Development of a unified fatigue constitutive model: from high to low cycle regime

In a context in which research lines such as optimised design, smart design, use of new materials, weight reduction, etc. are becoming more and more common in the engineering field, techniques that allow for an accurate analysis of the real behaviour of materials, parts and structures are becoming essential. This involves understanding the actual overall response exhibited by a material subjected to a heterogeneous set of external forces, which is only possible by abandoning the reductionist view typically adopted in the design phases in which external forces are amplified, resistance properties are diminished and deterioration phenomena are studied one by one. A clear example of this is the treatment given to the study of fatigue phenomenon, which, in general, is limited to an extrapolation of results obtained in a controlled laboratory environment in order to predict failure, disregarding the process and focusing only on the consequences, thus preventing an integrated study of fatigue with any other inelastic process.

Unlike conventional approaches based on simplified analytical calculations or specific numerical models regimes, a unified treatment of fatigue is proposed in this thesis based on plastic-damage constitutive laws. Using the Finite Element method, a framework is built to capture the response of a material exposed to quasi-static loading states in both monotonic and fatigue regimes, resulting in the accumulation of plastic strains and/or stiffness degradation.

To reach this point, a study of the individual mechanisms of deterioration encompassed within the unified approach proposed in the thesis is carried out. On the one hand, the characterization of the constitutive response associated with plastic-damage processes is undertaken. This analysis is carried out by adopting three approaches that involve different levels of coupling in the description of damage and plasticity, resulting in three laws that are further exploited for their potential to be adapted for the study of fatigue processes, yielding to fluctuating plastic-damage models. On the other hand, the characterisation of the behaviour under fatigue loading conditions is addressed by studying the effects that cyclic loads inducing dominant tensile stresses have in a material, including scenarios where the stress level may exceed the yield limit. Having identified the inelastic processes associated with fatigue, the objective methodology is then constructed to coherently study and quantify the successive deterioration mechanisms to which a material may be subjected.

This sets the guidelines for further work in the simulation of complex processes involving multiple mechanical deterioration phenomena. Thus, this thesis serves as the first step aimed at: defining the foundations, outlining the applications and initiating the exploration of the potential of the proposed approach.