THE MECHANICAL INTERPRETATION OF JOINTS 709 



such tendency could be inferred from these joints, which intersect 

 uniformly at an angle close to 60°, with the obtuse angle facing 

 in the direction of the tensile stress. 



II. hartmann's law 



Following the clue given by these observations, the author 

 became acquainted with a book published in 1896 in Paris by 

 L. Hartmann under the title Distribution des deformations dans 

 les metaux soumis a des efforts,^ containing a wealth of experimental 

 data and a fascinating discussion of the lines forming on the sur- 

 faces of metals when strained beyond the elastic limit, known as 

 Liiders' lines.^ 



When a highly polished plate of metal is subjected to a very 

 gradually increasing simple tensile stress, the first permanent 

 deformation is accompanied by the sudden appearance of one or 

 several delicate straight lines or bands cutting in an oblique direc- 

 tion across its surface. Suitable illumination shows them to be 

 depressions. When the stress is further increased, the existing 

 lines widen and new ones appear, forming two conjugate systems 

 of oblique lines, symmetrical to the direction of maximum stress 

 and intersecting at a constant angle which in most metals (and 

 rocks) is greater than 90°. •^ This angle remains unchanged 

 with growing tension and is thus independent of the intensity of 

 the stress. The final rupturing may entirely or partly follow these 

 lines or cut across them at right angles to the tension. 



Under compression, similar systems of lines form, but now 

 the angle of intersection bisected by the direction of the compressive 

 stress, for most rocks and metals, is smaller than 90°, and for the 

 same material is the supplement of the one obtained under tension. 



' Berger-Levrault, Paris, 1896. 



^ Called after Liiders of Magdeburg who first described them iuWy in i860, 

 "tjber die Ausserung der Elastizitat an stahlartigen Eisenstaben und uber eine beim 

 Biegen solcher Stabe beobachtete Molekularbewegung, " Dingier' s Polytech. Jour., 

 Vol. CLV (i860), p. 18 (not seen). 



3 Ten good illustrations of strips of low steel showing yield lines developed under 

 tensile stress, are given in H. Marten's Handbook of Testing Materials (translated 

 by Gus. C. Henning), John Wiley & Sons, N.Y., 1899, Vol. I, PL i, Figs. 3, 5, 12, 

 14-20. 



