490 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1952 



wire used to produce the wear on the plastic was always very much less 

 than tliat of the plastic. The reason for this as seen from Fig. 14 is that 

 since the displacement for a given force to break the bond between two 

 high points is going to be inversely proportional to the shearing stiff- 

 nesses of the two materials, the disphicement for stainless steel with a 

 shear stiffness of 8 x 10^^ dynes/cm" will be ^ that of the plastic with 

 a shear modulus of 2 x 10^^ dynes/cm^. Hence, the shearing strain for 

 the stainless steel is much further below its limiting strain than is the 

 shearing strain for the plastic. When the stainless steel wire was run 

 against a bar of synthetic sapphire — which has a much higher shear con- 

 stant — the stainless steel wire was soon worn through, while little wear 

 occurred on the sapphire. 



IV. THEORETICAL AND EXPERIMENTAL INVESTIGAIION OF THE NO GROSS 

 SLIDE REGION 



Since in the no gross slide region, the shearing strain is less than in 

 the gross slide region, the rate of wear should be considerably less. This 

 is confirmed by direct tests of the wear as shown by Fig. 11, and by 

 supplementary tests. Hence a further experimental and theoretical in- 

 vestigation has been made of this region which is defined by the condi- 

 tion that the tangential force is less than the product of the normal force 

 by the coefficient of friction. If sliding motions can be kept small enough 

 to be in this region, very little wear should occur. 



Using a shear ceramic for measuring the tangential force, the static 

 load was varied and the motion required to produce no gross slide was 

 determined. Oscillograph figures of the type shown by Fig. 9 were used 

 and when the figure was broadened out as shown by the third figure it 

 was assumed that slide had occurred. Fig. 15, upper curve, shows the 

 total motion in mil inches, plotted against the static force in grams, which 

 will just cause gross slide. The bottom line shows the maximum shearing 

 force in grams. This is slightly lower than the force determined by the 

 coefficient of friction since the force becomes slightly larger as shown by 

 the pictures of Fig. 9, when gross slide occurs. The total displacement 

 for no slide increases as the two-thirds power of the static load. 



Since neither the wire nor the plastic material is smooth, contact be- 

 tween the two is established at only a few points. To interpret the results 

 obtained above, some calculations due to R. D. Mindlin are used. 

 These deal with the tangential forces and displacements of two lialls 

 pressed together, and are for conditions occurring before gross slide 

 begins. 



