BELA VIOUR OF MATERIALS IN TESTING MACHINE 173 
s in in the neighbourhood where the fracture will occur, and the 
ubsequent elongation is mainly in this neighbourhood. But the length 
ver which the local extension takes place is greater the larger the area of 
the cross section of the specimen, and is approximately proportional to 
the diameter, or, in the case of non-circular sections, to the square root of 
the area of the cross section. 
Professor Unwin has shown * that within a considerable range of 
- dimensions, the percentage elongation ¢, on a gauge length s ie a specimen 
leh ® cross sectional area is a, is given by the equation, e= =" = b, where 
re vi s represents the local extension, and ) the general extension, ¢ and } 
og. x constants for a given material. 
. he following are a few values for c and 0, given on the authority of 
Professor Unwin :— 
4 Material. ¢. b, 
| Mild steel plates not es thick, rene Ml te ene 18 
Gun-metal (cast) . : - . 8°3 10°6 
| Rolled brass . : . : : < 4 is - | 101°6 97 
ee CODER ws gee el OS Ppa | 84 0°8 
| p Annealed ee. eee al ied s, ooh oY Ae 35 
- 163. Position of Fracture in a Tension Test Bar.—When a test 
bar is gripped at the ends the outer surface of the bar at the ends first 
receives the tension, and this tension is transferred towards the axis of the 
bar by means of the longitudinal shear stresses between the different 
co-axial layers of material. It is therefore evident that at cross sections 
the ends of the bar the tensile stress will be greatest at the 
ae e, and that it will diminish towards the centre. But at sections 
urther and further from the ends the distribution of the tensile stress will 
e more and more nearly uniform. Hence the section at which the 
fires most nearly uniform will be at the centre of the length of 
When a ductile material is loaded in tension it stretches, and the 
tendency to stretch is greatest where the stress is greatest. But where 
* h occurs there must be a contraction of cross section, and the 
greater the tendency to stretch, the greater is the tendency to contract. 
Now if the stress is greater on the outside of a bar than on the inside, 
ie tendency of the outside to contract is opposed by the inside, where 
e tendency to contract is less. Hence it is evident that contraction 
be greatest where the stress is most nearly uniform, and this is at 
@ centre of the length of the bar. But fracture will oceur where the 
Beeection is greatest, therefore a bar of ductile material of uniform 
ength should break at the centre, and this is what generally happens. 
If the bar is not of uniform strength throughout it will of course 
tend to fracture at its weakest section, but it will not break there unless 
the difference between its strength at that section and its strength at the 
_ ™ Proceedings of the Institution of Civil Engineers, vol. cly. p. 180. 
