128 Ductile Materials under Combined Stress. 



Mr. Smith's results are not shown plotted here, but they 

 are found to give, — 



Smith's Solid Steel. Series SC. Table A. Pj-1'09 P 3 = 41000. 



Series AD. Table C. Pi-0'775 P 3 = 36300. 



„ Hollow Steel. Series SB. Table D. Pj-POl P 3 = 47600. 



It is evident from the diagrams that the points are not 

 always very close to the straight lines, so that it is difficult 

 to assign an exact value to " in " for a given series of tests. 

 But when average values are taken for " m," they are found 

 to differ considerably for different tests, even when these are 

 made under very similar conditions. For steel tubes, Guest's 

 "m" varies from about 0*9 to 1*9. The copper tubes give 

 consistent results, but one brass tube gives " m " equal to 

 1*03, and the other has "m" equal to 1-34 ; the points are 

 very irregular. It is evidently not necessary to give a more 

 elaborate method for finding " m" since it varies so much. 

 Mr. Smith's values for steel are 1*09, l'Ol, and 0*775. 



An examination of Guest's results shows that the third 

 principal stress has no appreciable effect on the other stresses 

 at failure. 



Conclusion. — In most cases the deviations from the shear- 

 stress law are opposed to a constant maximum stress, and 

 this is always so with bending. But it is probable that the 

 value of u m" varies somewhat for ductile materials, because 

 there are degrees of ductility. The writer has shown that 

 cast-iron behaves quite differently to a ductile material *, but 

 it does not conform to any exact law. He hopes shortly to 

 publish results which prove that a strictly brittle material 

 iDehaves differently to cast-iron and ductile materials. It 

 is therefore not surprising that the results from ductile 

 materials vary somewhat, and it is desirable that a stress- 

 strain diagram for a tension test of the material should be 

 considered in order to estimate its ductility. It is possible 

 that the behaviour of all materials might be expressed in 

 one form, Pi + mP 3 = constant, in which m depends on the 

 degree of ductility of the material. But in the present state 

 of our knowledge it may be fairly claimed that the shear- 

 stress or stress-difference law expresses the average behaviour 

 of ductile materials under combined stresses, and that the 

 maximum stress and maximum strain laws are not true for 

 ductile materials. 



* Proc. Phys. Soc. vol. xs. 



