Endowing Griffith's fracture theory with the ability to describe fatigue cracks
In this paper, a possible extension of Griffith's fracture theory to describe fatigue-induced crack propagation is proposed. To this end, an energy-based model is presented, taking Griffith's model as the point of departure and employing the concept of state-dependent fracture toughness. Therein, fatigue degradation is achieved through a suitable history variable endowed with a functional form that is able to consider crucial aspects of fatigue, including the crack-tip singularity, the identification of fatigue-inducing loading conditions, and mean load effects. Simple paradigmatic examples indicate that the model provides a unified description of different fatigue responses and unveils peculiar regimes in the crack propagation process, always preserving the link to classical fracture mechanics. In this context, analytical results establish a clear relation between Griffith's fracture theory and Paris' law. The proposed modeling framework paves the way for future developments in modern fracture mechanics, e.g., to derive a novel generation of variational fatigue phase-field fracture models suitably rooted in a Griffith-based theory.
© 2023 Published by Elsevier. Roberto Alessi wishes to acknowledge the support of: the Italian National Group of Mathematical Physics INdAM-GNFM; the University of Pisa through the project PRA 2022 69 "Advanced modelling of ultra-lightweight materials and structures"; the Project PRIN 2017 20177TTP3S; the program FSE REACT EU-PONRI 2014–2020. Roberto Alessi is also thankful to Prof. Giovanni Lancioni for insightful discussions on the topic. CRediT authorship contribution statement. Roberto Alessi: Writing – review & editing, Writing – original draft, Methodology, Formal analysis, Conceptualization. Jacinto Ulloa: Writing – review & editing, Writing – original draft, Methodology, Formal analysis, Conceptualization. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.