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Description and wear of materials with heterogeneous and anisotropic microstructures
Wear, 111 (1986)
391
391 - 402
RESORPTION AND WEAR OF MA~R~LS WITH HE~ROGE~OUS AND ANISOTROPIC MICROSTRIJCTURES* ERHARDHORNBOGEN Institut fiir Werkstoffe, fF. R.G.)
R~hr-~~i~~it~t
(Received September 2,1985;
Bochum,
P~stf~eh
102148,
D-4630
Bochum
accepted September 20,1985)
Summary Some principal features are discussed of materials which consist of more than one microstructural component. Such microstructures are characterized by volume fractions, type and anisotropy. Attempts have been made to derive quantitative models for the description of bulk wear rates as functions of the volume fractions f, and fp, properties of the phases ff and 0 and interface ~$3 and of the different types of microstructure. A change in volume fraction can be associated with a transformation of one type of microstructure to another and thus with a discontinuous change in wear resistance. For anisotropic structures tensors can be used for a complete descrip tion of the tribological properties. This is of concern, for example, for many composite materials such as fibre composites and lamellae. Materials exposed to sliding and abrasion can be subdivided into structures with one (isotropic), three and six components of the tensor of the volumetric wear rate Wij = dUi/dXj. For erosion the number can reach 9, or even 18, if the wear dai depends on the sign of the particular direction of loading +x~
1. Heterogeneousmicrostructures The term “heterogeneous” is used for materials which are composed of two or more phases or other discrete microstructural components [ 1, 21. The latter could apply for example for tempered martensite or for a thermoplastic polymer with additives. Thus microst~c~ral components may *Paper presented at the International Conference on Wear of Materials, Vancouver, Canada, April 14 - 18, 1985. 0043-1648J86/$3.50
@ Elsevier S~uoia/~inted
in The Netherlands
392
consist of more than one phase, e.g. in the form of an ultrafine dispersion. A wide variety of materials can be included in this definition. Many of them can form the elements of useful tribological systems. Their microstructure may originate from the following processes [ 31. (a) Solidification or solid state reactions using heterogeneous thermodynamic equilibria. (b) Sintering reactions which can combine even non-equilibrium phases and volume fractions. (c) Methods such as impregnation or vapour deposition which can produce artificial morphologies of composite materials. The morphologies may range from simple dispersions to the sophistication of integrated circuits. A systematic approach is taken to some aspects of wear which all heterogeneous materials have in common. The discussion is focused on quantitative relations with microstructural parameters. It is the purpose of this paper to discuss such microstructural aspects especially of systems which consist of combinations of soft and hard microstructural components, e.g. reinforced polymers or sintered hard metals. A description of a heterogeneous microstructure [3] requires information on the following (Figs. 1 and 2). (a) The volume fractions f,, fO etc. of the phases (x, /3 etc. (or microstructural components). (b) Microstructural elements, the most important of which are grain boundaries (Y(Y and &3, interfaces c$ and their densities pororand pap. (c) The type of two-phase microstructure. Dispersion, duplex, cell and net structures can be defined using the densities of the boundaries and/or the percolation behaviour of the microstructural parameters. (d) The degree of microstructural anisotropy. For its description a tensor may be used. Principal axes have been introduced similar to those used for the description of crystal structures. A complete description of a heterogeneous microstructure requires a set of statistical functions. For a dispersion type the particle size, shape, local distribution and orientation of non-spherical particles (Figs. 3 and 4) are required.
(a)
(b)
(c)
(d)
(e)
Fig. 1. Schematic diagrams of types of isotropic microstructures: (a) homogeneous grain structure; (b) duplex structure; (c) dispersion structure; (d) net structure; (e) cell structure ((b) - (e), heterogeneous structures).
393
I
I 0
components of wew
tensor
w
0
type al microstruclilre
I
4
-4
= qPP&~O
Fig. 2. Schematic diagrams of types of mi~rost~c~res tural anisotropy.
showing the degree of microstruc-
Fig. 3. Designation of the material dimensions ai and the directions of sliding or erosion xi (compare with Fig. 12(a)).
