AVERAGE MECHANICS AND GEOMETRY OF FRACTURE STRAIN.*
Granted that the material of the solid is statistically homogeneous and isotropic in all relevant qualities, it is reasonable to suppose that so far as the material itself is concerned it is as likely to yield new surface by fracture at one physical point as at another and that no orientation of the surface is preferred. Assume that such a material composes an ensemble of solids. Through the fracturing action of arbitrary external forces new surface is produced. Failure is supposed to initiate only by parting along a surface of positive tension. 3, ~, 5 The material is perfectly elastic and obeys Hooke's Law up to the point of failure. There is no friction or hysteresis and the temperature of the solid is constant and far from its melting point. All displacements are small. It is then asked what are the necessary average conditions on the displacements and forces at the boundary, and within the solid, if the new surface produced is random in distribution and orientation. Given these conditions it is asked what the expected form of new surface and fragment will be.
To avoid repetition, the term " point " will be understood as the physical point. Continuity is a property of the macroscopic or mean stresses and motions. About these mean values random fluctuations may be discoverable if we can exercise the necessary discrimination within the physical point, and choose to do so. To the relative order of precision defined by the physical point and the mean diameter of the * The experimental work is understandable without a prior reading of this attempt to anticipate the shape and size probabilities. 673 C.C. LIENAU.