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XX. On the Behaviour of Steel under Mechanical Stress. 

 By C. A. Carus-Wilson, B.A., A.M.LC.E., Demonstrator 

 in the Mechanical Laboratory at the Royal Indian Engineering 

 College, Coopers Hill *. 



[Plates III.-V.] 



THE effect of uniform longitudinal stress on a steel bar is 

 threefold 



(i.) The molecules are strained, 

 (ii.) The elements are strained. 



(iii.) In virtue of the straining of the elements " flow " is 

 produced. 



The strain usually observed is the elongation due to flow, 

 which may be recoverable or irrecoverable. The strains of 

 an element can be shown to be a uniform dilatation combined 

 with a uniform shear about an axis parallel to that of the bar ; 

 hence the elongation due to flow consists of a sliding combined 

 with an increase of volume. 



The state of strain of an element may be conveniently 

 described by defining the shape, size, and orientation of the 



strain quadric, which is a sphere of radius 3 a/ — combined 



with an hyperboloid of two sheets whose principal senii- 



/Sn 

 diameter is a/ — and axis parallel to that of the bar ; where 



p is the intensity of longitudinal stress, n the rigidity, and 

 k the bulk modulus. 



Up to a certain stress the elastic properties of the steel are 

 such that the strain produced is recovered when the load is 

 removed, but at that stress the elastic resistance is overcome, 

 and the molecules slide over one another, the strain being 

 permanent. 



This sliding beyond the limit of elastic resistance does not 

 continue. The elastic resistance is raised by the sliding, and 

 consequently the sliding is limited. 



A stress-strain curve can be drawn which shows the in- 

 crease of the limit of elastic resistance p with sliding ; the 

 rate of increase of the former at any point may be measured 

 by observing the angle which the tangent to the curve at that 

 point makes with the axis of strain ; I will call this angle <f>. 



The initial value of p is often taken as an indication of the 

 " hardness " of the steel, and when p is raised by permanent 

 strain the steel is said to be " hardened " thereby. This, how- 

 ever, conflicts with a measure of hardness usually employed, 



* Communicated by the Physical Society : read December 6, 1889. 