2. Wear of isotropic heterogeneous microstructures
The analysis of the wear behaviour is based on Archard’s equation [4] (eqns. (l), (2) and (4)) which defines the wear coefficient Jzas the probability of decohesion of wear particles in the effective relative asperity area A,-JA * o/H (where e is the pressure). In heterogeneous materials formation of wear particles may start in the phases ~1and j3 or at the interphases. The question arises whether the bulk hardness H or the partial hardness Ba and.& becomes important. It is known that this can principally be due to (a) brittle or (b) ductile mechanisms or combinations of both f5 - 81 (Figs. 5 and 6). Unstable
kr 4 0
Fig. 4. Designation of the surface fractions of the microstructural anisotropic microstructures.
components
fij for
Fig. 5. Schematic diagrams of components of the wear coefficient. kd: plastic deformation (A and C); ploughing (I3 and D); chip formation. kf, microcracking (C and D).
(4 -650
I
/
*600
”
-300
.250 I
I 10
20 Carbide
(b)
30 Volume
40
50
7. (c)
Fig. 6. Effect of microcracking on abrasive wear. (a) Wear resistance of metals and ceramic glasses as a function of the fracture toughness Kro. KIT controls w-’ for brittle materials 161. (b) Wear rate of au&&tic white cast irons (as-cast and 2 h at 200 “c) as a functjon of the volume fraction of the carbide M&: 0, abrasive wear loss; a, hardness. There is increasing wear at Q > 0.3 owing to microcracking of the carbide [S 1. (c) Prerequisite for increasing wear with increasing hardness.
(brittle) or stable (fatigue) crack growth as well as ploughing and chip formation are to be distinguished. They will be modified by the particular surface microstructure in the heterogeneous alloys. In the present paper the frictioninduced formation of structural gradients and reactions with the env~anment have been neglected as.they are suggested for example by the work of Moore
395
and Douthwaite [ 81. There is little experimental work to be found in the literature similar to the work in this paper. The results presented in the figures and the table come from the references cited of our own work. This paper is predominantly thought to set a direction in the design of new experiments and the interpretation of data. Heterogeneous structures are characterized by the volume fractions and properties of the phases, of the boundaries and of the type of microstructure (Figs. 1 and 2) [l-31. For the derivation of their behaviour a sequential or a simultaneous arrangement of microstructural components in the plane of sliding is the limiting situation [ 9 - 121. These are represented by the anisotropic structural species, lamellae and uniaxially aligned fibre composites (Figs. 2,7 and 8).
.¶
-fp P volume froctcon
volume fraction
Fig. 7. Derivation of qu~ti~tive models for the wear rate. Sequential removal Aa3 of Q and fi by sliding in the directions x1 and x2 (lsmella structures). Fig. 8. Simultaneous removal Aa, of Q and fl by sliding in directions xl and x2 (fibre structure and dispersion structure).
The wear of a lamella in direction x3 must occur simply by removal, layer by layer, of the individual components with partial rates w, and wp. The macroscopic wear rate w is in the case of good bonding (Fig. 7)
w=-
dai
= d3ci
(1)
For equivalent wear mechanisms in both phases the relation may become (with the wear coefficients k, = k, = k, Fig. 8) w=ok($-
+ $)
(2)
It becomes evident that the bulk wear resistance is not comparable with an average bulk hardness as follows from the rule of mixtures
H = f,H, + f&
(3) Assuming that the macrohardness is determined by the rule of mixtures (eqn. (3)) a relation can be derived which implies that the wear resistance
396
W1 of the (4) - (7)) w=-
ho
phase
H
to their
bulk hardness
(eqns.
(4)
H&f, + Hpfp
w.-1 = _
=
ha
W=
is proportional
ho
=
H
mixtures
&Lfa
+
(5)
Hpfo)
W&p
(7)
f&a + fpp
This relation is found for many heterogeneous materials, e.g. the abrasion of a soft matrix containing a fine dispersion of a hard phase (Figs. 9 and 10). A prerequisite is that the width S, of the abrasive groove is much larger than the particle size d, and spacing S, and there is perfect bonding between CYand /3 (Fig. 10(a)).
(8) (9)
*
Fibre weight fraction
[%I
Fig. 9. Wear rate as a function of the volume fraction fp of a hard microstructural component [ 131. Abrasion by A1203 paper: A, grain size 70 pm:“, grain size 7 pm. 0, sliding against polished 100 Cr 6 steel rings.
