within the surface layer ~3-1~8~4/$07.~ (0 1994 Elsevier Sequoia. All rights reserved SSIX 0043-1648(93)06382-E
Fig. 1. Compact phosphorized layer on iron: upper layer, Fe& underneath, Fe3P and a base.
results in the weakening of the bonding between the compounded zone and the base. As a consequence, a gap arises, and between the base and the layer (Fig. 3) is filled by porous FeP phosphide. The gap starts to form during the advanced stage of the layer growth, as result of an increase in the residual stresses and stiffness of the system. This state is a function of the gaseous process parameters. 2. Method of investiga~n The aim of the investigations was to define the relations among the parameters of the gaseous phos-
J. Nowacki I Descn’ption of fiction
of difisive
phosphorized
iron
p.
a)
0.3
b)
0.3
0.4
0.5
d
Fig. 2. X-ray analysis of diffusive phosphorized
0.6
0,7
04
0 ltadl
Oh 0,7 0.8 B lradl iron: (a) surface; (b) below the first layer (Fe*P); (c) below the second layer (Fe#).
phosphorized layers were made on the tribometer AMSLER A 135. Armco iron was used as a base to eliminate the influence of other alloy components on the diffusive layer properties. Standard specimens [ll] of Armco iron after the gaseous phospho~~ng treatment and counter-specimens of steel 0.4% C, 1% Cr after toughening up to 58 HRC were used. Rotary speed of the counter-specimen of 30 rad s-‘, and normal pressure of 294 N were applied over fixed time intervals of 1800 S.
Fig. 3. Phosphorized layer on iron with a gap: upper layer, Fe,P; second iayer, Fe,P; underneath, gap @led with porous FeSP and the base.
phorizing treatment and tribological properties of the iron after that treatment. The investigations of the wear resistance and measurements of the dry sliding friction coefficient of the
The influence of the gaseous phosphorizing parameters - time (3600 s df d 18 000 s), temperature (800 K
J. Nowacki i Description of friction of diffusive phosphotied
iron
TABLE 1. Weight wear m, (mg) and dry friction coefficient b of phosphorized Armco specimens as function of phosphorizing parameters Modified variables
Phosphor&g parameters P (Pa)
t 6) 3600 10800 18000 3600 10800 18000 3600 10800 18000 3600 10800 18000 3600 10800 ‘18000 3600 10800 18000 x00 10800 18000 3600 10800 18000 3600 18000
(by eg. 1)
800 800 800 950 950 950 1100 1100 1100 800 800 800 950 950 950 1100 1100 1100 800 800 800 950 950 950 1100 1100 1100
By introdu~ng
600 600 600
600 600 600 600 600
1800 1800 1800 1800 1800 1800 1800 1800 1800 3000 3000 3000 3000 3000 3000 3000 3000 3000
Experimental values p
$)
2)
-1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1
-1 -1 -1 0 0 0 1 1 1 -1 -1 -1 0 0 0 1 1 1 -1 -1 -1 0 0 0 1 1 1
:a)
Gg)
-1
31 20 17 23 10 9 23 13 11 29 19 1.5 21 9 10 22 11 13 27 18 14 23 10 12 23 12 15
-1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1
0.29 0.28 0.28
0.27 0.27 0.28 0.28 0.29 0.31 0.28 0.27 0.27 0.25 0.25 0.26 0.26 0.27 0.29 0.28 0.28 0.27 0.25 0.25 0.26 0.26 0.26 0.28
new variables tI, T,, pl, where
t,=7200-*x(t-10800) T,=150_‘X(T-950) p,=1200-lx@-1800)
-l<&
(1)
the coordinate system of variables (r, T, p) has been moved to the center of the experiment, which simplified the calculations. One essential target of the investigations was then to define the phosphorizing process parameters at optimum values of m, and p whereby the minimum wear at a given friction coefficient was taken as a criterion. This problem was solved by means of the Fiacco - McCormick optimization procedure [12] with constraints of inequalities:
where r, is a positive constant. The optimization task consisted of successive sequential modifications for corresponding discrete monotonically decreasing values of r,, which resulted in the extreme for r&+0, i.e.
