THE MECHANICAL INTERPRETATION OF JOINTS 713 

 III. hartmann's law applied to experimental and field 



OBSERVATIONS 



Hartmann's law enables the geologist as well as the mechanical 

 engineer to reconstruct the position of the principal axes of stress 

 in any given body subject to mechanical deformation— be it a test 

 specimen in the laboratory or the exposed portion of a fractured 

 rock-mass^ — by analyzing from point to point the position of the 

 planes of shearing. The direction bisecting the acute angle 

 formed by the planes of shearing corresponds to that of the greatest 

 principal axis of compressive stress, while the bisectrix of the 

 obtuse angle gives the direction of the least stress, which in most 

 cases represents active tensile stress. The direction of the inter- 

 mediate principal stress coincides with the line of intersection of 

 the two planes of shearing. 



It is essential, however, to realize at the start the limitations 

 of this law. 



a) It applies only to brittle substances. 



b) Not all lines of fracture are lines of shearing. Brittle 

 materials, such as cast iron or hard steel, and most rocks under 

 simple tension habitually fail along planes of fracture at right 

 angles to the direction of maximum tensile stress.^ Soft steel, on 

 the other hand, fails along inclined planes of shearing under tension 

 as well as under compression. 



c) The position of the planes must be studied in space, not 

 in any accidental plane of exposure. 



d) The principal stresses inferred from them need not be 

 identical with any real stresses, but may be only the resultants of 

 the combined action of several stresses ("equivalent" stresses). 



We may now proceed to test the usefulness of Hartmann's 

 law by applying it to a few selected experimental data and geo- 

 logical field observations. 



I. Compressive stress vertical, tensile stress horizontal. — a) When 

 a cylindrical test piece is subjected to compression beyond the 

 elastic limit, Liiders' lines make their appearance on its surface, 

 forming a characteristic pattern of symmetrical intersecting spiral 



' See, for instance, A. L. Jenkins, "Combined Stresses," Jour. Amer. Soc. Mech. 

 Engineers (19 17), p. 696. 



