STRESS AND DEFORMATION 5 



The upper end A of the initial line, or point where the diagram 

 begins to curve, is called the elastic limit. The point B, where the 

 deformation becomes very noticeable, is called the yield point. As 

 these two points occur close together, no distinction is made between 

 them in ordinary commercial testing. 



The maximum ordinate to the strain diagram represents the 

 greatest unit stress preceding rupture, and is called the ultimate 

 strength of the material. 



In the case of shear let q denote the unit shearing stress and 

 <f) the corresponding angular deformation expressed in circular 

 measure. Then, by Hooke's law, 



where G is a constant for any given material, called the modulus 

 of rigidity, or shear modulus. For steel and wrought iron G = .4 E, 

 approximately. 



Average values of E and G for various materials are given in 

 Table I. 



5. Elastic limit. It is found by experiment that as long as the 

 stress does not pass the elastic limit, the deformation disappears 

 when the external forces are removed. If the unit stress (or, more 

 properly, the unit deformation) exceeds the elastic limit, however, 

 then the deformation does not entirely disappear upon removal of 

 the load, but the body retains a permanent set. At the elastic 

 limit, therefore, the body begins to lose its elastic properties, and 

 hence, in constructions which are intended to last for any length of 

 time, the members should be so designed that the actual stresses lie 

 well below the elastic limit. 



It has also been found by experiment that, for iron and steel, if 

 the stress lies well within the elastic limit, it can be removed and 

 repeated indefinitely without causing rupture ; but if the metal is 

 stressed beyond the elastic limit, and the stress is repeated or alter- 

 nates between tension and compression, it will eventually cause 

 rupture, the number of changes necessary to produce failure 

 decreasing as the difference between the upper and lower limits 

 of the strain increases. This is known as the fatigue of metals, 



