A note on the relation between the abrasion resistance and the hardness of metals

70

WEAK

A NOTE ON THE RELATION AND THE HARDNESS

BETWEEN

THE ABRASION

RESISTANCE

OF METALS

C. RUBENSTEIN Mechanical Engineering (Gt. Britain) (Received

Department,

Manchester

College

of Science c’r Technology, Manchester

July zz, 1964)

In 1958, KHRUSCHOV~ reported the results of an investigation to determine the dependence of the wear resistance of metals on their hardness by rubbing them against an abrasive surface. The metal specimens traversed a spiral path over the abrasive surface so that contact between specimen and unused abrasive was maintained throughout. In order to eliminate the influence of fluctuations in the abrasive ability of different regions of the abrasive surface, the wear of any specimen was determined simultaneously with that of an arbitrarily chosen standard material tested on a different part of the same abrasive surface under identical conditions. Wear was measured by the diminution in length of the specimen after sliding a distance of 15 m under a standard load of 300 g at constant speed. The results were presented as the relative wear resistance E, against the specimen hardness H. E is defined by the ratio Als/Alm, where AZ, represents the linear wear of the standard material and Al, that of the specimen under test. For technically pure metals ranging in hardness from lead to tungsten and for annealed steels a linear relation between E and H was obtained. This line passes through the origin and its slope “was found to be the same for metals with cubic and hexagonal lattices”. It was also noted that the linear wear for a given sliding distance was directly proportional to the nominal pressure. In the following it will be shown that these results may be explained very simply. For simplicity, consider the abrasive grains to be conical, all of semi-angle 13. Let the cross-sectional area of specimen be A, the load carried by the specimen be L and rcobe the number of abrasive particles per unit area. Then each grain carries a load Li = L/noA. Let the depth of penetration of a grain into the specimen be h and the radius of the projected, circular, area of contact between grain and specimen be Y. Then, h = r cot 8 If H is the hardness of the specimen, H = L&72. Consider a single grain. In moving a distance S, a volume rhS of material is removed. Hence the total volume removed when the specimen moves a distance S Wear, 8 (1965) 70-72

ABRASION RESISTA~CE/HARD~ESSOF METALS

71

is noArkS = AV. Thus, the reduction in length dl, E,

= -

dV/A ;;

=:

m

where

Hm

=

rcoYJ2.s

6 esz = r,2ye2 cot cot 8

r=:_.--_=-

no~&rS

Lr H,

Hw,

Hm

Li

H,

is the hardness of the specimen and H, is the hardness of the standard

material. Hence, it follows (i) the relation between Em and Hm is linear, passing through the origin. (ii) a linear relation between Em and H, will result irrespective of which particular material is chosen as standard. (iii) the slope of the E, vs. H, line is the reciprocal of the hardness of the standard material and hence, for a given standard material, this slope will be the same “for metals with cubic and hexagonal lattices”. (iii) follows from KHRUSCHOV’S empirical observation that E = cH, where c is the slope of the E vs. H line for, if we consider the particular case when the specimen is the standard material,

Al, = Al,, i.e. E = I, and H = Hs i.e.x= cH+. or c =

xjEis

KHRUSCHOV chose as standard material a lead-tin alloy, the composition of which was not quoted. From the reciprocal of the slope of the resulting En DS.H, line, the hardness of this alloy may be deduced to have been 7.2 kg/mm2, which is of the right order of magnitude but is rather lower than the hardness quoted by TABOR~ for Pb 30 : Sn 70 solder (BHN = 12 kgjmm2). It has been shown in eqn. (I) that dl,

= rtiJrh.s= +2&s cot e = rto (L&H)S

cot 8

= (noS/?zcH)* (L/noA) cot 8 = (S cot O/kH) P where P = L/A, i.e. the nominal pressure. Hence, for a given material (H constant), sliding a given distance (S constant) in contact with a given abrasive surface (0 constant), the linear wear A&, is directly proportional to the nominal pressure P. It can be seen that this simple analysis has given an explanation ‘of the experimental observations quoted by KHRUSCHOV and, further, suggests that a better presentation of data would be given by plotting Em against the relative hardness defined by H,/H, which would yield a straight line passing through the origin and having a slope of unity, this relation being independent of the material chosen as standard. It must be pointed out here that the wear behaviour of heat-treated Steels does not conform with eqn. (I). KHRUSCHOV found that, for these materials

E = Eo+CI(H-

Ho)

where EQ is the relative wear resistance of the steel in its annealed condition, file is Weav, 8 (1965) 70-72

(‘.

72

RUBENSTEIN

the hardness of the annealed steel and CL is a constant, the value of which depends on the composition of the steel. No explanation of these results was offered in the original paper’ and the analysis given above is equally incapable of explaining them. REFERENCES I M. M. KHRUSCHOV,

Proceedings of the Conference on Lubrication and Wear, Institution Engineers, London, 1958, Paper 46. 2 D. TABOR, The Hardness of Metals, Oxford University Press, London, 1951, p. 169. Mechanical

Wear, 8 (1965) To-72

of