=w”(fl’, T,‘,~1’)
where tl’, TIo, pIo mean the extreme points, so that the region X0 is restricted: G,=t,+l>O,
(5)
G,=T,+l>O,
(6)
G,=pl+l>,O,
(7)
G,=l-t,&O,
(8)
G,=l-T,>O,
(9)
G6=1-~~30,
(10)
G, = p” - EL@,,TI, PI) 2 0
(11)
where p” means the value of the restricted function ct=&, TI, pl), as above. After the friction tests, the following investigations were made: o metallographic 0 gravimetry analysis l X-ray analysis l Auger electron spec~oscopy
3. Results of investigations Based on the measurements, the dependence of wear m, and the coefficient of friction P on the parameters of the gaseous phosphorizing process is defined by the following equations: m,= 10.15 -5.89t, -2.61T, -0.17~~ +5.22&’
+t, TI -k 0.67trpl + 4.39T12 + T,=p12+ 0.72p12
i= 1, 2, .... M
(2)
The modified objective function comprises primitive and penalty functions:
(12)
/L= 0.252 f O.O05t,-O.OOlT, - O.OlOp,+ 0.005t12 + O.O09t,TI +0.002&p, + 0.018T12 + 0.007p,2
Gi(tl, TI,PI)~O
(4)
(13)
From the flat cross-sections of eqns. (12) and (13) which are represented in Figs. 4-9, it results that the specimen wear m, shows a strong dependence on the
54
J. Nowocki I Description of friction of difisive phosphorized iron
032f
I
I 3,s Fig. 7.
‘22
14
l&d
p=f(t) for: 1, T=800 K, p=6m Pa; 2, Pa; 3, T=950 K.,p=1800 Pa; 4, T=%O & T=llOO K, p=600 Pa; 6, T=llOO K, p-R300
Dependence
T=~IJCI~,p-3000 Fig. 4. Dependence m,=f(t) for: 1, T-800 K, ~~600 Pa; 2, T=8# &p=3OOO Pa; 3, T=950 I&p=1800 Pa; 4, T-950 K, p=3ooO Pa; 5, T=llOO K, p=1800 Pa; 6, T=llOO K,p=3OOO Pa.
IiD t fsl
P=~CJI)O Pa; 5, Pa.
0,30 q 0,28
1
800
900
TM3
1000
w0f.l
Fig. 8. Dependence F=~(T) for: 1, t -3.6 t-18.0x1@ s, p=600 Pa; 3, t=l0.8Xld t-3.6x1@ s, p=3000 Pa; 5, t=lS.Oxld t-18.0~10~ s, p=3000 Pa.
T[Kl Fig. 5. Dependence m,=f(T) for: 1, t=3.6~ t=10,8xld s, p=600 Pa; 3, t=3.6xl@ t=18.0xld s, p=1800 Pa; 5, t=10.8xld t=18.0xld s, p=3000 Pa.
30%
'i
ld s, p=600 Pa; 2, s, p=1800 Pa; 4, s, p=3OOO Pa; 6,
X
lo3 s, p = 600 Pa; 2, s, p=l800 Pa; 4, s, p=3000 Pa; 6,
0321’
I I
600
Ii00
l&o
2400
3000
p Ipa Fig. 9. Dependence p=f(p) for: 1, t=3.6~ ld s, T=800 K, 2, t=3.6x1O%,T=950K,3,f=l0.8xlds,T=8OOK,4,t=10.8xld s, T=llOO Ic; 5, t=18.0 xld s, T=950 K; 6, t=18.0xld s, T=llOO K.
p CRJl Fig. 6. Dependence m, =f(p) for: 1, t = 3.6 x Id s, T= 800 K, 2, t=3.6xld s, T-1100 K, 3, t=10_8xld s, T=SOO K; 4, r=18.0xld s, T==800 K; 5, r=18.0 xld s, T=950 K; 6, t=l8.Oxl@ s, T=llOO K.
