Failure criteria for polymeric solids

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Abstract
A theory for predicting the stress–strain characteristics of polymeric solids is developed in terms of a description of microdefect formation. The process of irreversible change in these solids is assumed to be a combination of nucleation of submicroscopic defects at stress inhomogeneities and their subsequent growth to macroscopic dimensions. Straining results in the generation of crazes and cracks which can lead to catastrophic failure through either a general yielding of the material or by brittle fracture. It is assumed that nucleation of submicroscopic defects is an activated process and that defect growth is one‐dimensional and linear. The total strain is expressed as the sum of an elastic recoverable strain and a nonlinear, nonrecoverable strain, and expressions are obtained for the stress as a function of time, temperature, and loading history. The criterion for yielding is defined in terms of a gross volume change associated with cavitation within crazes. The sum of the normal Poisson expansion plus this additional volume change leads to a deflection of the stress–strain curve. The criterion for brittle failure is defined in terms of a critical defect size. If the defects grow to their critical size before the stress–strain curve reaches a maximum, brittle failure occurs. The parameters of the resulting model are calculated for polyphenylene oxide polymer based on constant rate of loading experiments, and then the general creep behavior, including the time required under constant load for cold flow, is predicted. Experimental data are shown to agree with these predictions.

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