488 



THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1952 



But u the displacement is 



u = 



du 

 dz 



dz — S dz 



(7) 



and hence the total work done is 



W = ^nS' dxdydz = Km'S") X volume of material (8) 



If the force is increased, the shearing strain S increases until it reaches 

 the limiting strain that the material can stand. This limiting strain 

 depends on the material and whether the strain is long repeated so that 

 the material becomes fatigued. For most plastics this limiting strain is 

 in the order of 1 per cent and for most metals the value is less than this. 



Fig. 14 — Representation of points of contact and their displacements for plastic 

 and wire. 



Hence the energy to break up one cubic centimeter of material is 



W = ^fxSl (9) 



where S^f is the breaking strain. For a plastic having a shear stiffness 

 of M = 2 X 10 dynes/cm and a breaking strain of 0.01, the energj'^ is 

 10 ergs per cubic centimeter. 



This rough calculation and the amount of wear observed for various 

 length strokes and forces allow a determmation of the amount of energy 

 going into wear production. The amount of work generated by a dis- 

 placement of 0.002 inches or 0.005 cm with a normal force of 30 grams is 



W = 0.005 X 30 X 980 X / in ergs 



(10) 



where / is the coefficient of friction. Since this is about 0.25 the work per 

 stroke is 37 ergs. Twice this amount results from a complete cycle and 

 for 10 cycles the work done is 



W = 37 X 2 X 10' = 7.44 X 10'° ergs 



(11) 



The volume of wear observed for this condition is about 1 X 10 

 cubic cm for the A phenolic and hence we find that the part of the energy 



