Abstract
It is intended in designing the present model to make clear the macroscopic features of nearly homogeneous materials when they yield to simple tension and break down leaving many small cracks.
(1) Let us assume that a certain material contains only one part where the defect structure is mechanically of nonlinear character, and that in that defective part Young's module E is dependent on the relative elongation ε as is to be represented in the formula E=E0(1-βε) where E0 and β are constant. Then it is found that the material breaks down at stress E0/4β and that β is nearly in the range 10∼350 with glass, several metals and wood. The physical import of the present model is shown in the interatomic potential curve for the one dimensional single crystal.
(2) Or let us suppose, on the other hand, a number of areas of defect structure in the material for so many small cracks, which are considered as nuclei respectively of the defect, their distribution in the material can be expressed in a nonlinear factor as function of the coordinates to be defined by three parameters.
(3) The defect structure seems to consist of various common kinds in the case of single crystals, but in the case of polycrystals, of cavities of size described as of optical order.
It is found that the present model will efficiently explain macroscopic structure in the material from the distribution of the defect structure.