397
-/ :spr
+I’? dp
(b)
(4
Fig. 10. (a) Influence of the degree of dispersion of very hard particles fl on the mechanism of wear. Hardness of the abrasive Hal, pi:Hp. (b) Comparison of the wear resistance of a very fine dispersion (tempered martensite (MA)) and a coarse dispersion (dual-phase structure (DP)) of equal bulk hardness (martensite (MS), martensite and ferrite (MF)): X, macrohardness; 0, microhardness. High strength low alloy steel, 0.11 wt.% C, 1.54 wt.% Mn, 0.50 wt.% Si and 0.15 wt.% MO.
The following special cases are of interest for composite materials. (a) A material which contains one phase, the hardness of which is equivalent or higher than that of the abrasive partner iYP > H&. If this phase is dispersed finely in a soft matrix, so that the particles can be shifted during (plastic) ploughing, together with the matrix, eqns. (4) - (7) are valid [9]. If, however, the dimensions of the hard phase become larger or if it is anchored in the matrix as a net or cell structure, a supporting effect will impede the wear of the soft matrix. The wear resistance will rise to a value which is determined by the harder phase alone (Izp Q k from eqn. (5)) (Fig. 10(b))
For dispersion structures this effect is related to the groove width. It is, therefore, a function of 0. A high resistance should be expected below the critical pressure (T, which produces grooves of diameter S, less than the particle size d,, d, > S, for u < B, (eqns. (8) and (9)) w-1
=
fP%
k,O < uc)
(11)
(b) A material in which one component increases its probability of fracture with increasing volume fraction, particle size or type of structure. This situation can be expressed by an increase in k, to k,+ = k,, + k,,, for example by the onset of brittle fracture above a pressure u, or a particle size dPC. The ratio of critical crack size a, to particle size d, can explain such a transition (Figs. 6(b), 6(c) and 11)
398
motrlx
cr
(4
(b)
W;
-a .
brittle
P
P corblde 0
(cl Fig. 11. Consequences of microstructural transformation on the wear resistance. (a) Increased resistance due to the transition from a dispersion structure to a net structure. (b) Wear resistance of sintered hard metals [6]. (c) Ductile-to-brittle transition inducing a decreasing wear resistance above a certain volume fraction (see Fig. 6(b)).
1 fcl __=-+--
fp_
w
Wb
w,
1
f,H,+fpH (Q
(12)
An additional probability for wear due to the separation of interfaces can be explained in a corresponding way (Fig. 9).
3. Wear of anisotropic structures An additional feature of anisotropic structures is the directionality of their friction and wear properties [ 13 - 161. Tribological tensors are required for a full description of such materials. An understanding of the components of tribological tensors can be baaed on the directionality of the mechanisms
399
TABLE
1
Friction direction
and wear of carbon-fibre-reinforced of sliding [ 17 ]
epoxy
(U = 2.22 MPa) as a function
of the
carbonfibrerein forced epoxy
A brasion by 70 pm grain size AltO3 paper Na APa Pa
Abrasion by 7pm grain size A1203 paper
Wear using a diamond needle
N
AP
P
N
AP
P
P
0.69
0.64
0.58
0.64
0.50
0.46
0.62
0.54
0.27
3.2
6.1
4.5
0.35
0.32
0.32
-
-
-
W
a
( lo4 MPa-‘) ‘Abrasion and wear normal direction of the fibre axes.
(N), parallel
(P) and perpendicular
which have been described earlier in this paper. from the types of phase [3] and of microstructure. Using the coordinate system of Fig. 3 for expressed for anisotropic rnicrost~~~~s (Table change in the directions i = 1, 2 and 3 by sliding j = 1,2 and 3 (Figs. 3 and 12) respectively [ 181 Aal=
(antiparallel)
Anisotropy
can originate
w, these properties can be 1). Aaj is the dimensional in the directions Xi, where
z-x,+ 2x2+h
(134
---x3
2
1
AcrZ= 2x,+ 1
6x3
&a2
-x2
+
6x2
(AP) to the
6a2 -x3 6x3
(13b)
For sliding and abrasion three components must become zero (Fig. 12(b)) &al -= 6x1
&a2 -= 6x2
&a, -= 6x3
0
(14)
Erosive loading conditions may provide a component perpendicular to the surface. Consequently, the components given in eqn. (14) may not be equal to zero under these circumstances (Fig. 12(c)), The general formulation of the wear rate is daj
wij = -
(15)
dxi
For sliding and abrasion the six component
of the wear tensor am
(b) b
materrol dIrectIon of erosive force
Fig. 12. (a) Dry friction of thermoplastic polymers as a function of the angle o between the direction of sliding and molecular orientation. Isotactic polypropene with a 5 vol.% [ 11) and 20 vol.% [ 131 admixture of atactic polypropene [ 171, (7 = 10s Pa. (b) Schematic diagram of a microstructure for which the friction and wear depend on the direction of sliding +x. (c) Conditions for the most general case of the tensor: anisotropic material, a = ai, b = u2, c = 43; three directions of erosive load, x = x1, y = x2, t = x3.
