Brittle Materials under Combined Stress. 



915 



ellipse. Three such mean curves have been drawn in, one 

 for each group of specimens. Considering the difficulties 

 encountered in making the tests, the points lie fairly evenly 

 about the curves. The deviation is most noticeable for the 

 group which contains bars 6 and 11. 



The author has expressed the opinion that the behaviour 

 of all isotropic, homogeneous materials may be expressed in 

 one form, that P 1 ~77iP 3 = constant, at the failure of the 

 material, in which equation " m " is a constant whose value 

 depends on the degree of ductility of the material*. P 2 

 does not appear in the equation because it is zero for the 

 system of loading adopted, but even in the more general 

 case, in which there are three principal stresses, the available 

 evidence indicates that the intermediate stress P 2 does not 

 affect the values of F r and P 3 at failure, with the loadings 

 w^hich are met w r ith in engineering practice. The advantage 

 of the above equation is that when m = 0, it represents the 

 maximum principal stress hypothesis, when ?>i=77, it indicates 

 a constant maximum strain, and m=l corresponds to the 

 stress difference law. The maximum and the least principal 



Fig. 4. 



Hardened Cast Steel 

 Maximum ^Minimum PrincipalStresses 



ilk 



l2CX v 



*iL 



3LX 



x*c. 



XIIC 



X9C 



X4L 



-a 



-6 -5 -4 "3 -2 



Minimum Principal Stress /ioooo 



K 



\zo 



z: 



110% 



100 £ 



90S 



9HX °3 

 I2HX 2 



^ 



IICX 



50 



-/ 



LBS/S.IN. 



40 



stresses at rupture have been plotted in fig. 4. This least 

 principal stress is the P s at the point at which the maximum 



Proe. Phys. ISoc. Loudon, vol. xxii. ; also Phil. Mag. Jan. 1910. 



