Principle Strains in Cable Sheaths and Other Buckled Surfaces

Equations arc developed for rigorous determination of magnitudes and directions of principal strains in plastic deformation, by means of measurements of rectangular strain rosettes. Application to the study of telephone cable sheath is described. In the course of certain studies of the polyethylene used in the sheath of telephone cable, it was necessary to calculate the magnitudes and directions of the principal strains from data obtained by measurements of the distortion of a square grid which had previously been printed on the surface of the cable. The strains were large, rendering useless the usual expressions for analysis of strain rosette data1. Such large strains are characteristically sustained for a wide variety of high polymeric materials of increasing importance for wire and cable sheathing as well as other structural uses. In this article the requisite formulas are developed. The basic assumptions are: (1) The strains may be large. (2) The strains are uniform over any square of the grid (equivalent to the condition that a square transforms into a parallelogram). (3) The square may be regarded as plane. (4) Two of the principal strains are parallel to the surface. We shall first consider only the two principal strains in the plane of the surface of the cable. Suppose these two strains to be parallel with the x and y coordinate axes, respectively, and that one side of the square is aligned, before straining, at the angle trated in Fig.