Composite materials can be subdivided into three classes in order of increasing asymmetry and, consequently, consisting of one, three and six principal wear rates (Table 1). W12+W13+
w21 #W23+
W 12 = W21 f
W 13 = w23 +
WI2 = W13=
W21 = W23=
W31fW32 w31 = w32 W31 = W32
(174 (17b)
(17c)
The symmetrical structures (eqn. (17a)) have been discussed already. Uniaxial anisotropy (eqn. (17b)) implies three components of the abrasive wear rate. It is represented by lamellate and uniaxial fibre enforcement. The number of components is doubled if wear depends on the direction of sliding. This is the case for fish-scale-like structures (Fig. 12(b)).
401
Relations which control the bulk wear have been obtained from a discussion of the different types of isotropic structures. They must be valid for the particular surfaces of the anisotropic materials. A lamella can be described by the following components (Fig. 7): W 31 = w32 =
(18)
wafa + wpffl
W 23 = w 13
perpendicular
W 21 = w 12
parallel
to the lamellae i
The reason for the difference W 23 = W13#
represented
by
w21 = w12
may be due to the fact that a perpendicular passage of lamellae (or fibres) will favour separation of the o$ interface, but a parallel passage will not (Fig. 8). The description of the components follows eqns. (4) - (12). An important implication of microstructural anisotropy is that the direct relations to volume fractions become invalid (e.g. eqns. (8) and (9)). Geometric relations should exist between the volume fraction fp and for example fp31.The index 31 indicates the fraction of fl phase encountered during sliding in the plane perpendicular to a3 in a direction x1. Equations (8) and (9) become eqns. (13) - (15)
w31
-l=-_-
f LY31 + _fp31 W,
(19)
WP
The wear resistance of a composite can be optimized by adjusting the direction and plane of sliding to the optimum orientation of the material if the complete wear tensor is known. Systematic experimental work on the effects of the type of microstructure and microstructural anisotropy on friction and wear is still in an early stage [ 151. Composite materials and sintered metals will provide a wide field for such work with a good perspective on the improvement of wear systems. The general principles outlined here could form a framework for such developments. The formulations describe relatively simple structures. There is a long way to go for a full and quantitative understanding of more complex or hybrid composite structures.
Acknowledgment The support of this work by the Ministry for Science and Research Nordrhein-Westfalen (NRW-Project IV B 5 - FA 19) is gratefully acknowledged.
402
References 1 S. A. Saltikow, Stereometrische Metallographie, Volkseigner Betrieb Grundstoffindustrie, Leipzig, 1974. 2 E. E. Underwood, Quontifatiue Stereology, Addison-Wesley, Reading, MA, 1974. 3 E. Hornbogen, On microstructure of alloys, Acta Metoll., 23 (1984) 615 - 627. 4 J. F. Archard, Contact and rubbing of flat surfaces, J. Appl. Phys., 24 (1953) 981. 5 E. Hornbogen, The role of fracture toughness in the wear of metals, Wear, 33 (1975) 251. 6 K.-H. Zum Gahr, Einfluss der Bruchzlhigkeit auf die Reibungskraft bei abrasivem Verschleiss, 2. Metal&d., 67 (1967) 678 - 682 and Furchungsverschleiss. In K.-H. Zum Gahr (ed.), Reibung und Verschleiss, Deutsche Gesellschaft fur Metallkunde, Oberursel, 1983, pp. 135 - 156. 7 A. R. Rosenfield, Wear and fracture mechanics, J. Mater. Sci., 15 (1980) 221 - 231. 8 M. A. Moore and R. M. Douthwaite, MetaN. Trans., A. 7 (1976) 1833 - 1839. 9 J. Becker, E. Hornbogen and K. Rittner, Abrasiver Verschleiss von Stahlen mit DualPhasen Gefiige, Sonderb. Prakt. Metall., 15 (1983) 342 - 352. 10 S. V. Prasad and P. D. Clavert, Abrasive wear of particle-filled polymers, J. Mater. Sci., 15 (1980) 1746 - 1754. 11 H. M. Hawthorne, Wear in hybrid carbon/glass fibre epoxy composite materials. In K. C. Ludema (ed.), Proc. Int. Conf. on Wear of Materials, Reston, VA, April I1 - 14, 1983, American Society of Mechanical Engineers, New York, 1983, pp. 576 - 582. 12 T. Tsukizoe and N. Ohmae, Friction and wear of advanced composite materials, Proc. 4th Int. Conf. on Composite Materials, Milan, Italy, 1980. 13 K. Friedrich, Wear of polymer composites, Composite Designer Guide, Vol. 4, University of Delaware Press, DE, 1983. 14 K. Tanaka and S. Rawakamik, Effect of various fillers on the friction and wear of PTFE-based composites, Wear, 79 (1982) 221. 15 N. H, Sung and N. P. Suh, Effect of fiber orientation on friction and wear of fiber reinforced plastics, Wear, 53 (1979) 129. 16 T. P. Harrington and R. W. Mann, Characterization of microstructural anisotropy in orthotropic materials using a second rank tensor, J. Mater. Sci., 19 (1984) 761 - 767. 17 E. Hornbogen and K. Schafer, in D. Rigney (ed.), Fundamentals of Friction and Wear of Materials, American Society for Metals, Metals Park, OH, 1980, pp. 409 - 438. I8 M. Cyffka and E. Hornbogen, Description of anisotropic wear rates of polymer-based composites, J. Mater. Sci. Lett., 5 (1986) 424 - 426.
