Time-dependent fracture strength of oriented polymers

A statistical consideration based upon a theory of microscopic molecular kinetics is developed to describe the time-dependent fracture process for oriented polymers. The interrelation between the macroscopic fracture strength and the microscopic behaviors is formulated with the aid of a double Fourier series expansion. The microscopic behavior in the vicinity of a point is expressed in the form of a spherical function which can be expanded into a series of symmetric tensorial terms. Subsequently, the fracture strength of polymers is evaluated in terms of both time and molecular orientation. By taking account of the individual values of the directional fraction of integrity, the time to fracture and the most probable direction of fracture within any volume element in a medium are predicted.