Abstract
The study at hand introduces a new approach to characterize fatigue crack growth in small strain linear viscoelastic solids by configurational mechanics. In this study, Prony series with n-Maxwell elements are used to describe the viscoelastic behavior. As a starting point in this work, the local balance of energy momentum is derived using the free energy density. Moreover, at cyclic loading, the cyclic free energy substitutes the free energy. Using the cyclic free energy, the balance of cyclic energy momentum is obtained. The newly derived balance law at cyclic loading is appropriate for each cycle. In the finite element framework, nodal material forces and cyclic nodal material forces are obtained using the weak and discretized forms of the balance of energy momentum and cyclic energy momentum, respectively. The crack driving force and the cyclic crack driving force are determined by the nodal material forces and the cyclic nodal material forces, respectively. Finally, numerical examples are shown to illustrate path-independence of the domain integrals using material forces and cyclic material forces. The existence of the balance of energy momentum and cyclic energy momentum are also illustrated by numerical examples.
Highlights
A lot of structures or materials exhibit stress relaxation and creep
In case of fatigue crack propagation, a continuum is subjected to cyclic loading, a new balance of energy momentum is derived in our previous work Khodor et al (2021) and is called balance of cyclic energy momentum
The focus of the study at hand is mainly on small strain viscoelastic solids, that are characterized by Prony series with n-Maxwell elements
Summary
A lot of structures or materials exhibit stress relaxation and creep. To describe this behavior, viscoelastic material models are employed. In the work Nguyen et al (2005), material forces are derived for small strain linear viscoelastic solids, that are characterized by the Prony term with one Maxwell element. Ochensberger and Kolednik (2014) derived the elasto-plastic cyclic J -integral ΔJ ep using configurational forces, that is appropriate for fatigue crack growth at non-proportional loading. In a further work of Ochensberger and Kolednik (2015), an appropriate parameter known as the active plastic zone elasto-plastic cyclic J -integral ΔJaecptPZ is derived This parameter is able to depict the overload effect in elasto-plastic materials. The aim of the study at hand is to derive a pathindependent domain integral to describe fatigue crack growth in viscoelastic solids at cyclic loading.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