391
391 - 402
RESORPTION AND WEAR OF MA~R~LS WITH HE~ROGE~OUS AND ANISOTROPIC MICROSTRIJCTURES* ERHARDHORNBOGEN Institut fiir Werkstoffe, fF. R.G.)
R~hr-~~i~~it~t
(Received September 2,1985;
Bochum,
P~stf~eh
102148,
D-4630
Bochum
accepted September 20,1985)
Summary Some principal features are discussed of materials which consist of more than one microstructural component. Such microstructures are characterized by volume fractions, type and anisotropy. Attempts have been made to derive quantitative models for the description of bulk wear rates as functions of the volume fractions f, and fp, properties of the phases ff and 0 and interface ~$3 and of the different types of microstructure. A change in volume fraction can be associated with a transformation of one type of microstructure to another and thus with a discontinuous change in wear resistance. For anisotropic structures tensors can be used for a complete descrip tion of the tribological properties. This is of concern, for example, for many composite materials such as fibre composites and lamellae. Materials exposed to sliding and abrasion can be subdivided into structures with one (isotropic), three and six components of the tensor of the volumetric wear rate Wij = dUi/dXj. For erosion the number can reach 9, or even 18, if the wear dai depends on the sign of the particular direction of loading +x~
1. Heterogeneousmicrostructures The term “heterogeneous” is used for materials which are composed of two or more phases or other discrete microstructural components [ 1, 21. The latter could apply for example for tempered martensite or for a thermoplastic polymer with additives. Thus microst~c~ral components may *Paper presented at the International Conference on Wear of Materials, Vancouver, Canada, April 14 - 18, 1985. 0043-1648J86/$3.50
@ Elsevier S~uoia/~inted
in The Netherlands
392
consist of more than one phase, e.g. in the form of an ultrafine dispersion. A wide variety of materials can be included in this definition. Many of them can form the elements of useful tribological systems. Their microstructure may originate from the following processes [ 31. (a) Solidification or solid state reactions using heterogeneous thermodynamic equilibria. (b) Sintering reactions which can combine even non-equilibrium phases and volume fractions. (c) Methods such as impregnation or vapour deposition which can produce artificial morphologies of composite materials. The morphologies may range from simple dispersions to the sophistication of integrated circuits. A systematic approach is taken to some aspects of wear which all heterogeneous materials have in common. The discussion is focused on quantitative relations with microstructural parameters. It is the purpose of this paper to discuss such microstructural aspects especially of systems which consist of combinations of soft and hard microstructural components, e.g. reinforced polymers or sintered hard metals. A description of a heterogeneous microstructure [3] requires information on the following (Figs. 1 and 2). (a) The volume fractions f,, fO etc. of the phases (x, /3 etc. (or microstructural components). (b) Microstructural elements, the most important of which are grain boundaries (Y(Y and &3, interfaces c$ and their densities pororand pap. (c) The type of two-phase microstructure. Dispersion, duplex, cell and net structures can be defined using the densities of the boundaries and/or the percolation behaviour of the microstructural parameters. (d) The degree of microstructural anisotropy. For its description a tensor may be used. Principal axes have been introduced similar to those used for the description of crystal structures. A complete description of a heterogeneous microstructure requires a set of statistical functions. For a dispersion type the particle size, shape, local distribution and orientation of non-spherical particles (Figs. 3 and 4) are required.