parameters of the gaseous phospho~zi~g trea~ent, especially on the process time and temperature. Furthermore, the minimum of wear can be observed in intervals: 11000 s~t~15000 s and 950 K~T~1050 K. From the metallographic investigations f10,13] it results that the wear decreases together with the increase
55
J. Nowacld I Desctiption of friction of dij‘&sive phosphorized iron
extensive spalling after friction tests, which causes the increase of the wear (Figs. 10-12). As the result of qualitative investigations of chemical constitution of the phosphorized layer surface, before and after friction tests, carried out on Auger’s spectrometer, an increase of the oxygen concentration has been shown in the surface layer, which suggests the assumption of oxidizing of the layer during the friction time (Fig. 13). The estimated depth of the raised oxygen concentration in the surface layer valued (7.530) x 10e5 mm; was too small to be investigated by means of Xray tests. The investigations made on the powdered
Fig. 10. Cracked the friction test.
phosphorized
layer on iron with a gap after
Fe
Fig. 11. Surface of the compact phosphorized the friction test.
Fig. 12. Surface of the phosphorized after the friction test.
layer on iron after
layer on iron with a gap
of the layer thickness, up to the state when the process of gap creation between the layer and the base starts. The layers with the gap show a grid of cracking and
’ Ar c
200
O FeFe
400
600
Fe
800
lOO(
E IaVl Fig. 13. Auger electron spectroscopy of the compact phosphorired layer on iron after the friction test. Duration of etching by argonions: 1, non-etched; 2, 3 min; 3, 7 min; 4, 10 min.
56
J. Nowacki I Description of friction of di@sive phosphorized iron
The optimal parameters of the phosphorizing process determined as the result of calculations, and the tribological properties of iron corresponding to them, are compared to the tribological properties of non-phosphorized iron in Table 2.
4. Conclusions The increase of the wear resistance of iron subjected to the diffusion gaseous phosphorizing process is restricted by the hardness and anti-adhesion properties of the phosphides Fe,P and Fe,P as well as the good di~sional connection of the layer to the base. The gap generated between the layer and the base during the advanced stage of phosphorization causes a decrease in wear resistance. Based on the results of investigations, the following mechanism of the sliding dry friction of phosphorized
8(rod)
(b)
Fig. 14. Diffractogram of powdered extracted phosphorized layer (a) before the heat test, (b) after heating at a temperature of 630 K for 1800 s in air. TABLE 2. Optimal parameters of the gaseous phosphorizing process for which the wear and the friction coefficient achieve the minimum in comparison to non phosphorized iron Time t
Temperature
(s)
TK)
Partial pressure of phosphorus P 0%
950 11770 Non phosphorized
2508 Armco iron
Weight of wear m, (WI
Coefficient of friction p
9.51 74
0.25 0.43
extracted phosphor~ed layer confirmed indirectly the possibilities of its oxidation during friction. As the result of the gravimetric analysis of powdered formulations, the possibility of oxidation of the phosphorized layer at a temperature above 550 K was revealed. The speed of this process was increasing with the increase of the temperature. The specimen surface temperature defined on the basis of the martensite hardness changed during the time of the friction process of the counter-specimen, and was estimated to be 580-653 K. This temperature was higher than the temperature of the layer start oxidation process defined by the method of gravimetric analysis. As the result of X-ray examinations, the presence of iron phosphate Fe,PO, in the powdered extracted phosphorized layers held at a temperature of 630 K in an air atmosphere was identified (Fig. 14), which confirmed the friction temperature as the cause of the oxidation process of the phosphorized layer.
Fig. 15. Scheme of the friction process of the phosphorized compact layer: 1, oxidization on product film; 2, zone of phosphide F,P; 3, zone of phosphide Fe& 4, base.
IN
Fig. 16. Scheme of the friction process of phosphorized layer with the gap filled with porous phosphide Fe,P: 1, oxidization product film; 2, zone of phosphide Fe& 3, zone of phosphide Fe& 4, gap filled with porous Fe,P; 5, base. Visible cracks in the layer.
