124 Mr. W. A. Scoble on Ductile 



approximately constant. I£ the maximum stress were con- 

 stant, the maximum shear stress would decrease with 

 increasing bending moment ; but it is found that the shear 

 stress increases, so that the deviation from the shear-stress 

 law is opposed to the maximum stress theory, and it 

 disproves the maximum strain hypothesis, which is in effect 

 an intermediate law, as has been already explained. The 

 results are similar for each series of tests. 



Even before there were any reliable experimental results 

 available, certain elasticians, influenced possibly by the forms 

 of fractures, were convinced that a material failed by 

 shearing. But further, there was usually a stress perpen- 

 dicular to the plane of greatest shear, and it was believed 

 that this force across the plane affected the value of the 

 shear stress at the elastic failure of the material. The shear 

 stress tended to make the opposite surfaces at a section slide 

 upon each other, and therefore it appeared that a compression 

 across the section would introduce a resistance to the shear 

 analogous to friction. Since a material tended to flow or 

 fracture along an uneven section, so that the surfaces fitted 

 into each other to a certain extent, it was conceivable that a 

 tension across a section assisted the shearing stress, and 

 lowered its value at the breakdown. 



Many of the experimental results available were examined 

 in the former paper to determine whether the friction hypo- 

 thesis would explain the deviation from the shear-stress law. 

 The final conclusion was that : — " It must be concluded that 

 the maximum shear stress determines when yield takes place, 

 but this will vary slightly on account of the difference in the 

 shearing resistance in various directions, and any idea of a 

 force analogous to friction must be abandoned/' 



But the bending moment appears to be always greater 

 than the torque, and it was suggested that when a shaft was 

 under a torque, T, and a bending moment, M, the equivalent 

 torque, T P , should be calculated from the equation 



t 2 =t 2 +/^Ym j 



(f) 



in which /; is the shear stress, and ft is the tensile stress in 

 the material at yield under simple loading. This equation 

 represents an ellipse which replaces the circle of the shear- 

 stress law, and thus allows for the limiting bending moment 

 being greater than the torque. The present experimental 

 results -justify the above suo-aestion. 



The theories of failure under combined stress can be very 

 simply expressed in terms of the three principal stresses, P 1? 

 P 2 , and P 3 , of which P x is the greatest and P 3 is the least. 