(a)
(b)
(c)
(d)
(e)
Fig. 1. Schematic diagrams of types of isotropic microstructures: (a) homogeneous grain structure; (b) duplex structure; (c) dispersion structure; (d) net structure; (e) cell structure ((b) - (e), heterogeneous structures).
393
I
I 0
components of wew
tensor
w
0
type al microstruclilre
I
4
-4
= qPP&~O
Fig. 2. Schematic diagrams of types of mi~rost~c~res tural anisotropy.
showing the degree of microstruc-
Fig. 3. Designation of the material dimensions ai and the directions of sliding or erosion xi (compare with Fig. 12(a)).
2. Wear of isotropic heterogeneous microstructures
The analysis of the wear behaviour is based on Archard’s equation [4] (eqns. (l), (2) and (4)) which defines the wear coefficient Jzas the probability of decohesion of wear particles in the effective relative asperity area A,-JA * o/H (where e is the pressure). In heterogeneous materials formation of wear particles may start in the phases ~1and j3 or at the interphases. The question arises whether the bulk hardness H or the partial hardness Ba and.& becomes important. It is known that this can principally be due to (a) brittle or (b) ductile mechanisms or combinations of both f5 - 81 (Figs. 5 and 6). Unstable
kr 4 0
Fig. 4. Designation of the surface fractions of the microstructural anisotropic microstructures.
components
fij for
Fig. 5. Schematic diagrams of components of the wear coefficient. kd: plastic deformation (A and C); ploughing (I3 and D); chip formation. kf, microcracking (C and D).
(4 -650
I
/
*600
”
-300
.250 I
I 10
20 Carbide
(b)
30 Volume
40
50
7. (c)
Fig. 6. Effect of microcracking on abrasive wear. (a) Wear resistance of metals and ceramic glasses as a function of the fracture toughness Kro. KIT controls w-’ for brittle materials 161. (b) Wear rate of au&&tic white cast irons (as-cast and 2 h at 200 “c) as a functjon of the volume fraction of the carbide M&: 0, abrasive wear loss; a, hardness. There is increasing wear at Q > 0.3 owing to microcracking of the carbide [S 1. (c) Prerequisite for increasing wear with increasing hardness.
(brittle) or stable (fatigue) crack growth as well as ploughing and chip formation are to be distinguished. They will be modified by the particular surface microstructure in the heterogeneous alloys. In the present paper the frictioninduced formation of structural gradients and reactions with the env~anment have been neglected as.they are suggested for example by the work of Moore
395
and Douthwaite [ 81. There is little experimental work to be found in the literature similar to the work in this paper. The results presented in the figures and the table come from the references cited of our own work. This paper is predominantly thought to set a direction in the design of new experiments and the interpretation of data. Heterogeneous structures are characterized by the volume fractions and properties of the phases, of the boundaries and of the type of microstructure (Figs. 1 and 2) [l-31. For the derivation of their behaviour a sequential or a simultaneous arrangement of microstructural components in the plane of sliding is the limiting situation [ 9 - 121. These are represented by the anisotropic structural species, lamellae and uniaxially aligned fibre composites (Figs. 2,7 and 8).
.¶
-fp P volume froctcon
volume fraction
Fig. 7. Derivation of qu~ti~tive models for the wear rate. Sequential removal Aa3 of Q and fi by sliding in the directions x1 and x2 (lsmella structures). Fig. 8. Simultaneous removal Aa, of Q and fl by sliding in directions xl and x2 (fibre structure and dispersion structure).