.I. Nowacki 1 Descrtption of friction of di@sive phosphotized
iron
57
the hairline cracking of a layer with a gap is its local deformation during friction. Acknowledgment The author gratefully acknowledges the help of Dr S. Strzelecki, Technical University, in the translation from Polish to English and in tracing graphs. 0
40
t3l2co
400
600
I [ml
References
Fig. 17. Dependence of the friction coefficient /.Lon the friction path I in the rubbing test. Phosphorization parameters: t = 10 800 s, T= 950 K, p = 1800 Pa.
layers (Figs. 15,16) has been proposed. The layer which is generated as the result of the phosphorizing process in an atmosphere of pure argon and gaseous phosphorus is characterized by significant chemical cleanness, and the process of oxidation at ambient temperature and atmosphere does not occur because of the chemical resistance of the layer. Trace quantities of absorbed elements oxygen, sulphur and carbon can be observed on the layer surface only. These elements have some influence on the wear and friction coefficients at the first phase of the friction process. At this stage, seizure of the friction pair does not occur and the value of the friction coefficient is moderate because plastic deformations around the contact region of the layer with high hardness are not large and the adhesive joints are small. The process of oxidation of the friction pair starts with the increase of the layer surface temperature as a result of the friction heat. Iron phosphate Fe,PO,, a product of phosphide oxidation, is forming on the surface of the phosphorized layer. This process causes the decrease of the friction coefficient. The unstable relationship of the friction coefficient to the parameters of the phosphorizing process, its decrease with the increase of the friction path and then its stabilization at a constant level (Fig. 17) is the result of the forming of the iron phosphide, Fe,PO,, film. In the case of a layer with a gap, cracking and crumbling of the phosphide zone occurs during the friction. The reason for
5
6
7
8
9 10 11 12
13
M. Hebda and A. Wachal, Tribology, WNT, Warsaw, 1980 (in Polish). I.W. Manukan, Antifriction properties of sintered materials based on iron, Sintered Metallurgy, 11 (1977) 81. J. Nowacki, Properties of sintered iron-phosphor materials, Iniynieria Materiabwa, 3(32) (1986) 73-77 (in Polish). J. Nowacki and Z. Has, Method of heat-chemical treatment of steel and cast iron machine parts, Pal. Pat. RP 125719, February 21, 1986 (in Polish). J. Nowacki and W. Kamidski, A mathematical description of the chemical reaction in the gas-solid system, Proc. 4th Conf on Applied Chemistty, Unit Operations and Processes, Hungarian Academy of Science Veszprem, Hungary, Vol. 1, Hungarian Chemical Society, Veszprem, 1983, p. 15. A. Wustenfeld, Verfahren zur Eindiffusion der Elemente Bor, Silizium und Phosphor in Metalobertlache, insbesondere in der Obertlichen von Eisen und Stahl (Process for diffusion of the elements boron, slicon and phosphorus into metal surfaces, especially the surfaces of iron and steel), Ger. Pat. 2429948, 1976. J. Nowacki, Schichtwachstum und Eigenschaften von Eisenphosphidschichten (Film growth and properties of iron phosphide films), Harterei-Technische Mitteiiungen, 2(44) (1989) 107-112. J. Nowacki, The structure and properties of phospho-nitrided layers, J. Metal. Club, University of Strathclyde, Glasgow, Vol. 27, 1992, pp. 72-80. J. Nowacki, Gaseous phosphorizing of steel 40H, Sci. .I. Tech. Univ. Ed&, Mechanics, 70 (1986) 111-127 (in Polish). J. Nowacki, A mathematical model of the chemical reaction in the Fe-P system, Muter. Sci., 9(2) (1983) 133-140. Polish Standard PN-67/M-04305: Defining of Wear Resistance on the AMSLER Machine, (in Polish). A.V. Fiacco and G.P. McCormick, Nonlinear Programming- Unconstrained Minimization Techniques, Wiley, New York, 1968. J. Nowacki, Einflul3 von Phosphorbeimengungen zu Nitrieratmospharen auf Aufbau und Eigenschaften von Nitrierschichten (Influence of phosphorus impurities in nitriding atmosphere on the formation and properties of nitride films), Hiirterei-Technische Mitteilungen, 1(46) (1988) 47-51.