ABSTRACT

The goal of this Thesis is to propose a theoretical formalization of the high cycle fatigue process in ductile 
metals. That is a very complex interdisciplinary field, with many branches in various technological fields and 
with a very large and historically extensive experimentation, especially focused on metals and simple stress 
states. It is therefore considered that this thesis would include primarily the references and theoretical 
elements necessary for a suited subsequent exposure of the phenomenology, the associated modeling and 
the essential contributions of the research in this field. This objective is developed in the first chapter.

The first two sections of Chapter 2 are intended for the description of the current state of empirical 
modeling of high cycle fatigue in uniaxial processes and their damage accumulation. The third section of 
this chapter is a description of the current state of research on fatigue in general, and, specially, on the 
generation and evolution of damage, with particular reference on his thermodynamic background. The 
fourth section of this chapter presents a theoretical proposition appropriate to formalize such previous 
results and to develop research that is intended. Therefore, this proposed theoretical modeling is 
considered as a contribution, but not an essential contribution of this thesis, since it is an established ad 
hoc proposal to meet its research objectives.

Chapter 3 provides the first substantial contribution of this thesis. This chapter proposes a new theoretical 
modeling of damage that does not include an internal variable independent of damage. Indeed, it exposes 
the weakness of the models founded on the assumption of that hypothesis. Therefore, in this Thesis it is 
considered that the associated variable of the damage evolution cannot be other than the real tension in 
every moment and it is exposed a new damage formalization based on this concept. It has been found that 
the proposed model is a generalization of the classical damage model when it is applied to uniaxial 
processes and that it further solves the intrinsic difficulty that the classical damage model presents in 
anisotropic stress states resulted from any external action, checking its suitability with previous results 
obtained from the models with internal independent variables of damage.

Chapter 4 is intended to present a second essential contribution of this work, the proposal of new energy 
multiaxial hybrid criterion for initiation of fatigue, or damage. Then, it is defined a new boundary surface 
damage growth and its temporal evolution under equations formally equivalent to the plastic deformation 
evolution equations. This general approach has a great alignment with previous diverse experimental 
results multiaxial hybrid. The new model proposed in Chapters 3 and 4 shows an absolute formal 
parallelism with the theoretical model of plastic deformation process, thus allowing the development of 
simpler models of coupling damage with elastic or plastic deformations.

Chapter 5 introduces the concept of stress concentration, inherent in the evolution of damage by crack 
advance, and a theoretical description of accumulation of damage in high cycle fatigue is proposed and the 
phenomenology described by Wöhler curves is reproduced. Moreover, the stress concentration approach 
proposed here can be extended to aspects relating to rigidity and an application is developed in the case of 
a straight structural bar element. A final contribution is proposed in this thesis, with the proposal of a 
structural estimation model that includes joint stiffness due to high cycle fatigue.

Chapter 6 presents the analysis of the partial conclusions established in the development of this work and 
the formulation of possible further research.