Wear, 33 (1975) 251 - 259 @ Elsevier Sequoia S.A., Lausanne - Printed in the Netherlands

251

THE ROLE OF FRACTURE TOUGHNESS IN THE WEAR OF METALS

E. HORNBOGEN*

Battelle, Columbus Laboratories, 505, King Avenue, Columbus, Ohio 43201 (U.S.A.)

(Received January 28, 1975)

Summary

A model is proposed to explain increasing relative wear rates with decreasing toughness of metallic materials. It is based on the comparison of the strain that occurs during asperity interactions with the critical strain at which crack growth is initiated. If the applied strain is smaller than the critical strain, the wear rate is independent of toughness and Archard’s law is followed. Applied strain larger than the critical strain of the material lead to an increased probability of crack growth and therefore to a higher wear rate. The transition to an increased wear rate (Ranges I + II) depends on the conditions of the particular wear experiment, for example, pressure, strain rate, impingement angle, and on the properties of the material. In Range I the wear coefficient is constant at the minimum value, wear resistance increases proportional to hardness. Wear rate in Range II can increase (less than in Range I), be independent of, or decrease with hardness depending on the particular toughness

Nomenclature

a

A = a2nn

; = 2L/m2 C = a/P Y fd eff

Ef

EC eff

6*

E H

m radius of asperity after plastic deformation

- relative area of all contacts m empirical factor to obtain ed eff m empirical factor to obtain E, eff -

Jm- 2 surface energy - applied plastic deformation .- elongation to fracture measure in p.s.

tensile test - effective critical strain m crack opening displacement at fracture Nme2 Young’s modulus Nm- 2 indentation hardness

*On leave from Ruhr University, Bochum (Germany)

252

k = k0 IEd eff ) / (EC eff)

Kit ~~--3/2

L m

M -

pz me2 P Nmm2

OY NmF2

QB Nm- 2 ath * E/l0 NmB2 731

! * E/30 NmW2

W - G-1 -

1. Introduction

wear coefficient in Range I

wear coefficient in Range I1

plane strain fracture toughness effective gauge length for crack opening exponent of work hardening number of asperities in contact to applied pressure yield stress ultimate tensile stress theoretical fracture stress theoretical shear stress wear rate wear resistance

Archard’s equation correlates wear rate ti with the applied pressure p and the hardness of the material H [ 1 f .

;=k,!? H'

It is based on the assumption that the wear rate is proportional to the total area A of surface in contact during interaction: A = m2nJT, where n is the number of asperities in interaction and a is their average radius. A and fz are related to a unit area. The wear coefficient k, is defined as the probability that decohesion of a certain volume of matter occurs at a given area A. Be- sides the geometry of the surface morphology ho contains two types of physical properties of the material: the surface energy which is related to adhesion and frictional forces, and the mechanical properties of the material, that are responsible for the mechanism by which matter is separated from the surface. These are basically the theoretical shear stress for the onset of plastic deformation 7th or the critical stress to Sepmatf? atomic bonds 0th. Because defect-free metals and atomically plane surfaces are never dealt with mechanical properties such as yield stress CT~, ultimate, tensile stress CF~, work hardening exponent M, elongation to fracture Ed, fracture toughness X1, should be effective and contained in k0 [2].

There are two types of observations that are not in accordance with Archard’s equation. The first is the sometimes abrupt change in wear rate that is found if pressure or sliding velocity is changed, for example, of steels. This can be explained by the breaking or formation of oxide layers as a function of pressure or tempe~ture rise by friction [ 3 - 51. The second anomaly is the observation that the wear rate can increase, and not decrease as required by eqn. {l), with increasing hardness, if the velocity or the angle of impingement of particles is increased or if a thermal and/or mechanical

Data of Kruschov and Bobachev (1960)

Hardness, kg /mm’ Hardness (HI, kg/mm’

Fig. 1. Correlation of abrasive wear resistance and hardness of pure, annealed metals. (after ref. 6)

Fig. 2. Wear resistance of several steels (40, Y8, Y12, X12, RF are Russian notations) in different heat treatment conditions compared with the pure, annealed metals (straight line). The upper right ends of the lines represent martensite aged at 150 “C. (after ref. 6)

hardening treatment of the material lead to a state of low fracture toughness

[6,71. - The effects of chemical environment on wear (transition low wear -+

high wear) are not considered here. The second set of observations indicates that for high wear, fracture toughness will have an effect on wear rate and sometimes not. An attempt will be made to define the conditions at which this material property has to be taken into consideration.

