Ductile Materials under Combined Stress. 79 



bined stress +p and —p, and hence showing that q~p. This 

 is true in the elastic as well as in the plastic stage ; but the 

 combined stress +p and — p is merely another view of the 

 shear, and constitutes a very different condition to a simple 

 tensional stress, so that St. Venant's final step seems illogical.] 



18. The Maotimum Shearing - Stress criterion of Elastic 

 Strength. — A third theory of elastic strength, mentioned by 

 Cotterill in his ' Applied Mechanics/ is that the condition of 

 yielding is the existence of a shearing-stress of a specific 

 amount. Having regard to the behaviour of the material 

 when in the plastic stage, the assumption of continuity would 

 lead to this theory, but although the sheai'ing-stress law of 

 the plastic stage has been generally recognized, no formulas 

 for elastic strength in particular cases have been based upon 

 a similar law for the yield-point. The knowledge of Tresca's 

 results and the observation of the phenomena presented by 

 cold bending, tension and compression tests, punching, and 

 the general manipulation of metal, must have urged many 

 towards the conclusion that this is the true criterion of elastic 

 strength in a ductile material. 



19. Further reasons for adopting Thin Tubes as specimens. — 

 It has been stated above, that tubular specimens were used in 

 this series of experiments. In addition to the reason there 

 advanced, I was influenced by the advantage which tests made 

 by subjecting the tubes to internal fluid-pressure would have 

 in confirming, or not, the various theories. In such tests it is 

 evidently an advantage to have the thickness of the tube 

 small compared with the radius, as the stress will be more 

 uniform, and the yield-point in consequence more sharply 

 defined. 



20. Range of Stress covered by different types of experiment. 

 — If a specimen of circular section be submitted to torsion 

 and tension combined in various ratios, the stresses at the 

 exterior may be made to have all combinations between the 

 pairs —p, +p, and 0, +p [throughout I have considered 

 tensions and elongations as positive, owing to their more 

 frequent occurrence] ; and if compression were substituted for 

 tension the range between —p, +p, and — p, would be 

 included. Nothing- beyond these, i. e. no like principal 

 stresses can be produced by this method ; these, however, can 

 be readily impressed on the material of a hollow cylinder by 

 the use of fluid pressure. By the combination of tension with 

 internal pressure we can extend the range from , +p, to +p, 

 +p ; and by combining external pressure and axial force the 

 range from — p, to — p, — p could be covered, but owing to 

 the probable instability of a tube of suitable dimensions 



