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COMPLEX STRESS DISTRIBUTIONS IN ENGINEERING MATERIALS. 325 
(2) the development of permanent strain is associated with a change of physical 
state, from the crystalline to the undercooled liquid or ‘ vitreous’ state. In 
the developed theory the change from the elastic crystalline state to the vitreous 
is held to be essential for the explanation of the gliding movement. 
D1aGRAM FOR ELASTIC-LIMIT : Two PRINCIPAL-STRESSES. 
Fig. 13. 
Strain-energy hypothesis is represented by ellipse (Equation X2-+-Y2—20.X.Y=O0A2 
Poisson’s ratio 7=5). 
Rankine hypothesis for max. principal-stress, figure AlB2A’'3B’'4. 
St. Venant hypothesis for max. principal-strain, figure A5B6A'7B’8, 
Guest’s hypothesis for max. shear-stress, figure AlBA’3B’. 
Becker hypothesis for max. shear-stress and strain, figure A9, 10, 11, B12, 13, A’. 
Before this theory was advanced by Beilby, and developed by Ewing, 
Rosenhain, and others, there was no satisfactory explanation of permanent 
Strain. The difficulty is clearly defined in Professor James Thomson’s state- 
ment, written in 18612: ‘I have not any conception of continuous crystalline 
structure admitting of what may be called ductile bending—that is, bending 
2 James Thomson, Proc. Roy. Soc., 1861. 
