﻿of Ductile Materials under Combined Stress. 535 



above, it will be noticed that it is not justifiable to apply the 

 results of tests on ductile materials when dealing with brittle 

 specimens. The critical case in which internal pressure is 

 applied is that of a thick cylinder of cast iron, and it would 

 not be safe to treat this in the same way as a comparatively 

 thin boiler-shell. In the latter case the two theories held in 

 England give very similar results, but in the former the 

 material has properties different from those of the specimens 

 tested. This distinction should be remembered when reading- 

 all that follows. 



4. The Theories of Elastic Strength. 



The real need is a determination of the true complete theory 

 of elastic strength. The theory of elasticity and all engineer- 

 ing applications are based on Hooke's law. that strain is 

 proportional to stress. When this law fails the assumptions 

 are no longer true, consequently the formula? deduced are 

 incorrect and it is impossible to reason further with certainty. 

 In certain cases there will be a redistribution of stress, usually 

 varying from that satisfying Hookers law to a state of uniform 

 stress, reached after considerable yield, through all the inter- 

 mediate conditions. By the theory of elastic strength is 

 meant the conditions which determine when the law fails 

 and the uncertain stage is reached, the body considered 

 being also seriously deformed. Three theories have claimed 

 much support. That adopted by English engineers assumes 

 that the material yields when the maximum principal stress 

 reaches a certain value. The view generally held by Con- 

 tinental elasticians is that a definite maximum strain deter- 

 mines the failure of the specimen. A third theory state> 

 that yielding occurs when the maximum shearing stress 

 becomes a specific amount. Mr. Guest has shown that 

 neither the maximum stress nor maximum strain is even 

 approximately constant. The maximum shear is constant 

 within close limits ; and it has been suggested that the varia- 

 tion is probably due to something analogous to friction, related 

 to the force perpendicular to the plane of maximum shear. 

 This point will be considered later when the results are 

 discussed. 



5. The Yield-Point selected as the Criterion of Strength. 



Remembering that our accepted formulas are based on Hooked 

 law, which holds to the elastic limit, it would at first appear 

 that this point should be selected as a basis for comparison. 

 The yield-point has here been used throughout. If the 



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