916 Tests of Brittle Materials under Combined Stress. 



principal stress operates, and although it has been called the 

 minimum principal stress, it is not the algebraical minimum 

 for the whole bar, but only at the point at which rupture 

 commences. 



The notation in fig. 4 is similar to that of fig. 3. It is 

 easy to distinguish the three groups of tests. An increase 

 of the minimum, P 3 , does not regularly affect the maximum 

 principal stress, Pj. The maximum strain is certainly not 

 constant for a particular bar, and varies more than the 

 maximum principal stress. Although the points are very 

 irregular in this diagram, they are not more so than those 

 usually obtained for a ductile material. 



The angles between the surfaces of the fractures and 

 the axes of the bars were measured, and agreed with tho?e 

 -of the planes of maximum stress even better than in 

 the case of the earlier tests on cast iron. For example, in a 

 pure torsion test the angle which the plane of maximum 

 stress makes with the axis of the bar is 45°. The corre- 

 sponding angles measured from the fractured surfaces in 

 five pure torsion tests were 43, 46, 44, 44, and 44 degrees. 

 It was possible to measure the angles very accurately because 

 the fractures were wonderfully clean, and as true as if the 

 edges had been cut with a tool. 



Conclusion. 



The tests show that the maximum principal stress is the 

 best criterion of strength for a brittle material under combined 

 stress. 



It is interesting to compare the strengths of the bars before 

 and after hardening. None of these specimens were tested 

 unhardened, but other steel bars, of exactly the same size, 

 yielded at 2400 lbs. inches torque, or 2660 lbs. inches 

 bending moment*. The values for the present material 

 should probably be rather higher. It therefore appears that 

 when the bars are made very hard the bending moment 

 which they are capable of withstanding without fracturing 

 is slightly greater than that at yield in the unhardened con- 

 dition. But sometimes the strength to resist bending is 

 diminished by the quenching. Similarly, as an average 

 result, it may be stated that a hardened bar can withstand 

 about double the torque which would cause it to yield when 

 in its ductile state. 



* Proc. Phys. Soc. London, vol. xx. ; also Phil. Mag. Dec. 1906. 



