# DoITPoMS

The creeping coil experiment - variable stresses in a single specimen

In order to determine the value of n from a single experiment, it is necessary to have a range of stress levels acting within a single specimen. This is achieved by making the sample into a coil. The stress is provided by the weight of the coil itself, so that the upper part of the coil experiences more stress than the lower parts.

The stress in a particular turn of the coil is proportional to its number, N, where the turns are numbered beginning from the bottom turn and ending at the top. The shear stress τ in each turn varies from zero at the centre of the turn (axis of the coil) to a maximum value at the edge of the coil, given by:

The coil is then allowed to creep over a fixed amount of time (e.g. one minute) and at the end of this time the spacings, s, between the turns are measured giving information about the dependence of strain rate on stress.

The local shear strain γ in each turn is given by:

The average local strain rate is thus related to the spacing between turns, s, and the time, t, by:

It should be noted that, strictly, the above analysis applies only while the material remains elastic. As with all cases in which a moment (bending or twisting) is applied, such that the stress distribution is non-uniform, the situation becomes more complex after the onset of plastic deformation. The distribution of strain remains linear along the radius of the wire, but the associated distribution of stress tends to become more complex. For the creeping coil geometry, papers have been published covering various aspects – eg see IG Crosland et al, “The Use of Helically Coiled Springs in Creep Experiments with Special Reference to the Case of Bingham Flow”, J. Phys. D: Applied Physics, vol.6 (1973) p.1040-1046, and Measurements of Creep at High Temperatures using Helical Springs, FD Boardman et al, J. Strain Analysis, vol. 1 (1966) p.140-144. In fact, provided primary creep can be ignored (which is often doubtful), the procedure described here should be reasonably accurate as a method of estimating the stress exponent, as long as it is of the order of unity, ie not very large.