2. Modification of Archard’s equation

The independence of the wear coefficient k, in eqn. (1) of pressure and hardness implies that wear particle decohesion takes place by the same mechanism if the area of interaction changes with p or H. The different pure metals plotted in Fig. 1 are characterized by a low yield stress and ultimate tensile strength both roughly proportional to hardness, comparable work hardening coefficients and extremely high values of elongation at fracture and fracture toughness. Hardening of individual metals (by cold work, precipitation, etc.) leads to a decrease in wear rate w, of less than that expect- ed from the increase in hardness according to Fig. 1 (Fig. 2). Therefore, a wear coefficient h > ke is effective, i.e., the probability for wear particle formation has increased.

This probability can be related to the plastic strain ed efr produced

254

\ A /“of+ moterio

v I3 Hard material

w E sok High Toughness Low Toughness

Fig. 3. Schematic representation of asperity deformation, for materials of different toughness interacting at different pressures.

during an asperity interaction, and the critical strain at which cracks start to propagate in the material cc efl :

(2) EC eff

If E C eff 2 Ed eff the ductility of the material is so large and the mechanism of wear can be assumed to be constant: h = ho.

The effective strains are obtained in the following way. The area of an asperity produced during an interaction is [l] :

P a271 =-.

nH (3)

The strain is assumed to be proportional to the asperity diameter which is produced by plastic deformation, Fig. 3, and a factor (Y which contains the details of surface morphology, and n(p,H) the dependence of the number of interacting asperities with pressure and hardness.

a= (4)

(5)

If n = const, the maximum value of e,j eff is obtained, if n increases with pressure Ed eff decreases relatively.

255

Hardness of the Material

Fig. 4. Schematic representation of the correlation between wear resistance and hardness for different materials in various microstructural conditions.

To obtain the critical strain at which crack growth occurs spontane- ously, a semi-empirical formula is used [S] :

S”

Eceff =-v L

(6)

where 6 * is the crack tip opening displacement at fracture and L is consider- ed to be the effective gauge length. In turn, Hahn and Rosenfield suggested

L=;pm2, where /3 is an empirical constant and m is the strain-hardening exponent. Using the Bilby-Swinden model for S * in terms of rC,, [9] :

Ed effp

H= ko L\I p”m’Eo,p

6, eff 0 HIh K,2H ’

(7)

(8)

Equation (8) describes the wear rate of the material if Ed eff > e‘, efP The empirical constant factor c = e/p can be determined experimentally from the condition ed eff = E, eff. This is the condition at which in a w-r uersus H plot (Fig. 2) the wear resistance starts to increase less than the pure metal’s pro- portionality with hardness.

The properties indexed 0 are those of the material at the transition from wear rates determined by ho to higher values (Fig. 4). The material prop- erties K,,, H, m, uy have to be measured at a constant applied pressure p. in order to find Kleo, H,,, mo, uyo. E is not included because it is almost struc- ture insensitive for metals. If the pressure dependence of the tr~sition condition is of interest a second set of measurements at different pressures p is required to determine the critical pressure p. for constant material prop- erties. The constant c = CX@ obtained in this way should be characteristic for a certain wear process. It contains among other factors surface morphology,

256

Hardness, H, kg/mm2

Fig. 5. Comparison of the abrasion wear resistance of ductile metallic and brittle ceramic materials.

strain rate, angle of impingement, shape of abrading particles, etc. By sub- stituting a//3 from eqn. (9) into eqn. (8) it becomes evident that eqn. (1) is a special case of eqn. (8) for high ductility. For cu/P 5 (K,, 2H’/‘)/(m2Eo,p”) the wear rate increases relative to that of ductile material of the same hard- ness, This takes into consideration that fracture toughness becomes effective only after a threshold value is surpassed.

The question can be raised whether there is an upper limit of the wear rate for extremely brittle materials if K,, 2/E + 2-r. y is the surface energy of the cleavage plane. Evidence for such a limiting value is given by Fig. 5. Different brittle ceramic materials show the corresponding proportionality of wear resistance 24-l and hardness H as very ductile metals (Fig. 1). How- ever, wear rates are more than an order of magnitude higher: k,,, = 20 ho. This number applies to compact ceramic materials. Naturally, porous materials or materials that contain a more than average density of flaws should show much higher wear rates than k,,,.

Equation (8) is not adequate to deal with completely brittle materials. An intuitive relationship that expresses the approach to high brittleness is given by

ti = k, (1 + In - ed eff )X ec eff

(10)

which becomes identical with eqn. (8) if E, eff is not too much smaller than ed eff, and with eqn. (l), because negative values of the second term are not allowed.

