48 G. F. BECKER FINITE STRAIN IN ROCKS. 



Consider now the case in which n is very small and S great. This case 

 also bears some resemblance to a fluid. A cube of material with these 

 qualities would yield to the slightest pressure, and the strain ellipsoids 

 would be flattened to infinitely thin disks. The lines of maximum tan- 

 gential strain would therefore be perpendicular to the line of pressure. 

 To convert this solid into a liquid the elastic limit and the rigidity must 

 both disappear; but this is not of itself sufficient. The flow of a liquid 

 takes place perpendicularly to the direction of pressure; consequently, 

 in the solid which approaches infinitely near to the liquid state, the 

 strain ellipsoids must be infinitely flattened before flow begins. This 

 relation is secured if S is infinitesimal and n is an infinitesimal of the 

 second order. 



In the discussion of strains it was shown that the lines of maximum 

 tangential strain, or the lines on which flow must take place, make an 

 angle with o x, which has a certain value, m. It appears from the above 

 that this angle has a value of 45° for an infinitely rigid solid, even if this 

 solid is perfectly plastic and has no elastic limit, so that it is reduced to 

 molecular powder. For fluids, on the other hand, this angle is zero, and 

 the rigidity is an infinitesimal of the second order. Intermediate values 

 of m answer to solids of moderate rigidity. 



Rupture. — In a homogeneous mass under pressure, rupture must take 

 place on the lines of maximum tangential strain: for rupture is strain 

 carried to such an intensity that cohesion is overcome. A mass in which 

 flow has preceded rupture cannot be regarded as homogeneous, since in 

 the direction in which flow occurs the strength of the mass may be and 

 perhaps must be weakened. In the case of pressure this makes no dif- 

 ference, the tendency to flow and to rupture being in the same direction. 



Tensile stresses produce ruptures by a different method. One can 

 conceive of a mass breaking up by mere dilation or without any relative 

 tangential motion, while purely compressive forces cannot be imagined 

 as leading to rupture. In tensile strains shears cooperate with dilation. 

 Thus, if a bar under tension is homogeneous, the tension will be relieve. 1 

 by the smallest possible fracture, which is in a direction perpendicular 

 to the axis of the bar. If, however, the bar has undergone flow along 

 the surfaces of maximum tangential strain and has thus been sensibly 

 weakened in these directions, it may split diagonally to the axis or 

 irregularly along some other path of least resistance. Thus, a rubber 

 band when suddenly stretched almost always breaks as straight across 

 as if cut with scissors, but a bar of mild steel gradually stretched to the 

 breaking point often splits diagonally, while a wooden bar gives a most 

 irregular surface of fracture. 



In rocks, tensile rupture and fracture by pressure can often be distin- 



