490 REPORTS ON THE STATE OF SCIENCE. — 1919. 



Analysis of published experimental results. 



The following diagrams represent a summary of the results cf numerous 

 determinations of the elastic-limits of different metals under two- and three- 

 dimensional stresses. The diagxams for experiments with two-dimensional 

 or nearly two-dimer,sional stresses have been drawn up on the following 

 principle : The intensities of the principal stresses, under which permanent 

 strain was observed, have been expressed as ratios to the single principal 

 stress, which, acting alone as simple pull, produced permanent elongation. 

 The values of these ratios, X and Y, have been taken as the co-ordinates 

 of the points marked on the diagrams. Thus each point represents a 

 comparison between two experiments, one under complex stress and the 

 other under simple pull. The positions of the points record the stress- 

 ratios only, not the absolute values of the stresses. When ascertainable, 

 the elastic-limits of the test-pieces have been used as the basis of comparison, 

 but in several instances the yield points have been compared in the same 

 manner. 



The diagrams also show the ellipses representing constant limiting 

 strain-energy, and the figures corresponding to other hypotheses. The 

 positions of the experimental points, relatively to these loci, afford a 

 convenient and direct check on the validity of alternative hypotheses. 



Figure 18 reproduces that part of the two-dimensional stress diagram 

 which relates to pull, X, combined with a perpendicular pull or push, ±Y. 

 The majority of the experimental points represent Guest's experiments * 

 on steel, brass, and copper tubes subjected to combinations of tension and 

 torsion (quadrant XO = Y), or combinations of tension and internal 

 pressure (quadrant XOY). In the latter experiments, the metal was 

 subjected to three finite principal stresses ; but as the radial pressures 

 that constitute the third stress are small in comparison with the tensions 

 produced in thin-walled tubes, the third stress may be neglected ; or the 

 points may be regarded as slightly in relief above the plane of the paper. 



The values of m quoted for the steel tubi^s, deduced from determinations 

 of E and C, vary between 2-36 and 3-50 — a somewhat wide range ; but 

 it is recognised that this method of measuring Poisson's ratio, alt.hoiigh 

 convenient and theoretically correct, is liable to give erroneous values 

 when even small errors are present in the determination of the moduli. 

 The values quoted for the brass and copper tubes are respectively 20 to 

 2-2 and 2-3. Ellipses have been plotted corresponding to m = 20, 2-5, 

 and 31. 



Inspection of the diagram indicates that the points approximate to 

 the ellipses, at least as closely as to any of the straight-line loci. The 

 points lie outside the square HAEO where the two stresses are both 

 pulls but the one substantially greater than the other ; and fall within 

 the square near the corner A, where the stresses approach equality. And 

 in the same quadrant XOY, the change from steel to brass or copper is 

 accompanied by a general movement in the outward direction, as would be 

 anticipated on the assumption that the limiting strain-energy is constant. 

 In the lower quadrant, the points are widely distributed but generally 



* J. J. Guest, Phys. Society, May 25, 1900. 



