Behaviour of Steel under Mechanical Stress, 201 



namely the amount of permanent strain caused by performing 

 a given amount of work on a bar. 



Thus if a hard steel edge attached to a weight is allowed 

 to fall on the surface of a steel bar, the depth of the indenta- 

 tion is taken as a measure of the softness of the metal. 



If we draw the stress-strain curve P for the steel under 

 examination, the work done in producing a permanent strain 

 D is the area OPD. If Q represent the stress- strain 

 curve of a harder bar, the same amount of work, Q C will 

 clearly produce less permanent strain, C. The hardness 

 then is evidently determined by the form of the curve ; but 

 this depends upon the rate of increase of p with permanent 

 strain, i. e. upon the value of </>. Hence tan (/> is the true 

 measure of the hardness ; but tan <f> is not constant, it dimi- 

 nishes : therefore the initial value of tan <f> must be taken as 

 the measure of hardness. It will be seen that p cannot be 

 taken as a measure of the hardness, for p is the same at R and 

 P for the two bars, but the former is obviously the harder*. 



We can say, then, that permanent strain raises the limit of 

 elastic resistance, but diminishes the hardness — defined as the 

 rate of increase of p with permanent strain. 



I imagine it is because the harder steel has the greater value 

 of initial p that p has been taken as a measure of the hardness. 

 If a bar of soft steel be taken and cut in four pieces ; No. II. 

 " hardened " in oil ; No. III. in water [alkaline] ; No. IV. in 

 water [acid] ; if each piece is now tested we shall obtain stress- 

 strain curves as in fig. 1, Plate III. A curve can be drawn 

 through the points OABCDEF, which I will call the 

 " yield-line"; this will be the locus of all points such as A 

 and F for pieces of the same bar " hardened " to different 

 degrees. The points A, B, are called the " yield-points/' 



As the piece is harder the yield-point — or initial limit of 

 elastic resistance — is higher, and the yield A F is lessf . 



When the yield begins it continues until p is raised by a 

 given amount A. If we could show that X was the same for 

 each piece, then it would follow that the yields as A F, BE, 

 C D are direct measures of the hardness of the piece. 



If there is any inequality or want of homogeneity in the 

 bar due to unequal stresses in the manufacture, there may be 

 one plane or planes along which the limit of elastic resistance 

 is less than along any other. 



Hence when this resistance is overcome sliding will take 

 place throughout the bar parallel to that plane or planes until 



* If tan 0=0, the bar at that point is perfectly plastic. 

 t Fig. 2, Plate III. is a facsimile of an autographic diagram thus 

 obtained : the steel bar was cut in three pieces; A was soft, B hardened 