The wear of a lamella in direction x3 must occur simply by removal, layer by layer, of the individual components with partial rates w, and wp. The macroscopic wear rate w is in the case of good bonding (Fig. 7)
w=-
dai
= d3ci
(1)
For equivalent wear mechanisms in both phases the relation may become (with the wear coefficients k, = k, = k, Fig. 8) w=ok($-
+ $)
(2)
It becomes evident that the bulk wear resistance is not comparable with an average bulk hardness as follows from the rule of mixtures
H = f,H, + f&
(3) Assuming that the macrohardness is determined by the rule of mixtures (eqn. (3)) a relation can be derived which implies that the wear resistance
396
W1 of the (4) - (7)) w=-
ho
phase
H
to their
bulk hardness
(eqns.
(4)
H&f, + Hpfp
w.-1 = _
=
ha
W=
is proportional
ho
=
H
mixtures
&Lfa
+
(5)
Hpfo)
W&p
(7)
f&a + fpp
This relation is found for many heterogeneous materials, e.g. the abrasion of a soft matrix containing a fine dispersion of a hard phase (Figs. 9 and 10). A prerequisite is that the width S, of the abrasive groove is much larger than the particle size d, and spacing S, and there is perfect bonding between CYand /3 (Fig. 10(a)).
(8) (9)
*
Fibre weight fraction
[%I
Fig. 9. Wear rate as a function of the volume fraction fp of a hard microstructural component [ 131. Abrasion by A1203 paper: A, grain size 70 pm:“, grain size 7 pm. 0, sliding against polished 100 Cr 6 steel rings.
397
-/ :spr
+I’? dp
(b)
(4
Fig. 10. (a) Influence of the degree of dispersion of very hard particles fl on the mechanism of wear. Hardness of the abrasive Hal, pi:Hp. (b) Comparison of the wear resistance of a very fine dispersion (tempered martensite (MA)) and a coarse dispersion (dual-phase structure (DP)) of equal bulk hardness (martensite (MS), martensite and ferrite (MF)): X, macrohardness; 0, microhardness. High strength low alloy steel, 0.11 wt.% C, 1.54 wt.% Mn, 0.50 wt.% Si and 0.15 wt.% MO.
The following special cases are of interest for composite materials. (a) A material which contains one phase, the hardness of which is equivalent or higher than that of the abrasive partner iYP > H&. If this phase is dispersed finely in a soft matrix, so that the particles can be shifted during (plastic) ploughing, together with the matrix, eqns. (4) - (7) are valid [9]. If, however, the dimensions of the hard phase become larger or if it is anchored in the matrix as a net or cell structure, a supporting effect will impede the wear of the soft matrix. The wear resistance will rise to a value which is determined by the harder phase alone (Izp Q k from eqn. (5)) (Fig. 10(b))
For dispersion structures this effect is related to the groove width. It is, therefore, a function of 0. A high resistance should be expected below the critical pressure (T, which produces grooves of diameter S, less than the particle size d,, d, > S, for u < B, (eqns. (8) and (9)) w-1
=
fP%
k,O < uc)
(11)
(b) A material in which one component increases its probability of fracture with increasing volume fraction, particle size or type of structure. This situation can be expressed by an increase in k, to k,+ = k,, + k,,, for example by the onset of brittle fracture above a pressure u, or a particle size dPC. The ratio of critical crack size a, to particle size d, can explain such a transition (Figs. 6(b), 6(c) and 11)
398
motrlx
cr
(4
(b)
W;
-a .
brittle
P
P corblde 0
(cl Fig. 11. Consequences of microstructural transformation on the wear resistance. (a) Increased resistance due to the transition from a dispersion structure to a net structure. (b) Wear resistance of sintered hard metals [6]. (c) Ductile-to-brittle transition inducing a decreasing wear resistance above a certain volume fraction (see Fig. 6(b)).
1 fcl __=-+--
fp_
w
Wb
w,
1
f,H,+fpH (Q
(12)
An additional probability for wear due to the separation of interfaces can be explained in a corresponding way (Fig. 9).
3. Wear of anisotropic structures An additional feature of anisotropic structures is the directionality of their friction and wear properties [ 13 - 161. Tribological tensors are required for a full description of such materials. An understanding of the components of tribological tensors can be baaed on the directionality of the mechanisms
399
TABLE
1
Friction direction
and wear of carbon-fibre-reinforced of sliding [ 17 ]
epoxy
(U = 2.22 MPa) as a function
of the
carbonfibrerein forced epoxy
A brasion by 70 pm grain size AltO3 paper Na APa Pa
Abrasion by 7pm grain size A1203 paper
Wear using a diamond needle
N
AP
P
N
AP
P
P
0.69
0.64
0.58
0.64
0.50
0.46
0.62
0.54
0.27
3.2
6.1
4.5
0.35
0.32
0.32
-
-
-
W
a
( lo4 MPa-‘) ‘Abrasion and wear normal direction of the fibre axes.