257

Ed eff “C eff

Qeff j’ceff

Fig. 6. Schematic representation of the ranges with different wear behavior, for constant hardness H and pressure p, (a) The wear rate starts to increase, if the critical strain of the material becomes smaller from the applied strain (Range II), in Range I the wear rate is independent of fracture toughness. (b) For very low toughness of the material, a limiting value of maximum wear rate may exist: Range III.

3. Discussion and conclusions

It foliows from the proposed model that there are three ranges of wear behavior as a function of toughness of the material (Fig. 6). In range I Archard’s law is followed and not affected by toughness, which must be very high. For very high brittleness condition III is approached in which Archard’s law is fulfilled again, however, with a very much high wear coeffi- cient as compared to Range 1. The wear rate is a relatively complicated func- tion of the mechanical properties of the material in the transitional Range II,

An important problem for the application of eqn. (8) is to find the conditions for the transition at which the additional increase in wear rate starts. Factors which favor the transition are an increased pressure, strain rate and angle of impingement or a decreased fracture toughness. Least favorable for the Transition I + II are the conditions of sliding wear: the angle of impingement is close to 0” and the strain rates are usually much smaller than, for example, for impacting particles. This is the reason why Range I wear is found for a wide range of material properties for sliding.

The I + II transition can be easily observed for erosive wear, if either the velocity or impingement angle of impacting particles or the fracture

/ 5 mN/cm2

- A-A -A-A-A

3.8 mN/m?

0 ;/

‘XI I3 25 mN/cm2 wx 1 / I I 1 I I I

ml 400 600 800 IC

Hardness, kg/mm*

)OC

(b)

Carbon Concentrotlon, percent

(c)

Impingement Angle, p

Fig. 7. Examples for transition from ductile to brittle wear. (a) Reversal in the depen- dence of erosive wear resistance on hardness of steels with increasing particle energy (or velocity). (after ref. 6). (b) Reversal of wear resistance of steels as function of carbon content and impact energy (the velocity of the impacting particles for curve 1 and 2 was about 10 times that of 3). (after ref. 6). (c) Dependence of wear rate on the angle of impingement of the abrading particles for normalized mild steel (St37) and hardened carbon steel (C60H). (after ref. 7)

toughness of the material is varied (Figs. 2 and 7). For the dependence of wear resistance on hardness it is found that dti- ’ /dH1 = maximum. Range II is characterized by di-r /dH iII < d& ’ /d.H I~. This implies that dw- ’ /dH 3 0 with increased amount of work hardening, this can be understood from eqn. (8). Increasing work hardening causes a decreasing area of interaction and this effect is overcompensating the increased probability to crack growth caused by the decreasing toughness. Only if the toughness factors decrease relatively more than the hardness increases, wear resistance decreases with hardness. It may be noted that dti-’ /dH = 0 is not defined as the onset of I + II transition. Because the conditions for this transition depend on external experimental conditions such as pressure as well as internal mate- rials properties the exact transition parameters have to be determined experimentally as described in connection with eqn. (9).

259

The proposed model is based on the assumption that crack growth de- termines the wear behavior in Range II. This implies that it is Range I where subcritical crack growth can be expected, such as fatigue, thermal fatigue, stress corrosion cracking and corrosion fatigue, in addition to wear controlled by plastic deformation.

The proposed model is in good qualitative agreement with all observa- tions for which it is applicable. For a quantitative correlation data are lack- ing on materials for which all mechanical properties and the wear resistance were measured. Required are measurements for materials in a wide range of mechanical properties as produced by thermal and/or mechanical treatments. These should be exposed to well defined wear and erosion experiments at a wide range of conditions. From such experiments not only the conditions for optimum wear resistance should be obtained, but also those for the maximum rates of removal of the material during grinding.

Acknowledgements

I would like to thank Mr. W. A. Glaeser and Dr. A. R. Rosenfield for initiating my interest in this field and for many helpful discussions.

References

1 J. F. Archard, J. Appl. Phys., 24 (1953) 981. 2 E. Hornbogen, Metallurgical Aspects of Wear, to be published. 3 E. Kehl and E. Siebel, Arch. Eisenhiittenw., 9 (1953) 536. 4 I. V. Kragelskii, Friction and Wear, Butterworths, London, 1965, p. 88. 5 H. Uetz, Metalloberflache, 23 (1969) 199. 6 M. M. Khruschov, Wear, 28 (1974) 69. 7 H. Uetz and J. Fohl, Wear, 20 (1972) 299. 8 G. T. Hahn and A. R. Rosenfield, Application Related Phenomena in Titanium Alloys,

ASTM, Philadelphia, 1968, p. 5. 9 B. A. Bilby and K. H. Swinden, Proc. Roy. Sot. (London), A285 (1965) 22.