TRANSACTIONS OF SECTION G. 587 
2. The Behaviour of Ductile Material under Torsional Strain." 
By C. HE. Lararp, Assoc.M.Inst.C.H. 
The researches reported in this paper were carried out on different 
diameters of wrought iron, mild steel, and nickel steel, varying from half 
an inch to three inches. Some of the results obtained may be summarised 
as follows :— 
1. For ductile material there is no well-marked yield-point similar to 
that obtained for tension tests. 
2. When the maximum torque is reached failure takes place by the 
specimen commencing first to shear round the periphery over a small annulus 
of material, this shear gradually extending inwards from annulus to 
annulus at a reducing torque until the final fracture of a more or less 
central core in tension, accompanied by a loud report. This failure in two 
stages is brought about by the irregularity in the form of the fracture 
during shearing, whereby a wedging action is set up over the large annulus 
surrounding the core, thus producing compression across the annulus and 
tension in the core. The diameter of the tension core is roughly proportional 
to the diameter of the specimen. For a homogeneous material the relation- 
ship between torque and local twist is given by a rectangular hyperbolic 
curve. 
5. The torque-twist curve throughout the entire test, from the elastic 
limit to the breaking torque, follows a compound interest law, and an 
expression has been obtained by means of which the work to destroy the 
specimen can be calculated ; and the result has been confirmed by integrating 
by means of a planimeter the autographic torque-twist diagram. 
4. For a homogeneous material the work done is proportional to the 
volume, whatever the diameters and lengths of the specimens. 
5. For a homogeneous material the torque at fracture is directly pro- 
portional to the cube of the diameter of the specimen, when the diameter 
varies. 
6. (a) Principal transverse sections by planes at right-angles to the axis 
before twisting remain plane during twisting. 
(b) The unitary structural parts of the material at different radii in a 
given section undergo during torsion the same angular displacement. 
(c) Straight generating lines on the cylindrical surfaces before torsion 
are twisted up into helical lines, defining lines of helical shear. 
(d) Any sector of a homogeneous cylinder is twisted up so as to form 
a sectorial screw. 
(e) The shear stress at any radius and also along the helical lines may 
be calculated from the usual shaft formula. 
(f) For a homogeneous material the angle of the helical lines of shear 
tends to have a constant value for any diameter of a specimen ; consequently 
simple mathematical relationships between the variables of the experiments 
may be obtained. 
7. A specimen under torsion undergoes changes in its dimensions, there 
being an axial elongation following the compound interest law and a small 
reduction in diameter. Further, it would appear that when work is done 
in producing plastic deformation with corresponding increase in elastic 
resilience the volume is slightly increased. 
8. The elastic limit and the elastic resilience of material may be raised 
above the primary limit, which is purely an artificial one produced by 
manufacturing operations, (a) by overstraining, with full recovery of elas- 
ticity to a higher limit by heat treatment at low temperatures; (b) by in- 
definitely long rest after overstraining; (c) by continuous stressing of 
material at a fairly constant load above the primary elastic limit; (d) in 
* Published in Yngineering. 