(N), parallel
(P) and perpendicular
which have been described earlier in this paper. from the types of phase [3] and of microstructure. Using the coordinate system of Fig. 3 for expressed for anisotropic rnicrost~~~~s (Table change in the directions i = 1, 2 and 3 by sliding j = 1,2 and 3 (Figs. 3 and 12) respectively [ 181 Aal=
(antiparallel)
Anisotropy
can originate
w, these properties can be 1). Aaj is the dimensional in the directions Xi, where
z-x,+ 2x2+h
(134
---x3
2
1
AcrZ= 2x,+ 1
6x3
&a2
-x2
+
6x2
(AP) to the
6a2 -x3 6x3
(13b)
For sliding and abrasion three components must become zero (Fig. 12(b)) &al -= 6x1
&a2 -= 6x2
&a, -= 6x3
0
(14)
Erosive loading conditions may provide a component perpendicular to the surface. Consequently, the components given in eqn. (14) may not be equal to zero under these circumstances (Fig. 12(c)), The general formulation of the wear rate is daj
wij = -
(15)
dxi
For sliding and abrasion the six component
of the wear tensor am
(b) b
materrol dIrectIon of erosive force
Fig. 12. (a) Dry friction of thermoplastic polymers as a function of the angle o between the direction of sliding and molecular orientation. Isotactic polypropene with a 5 vol.% [ 11) and 20 vol.% [ 131 admixture of atactic polypropene [ 171, (7 = 10s Pa. (b) Schematic diagram of a microstructure for which the friction and wear depend on the direction of sliding +x. (c) Conditions for the most general case of the tensor: anisotropic material, a = ai, b = u2, c = 43; three directions of erosive load, x = x1, y = x2, t = x3.
Composite materials can be subdivided into three classes in order of increasing asymmetry and, consequently, consisting of one, three and six principal wear rates (Table 1). W12+W13+
w21 #W23+
W 12 = W21 f
W 13 = w23 +
WI2 = W13=
W21 = W23=
W31fW32 w31 = w32 W31 = W32
(174 (17b)
(17c)
The symmetrical structures (eqn. (17a)) have been discussed already. Uniaxial anisotropy (eqn. (17b)) implies three components of the abrasive wear rate. It is represented by lamellate and uniaxial fibre enforcement. The number of components is doubled if wear depends on the direction of sliding. This is the case for fish-scale-like structures (Fig. 12(b)).
401
Relations which control the bulk wear have been obtained from a discussion of the different types of isotropic structures. They must be valid for the particular surfaces of the anisotropic materials. A lamella can be described by the following components (Fig. 7): W 31 = w32 =
(18)
wafa + wpffl
W 23 = w 13
perpendicular
W 21 = w 12
parallel
to the lamellae i
The reason for the difference W 23 = W13#
represented
by
w21 = w12
may be due to the fact that a perpendicular passage of lamellae (or fibres) will favour separation of the o$ interface, but a parallel passage will not (Fig. 8). The description of the components follows eqns. (4) - (12). An important implication of microstructural anisotropy is that the direct relations to volume fractions become invalid (e.g. eqns. (8) and (9)). Geometric relations should exist between the volume fraction fp and for example fp31.The index 31 indicates the fraction of fl phase encountered during sliding in the plane perpendicular to a3 in a direction x1. Equations (8) and (9) become eqns. (13) - (15)
w31
-l=-_-
f LY31 + _fp31 W,
(19)
WP
The wear resistance of a composite can be optimized by adjusting the direction and plane of sliding to the optimum orientation of the material if the complete wear tensor is known. Systematic experimental work on the effects of the type of microstructure and microstructural anisotropy on friction and wear is still in an early stage [ 151. Composite materials and sintered metals will provide a wide field for such work with a good perspective on the improvement of wear systems. The general principles outlined here could form a framework for such developments. The formulations describe relatively simple structures. There is a long way to go for a full and quantitative understanding of more complex or hybrid composite structures.
Acknowledgment The support of this work by the Ministry for Science and Research Nordrhein-Westfalen (NRW-Project IV B 5 - FA 19) is gratefully acknowledged.
402
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