Principle Strains in Cable Sheaths and 

 Other Bnckled Surfaces 



By I. L. HOPKINS 



(Manuscrii)t Hccoived February 25, 1952) 



Equations are developed for rujorous determination of magnitudes and 

 direetions of principal strains in plastic deformation, by means of measure- 

 ments of rectangular strain rosettes. Application to the study of telephone 

 cable sheath is described. 



Ill the course of certain studies of the polyethylene used in the sheath 

 of telephone cable, it was necessary to calculate the magnitudes and direc- 

 tious 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 cal)le. The strains were large, rendering useless the usual 

 expressions for analysis of strain rosette data . Such large strains are 

 characteristically sustained for a wide variety of high polymeric ma- 

 terials of increasing importance for wire and cable sheathing as well as 

 other structural uses. In this article the reciuisite formulas are developed. 



The basic assumptions are: 



(1) The strains maj^ 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 

 llie .r and y coordinate axes, respectively, and that one side of the square 

 is aligned, before straining, at the angle willi the .v axis. This is illus- 

 trated in Fig. 1. 



Let ex = maximum principal strain 

 Cy = minimum principal strain 

 \x = I + ex 



\ = 1 ->r Cy 



1 Cf. for example, Max Frocht, "Photoelasticitj-," 1, p. 37, 1941. 



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