str (90)

Q.S ELASTICITY m

o duli

load increments, so that the I

appear as shown in Fig. 18.

fading

V.

%

Since n (shear modulus) is by definiti₀^^®

follows that n falls steadily, whether one 1 ^ it or unloading; but that when the sense of th ing is changed from load to unload, or ajgS then there is a sudden large rise in moduły materials which do not change their vo^’

^e %

Fig. i9-

■

compression or extension (Poisson s ratio = 0-5) the shear modulus n = 1/3 Young’s modulus ; and the shearing stress in a section where the shearing strain is equal to the tensile strain B 1/3 loading or tensile stress.¹

If there is also non-recoverable flow, the curve will appear as shown in Fig. 19.

¹ The effect of stress on all the elastic moduli for big strains, in cases where hysteresis and other anomalies are absent, is fully discussed by Birch. The shearing stress here used is not the maximum shearing stress, which is equal to 1/2 of the tensile stress, and operates at an angle of 45⁰. The author is indebted to Drs. R. K. Schofield and M. Reiner for making this point elear.

rurves very much like this are given by Nadai

°soft metals, for flour dough by Schofield and c° ott Blair, in a slightly different form for cheese g Davis, and for compressed foundation soils by

Terzdghi.    .

The author was once asked to detemune the viscosity of some rods of bitumen. These were clamped at one end, so as to hang vertically, and a suitable weight was hung from the lower ends. After a few days the weights were removed, the extensions were measured, and no recovery was apparent. A further few days’ resting resulted in the complete recovery of the apparently plastic flow. The materials were not flowing, but merely showed a very slow elastic after-effect. Over-stretched muscles sometimes behave similarly.

A good deal of work has been done in Russia on the loading of soils, especially of foundation soils. Pigulefskii is developing a theory of shear in soils, and the building engineers have done a great deal of work on this in connection with the subsidence of buildings.¹ There has also been extensive work on the flow of water through soils and other porous materials. This is important in drainage, irrigation and erosion problems.²

Kuselbach has worked on the hysteresis pheno-mena in cotton threads: and Clayton and Peirce have demonstrated the anisotropic naturę of cotton by finding an anomalous ratio of the bending to the torsion modulus. This ratio should be 2-5 for isotropic materials, but it differs considerably for cotton at different humidities. In generał, the modulus falls with increasing humidity. The torsion modulus, at least, shows hysteresis.

i See Hogentogler’s I Engineerin1 Properteof Soils.” a The reader is referred to a recent text-book by Muscat.