A Science-Based Theory of Reliability Founded on Thermodynamic Entropy

Failure data-driven stochastic and probabilistic techniques that underlie reliability analysis of components and structures remain unchanged for decades. The present study relies on a science-based explanation of damage as the source of material failure, and develops an alternative approach to reliability assessment based on the second law of thermodynamics. The common definition of damage, which is widely used to measure the reliability over time, is somewhat abstract, and varies at different geometric scales and when the observable field variables describing the damage change. For example, fatigue damage in metals has been described in several ways including reduction of elasticity modules, variation of hardness, cumulative number of cycle ratio, reduction of load carrying capacity, crack length and energy dissipation. These descriptions are typically based on observable changes in the physical or spatial properties, and exclude unobservable and highly localized damages. Therefore, the definition and measurement of damage is subjective and dependent on the choice of observable variables. However, all damage mechanisms share a common feature at a far deeper level, namely energy dissipation. Dissipation is a fundamental measure for irreversibility that, in a thermodynamic treatment of non-equilibrium processes, is quantified by entropy generation. Using a theorem relating entropy generation to energy dissipation via generalized thermodynamic forces and thermodynamic fluxes, this paper presents a model that formally describes the resulting damage. This model also contains cases where there is a synergy between different irreversible fluxes, such as in corrosion-fatigue damage where the mechanical deformation rate leading to fatigue is coupled with the electrochemical reaction rate leading to corrosion. Employing thermodynamic forces and fluxes to model the damage process, not only enables us to express the entropy generation in terms of physically measurable quantities including stress diffusion and electrochemical affinities, but also provides a powerful technique for studying the complex synergic effect of multiple irreversible processes. Having developed the proposed damage model over time, one could determine the time that damage accumulates to a level where the component or structure can no longer endure and fails. Existence of any uncertainties about the parameters and independent variables in this thermodynamic-based damage model leads to a time-to-failure distribution. Accordingly, such a distribution can be derived from the thermodynamic laws rather than estimated from the observed failure histories.