Introduction

Outline

This Thesis provides a collection of stress-life (S/N) models for fatigue life evaluation of both pristine and notched metallic components. The document is subdivided into five Chapters, the first being a Literature Overview of fatigue in general, and, in the specific, of the tools needed in the subsequent Chapters. In Chapter 2 the “crack like to blunt” notch transition is adapted to the stress-life approach using the theory of the critical distances, therefore a new S/N curve to model this transition is defined. Chapter 3 relies on the new S/N curve model for variable amplitude fatigue loading by demonstrating that fatigue life assessment under these conditions can be performed through a constant shift of the Wöhler curve if adopting a linear damage accumulation rule. The method is quite general since there is no need of hypothesizing specific constraints on loading history as the shift accounts for mean stress effects, albeit suffering from the weaknesses of the underlying linear damage accumulation rule. The models proposed have been experimentally validated through the SAE Keyhole test program data, publicly available online at https://www.efatigue.com/benchmarks/SAE_keyhole/SAE_keyhole.html.

Chapter 4 discusses the limits of validity of a linear damage accumulation rule, giving special attention to its relationship with crack propagation laws of the generalized Paris type. Specifically, the Chapter proves that supposing a linear damage accumulation exactly corresponds to integrating a power law of the stress and the crack size in the form of Paris’ or Walker’s law. Ergo, this result is valid even for non-zero mean stress, yet neither accounting for load sequence nor for crack closure is considered. Thenceforth, despite some clear limitations, no difference in terms of accuracy is expected between the application of a linear damage accumulation rule vs. integration of a crack growth equation. Finally, Chapter 5 presents an investigation of the advantages in the application of a (maybe more realistic) four parameters S/N curve directly obtained postulating that the two parameters curve corresponds to the first derivative of the former one in its inflection point. The accuracy of the new curve is compared with the former employing an experimental campaign fatigue data on steel and aluminum alloy conducted by the National Advisory Committee for Aeronautics (NACA).

Scope

This work has been conceived to develop fast fatigue tolerance evaluation models for both notched and pristine components under constant, but principally variable amplitude loading. We intended to keep every approach as slender as possible to provide immediate analytical techniques for preliminary fatigue design hence possibly avoiding finite elements model evaluations. All the work is devoted to the concept of practical applicability of the models proposed, both in academia and possibly in industry.

The first part of the work was motivated by the initial observation that Gaßner curves available in Literature seemed to have the same slope as the corresponding Wöhler curves. This was demonstrated to be valid, in principle, in one only limiting case: smooth specimen whose fatigue behavior can be described by a pure power-law S/N curve (no fatigue limit), and with a zero mean stress loading history. So, to gain some generality, we initially extended the model to notched and cracked components, then we focused on the spectrum and demonstrated that the formulation keeps its validity even when generic non-zero mean stress loading histories are applied. Finally, we have been able to introduce the concept of fatigue limit in the discussion by slightly modifying the damage accumulation rule.

In the last part of the work, we focused the attention on a more complicated S/N curve model, yet widely used in industry: Weibull’s law. In this regard, we proposed an analytical model relating this equation with the more common truncated power-law and built a robust and fast-fit of experimental data.