Engineering structures are often subjected to repeated, cyclic loading rather than a simple static load. It is well established that cyclic loading results in progressive degradation and can lead to catastrophic failures of structures. In this case, the structure fails at load levels that are well below the load levels required to fail the structure under static loading, and is commonly referred to as fatigue failures. Fatigue failures are initiated by imperfections in the structure that develop into micro-cracks followed by slow and steady growing fatigue cracks, “Paris-regime” crack growth.

Predicting fatigue crack growth and fatigue life is an important part of preventing fatigue failure. Up to now, experimental characterization has been the only realistic method to predict fatigue life, but is usually expensive, time-consuming and not always reliable. This dissertation attempts to propose a method to minimize the time required for experimental characterization by investigating numerical modeling techniques of fatigue crack growth. In particular, this work explores the concept of using plastically dissipated energy as a criterion for fatigue crack growth.

At the continuum scale, fatigue crack growth is due to cyclic material degradation in a process zone ahead of the crack tip. For ductile materials, the degradation is associated with plastic deformation, and the plastically dissipated energy is directly linked to the net accumulation of the plastic strain during loadings. The premise of the proposed method is that once the accumulated plastically dissipated energy has reached a critical value, the crack will propagate incrementally. The plastically dissipated energy criterion has previously been successfully applied to study Paris-regime crack growth for selected metals, utilizing the commercially available finite element program ABAQUS. This previous work also included a proposed method on how to establish the critical value of plastically dissipated energy. Here, the hypothesis and numerical scheme are adopted to study Paris-regime crack growth rate for a variety of polymers, including polymers whose Paris-regime crack growth behavior is independent of and those that is dependent on test frequency. Interestingly, the numerically predicted Paris-regime crack growth results are in good agreement with results obtained experimentally for both the frequency-independent and frequency-dependent polymers studied.

To demonstrate the versatility of a numerical scheme that predicts fatigue crack growth, the proposed method is applied to polymer electrolyte fuel cell membranes. In particular, the in-situ crack propagation in the membrane under relative humidity (RH) cycles is investigated. A two-dimensional representative volume element of a polymer electrolyte membrane fuel cell unit with a pre-existing crack is modeled. The model simulates a relative humidity (RH) protocol developed for testing the mechanical durability of the polymer electrolyte membrane. A range of wellestablished experimental observations are studied including crack propagation in unreinforced perfluorosulfonic acid (PFSA) membranes, and crack propagation in expanded polytetrafluoroethylene (ePTFE) reinforced PFSA membranes. The plastically dissipated energy criterion captures all of these observations qualitatively.

These analyses show that the plastically dissipated energy criterion can be used to estimate fatigue crack growth for a range of materials in a variety of engineering structures, and can therefore potentially reduce the cost to improve the reliability of engineering structures.