Abstract
Phase field modeling of fracture has been in the focus of research for over a decade now. The field has gained attention properly due to its benefiting features for the numerical simulations even for complex crack problems. The framework was so far applied to quasi static and dynamic fracture for brittle as well as for ductile materials with isotropic and also with anisotropic fracture resistance. However, fracture due to cyclic mechanical fatigue, which is a very important phenomenon regarding a safe, durable and also economical design of structures, is considered only recently in terms of phase field modeling. While in first phase field models the material’s fracture toughness becomes degraded to simulate fatigue crack growth, we present an alternative method within this work, where the driving force for the fatigue mechanism increases due to cyclic loading. This new contribution is governed by the evolution of fatigue damage, which can be approximated by a linear law, namely the Miner’s rule, for damage accumulation. The proposed model is able to predict nucleation as well as growth of a fatigue crack. Furthermore, by an assessment of crack growth rates obtained from several numerical simulations by a conventional approach for the description of fatigue crack growth, it is shown that the presented model is able to predict realistic behavior.
Highlights
The field of cyclic mechanical fatigue is one of the most important branches of post and current research in engineering
As an alternative to conventional crack growth simulation techniques, phase field modeling for fracture has gained attention within the past decade
The modification basically applies to the crack energy dV, where the fracture resistance Gc is degraded by a function of a plastic strain variable, which is accumulated over an increasing number of load cycles
Summary
The field of cyclic mechanical fatigue is one of the most important branches of post and current research in engineering. As an alternative to conventional crack growth simulation techniques, phase field modeling for fracture has gained attention within the past decade. This method provides a very useful tool for the numerical simulation of problems dealing with sharp interfaces, as it does not require procedures for mesh disconnection, element deletion, and re-meshing for an explicit modeling of the interfaces. The formulation is an extension of the model proposed by Kuhn and Müller (2010) for brittle fracture and as a linear elastic material model is considered within our work, the range of validity in terms of the number of cycles to failure NF may be restricted to high cycle fatigue, which covers NF ≥ 1000 for many metallic materials. The driving force for the phase field variable s(x, t) incorporates an additional energy contribution accounting for fatigue damage accumulation due to an increasing number of load cycles
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