Fatigue fracture in ductile materials, e. g. metals, is caused by cyclic plasticity. Especially regarding the high numbers of load cycles, plastic material models resolving the full loading path are computationally very demanding. Herein, a model with particularly small computational effort is presented. It provides a macroscopic, phenomenological description of fatigue fracture by combining the phase-field method for brittle fracture with a classic durability concept. A local lifetime variable is obtained, which degrades the fracture resistance progressively. By deriving the stress-strain path from cyclic material characteristics, only one increment per load cycle is needed at maximum. The model allows to describe fatigue crack initiation, propagation and residual fracture and can reproduce Paris behaviour. arXiv:1903.06465v3 [cond-mat.mtrl-sci] 23 Oct 2019 Recently, several propositions to extend the phase-field method to fatigue [16,17,18,19,20] have been published. Representatively for the range of different approaches, two models which are able to reproduce Paris behaviour shall be highlighted here: Carrara et al. [19] introduce a phase-field model for fatigue fracture in brittle materials. The basic idea of their approach is that due to repetitive loading the crack resistance decreases, allowing cracks to evolve even far below the static crack resistance. The fracture toughness is modified depending on a measure of locally accumulated elastic strain energy density. Mesgarnejad et al. [20] follow a similar approach, but link the lowering of the fracture toughness also to the phase-field, localising the degradation to the vicinity of the crack tip.Although the authors use different approaches, they are not yet overcoming one key challenge inherent to fatigue crack initiation and propagation: The immense computational effort related to the high number of load cycles. This issue is addressed in the present paper. In particular, we introduce an efficient phase-field model of fatigue fracture in ductile materials, such as metals. Analogously to [19], it is based on the reduction of the critical fracture energy, but uses a different local fatigue measure. In contrast to brittle materials, fatigue crack propagation in ductile materials is caused by cyclic plastic deformations. The straightforward way to treat the problem with an elasto-plastic material model is numerically expensive. Therefore, a different approach is chosen. With the help of the LSA, a local lifetime variable is introduced, accounting for cumulative elasto-plastic deformations. Since the stress-strain path within a load cycle is derived from material curves from cyclic experiments, the explicit simulation of each load cycle would be redundant and can therefore be avoided, saving computational costs. In other words, instead of introducing a ductile phasefield model, an elastic, brittle phase-field formulation which considers the elasto-plastic origins of fatigue is presented. As cracks are described on a macroscopic scale, microscopic effects are...

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Fatigue loads and fatigue failure come along with high numbers of load cycles. This makes the simulation of fatigue fracture computationally very demanding, if each load cycle is simulated comprehensively with its loading and unloading phase. We present a numerically efficient method for the simulation of fatigue fracture, which avoids resolving the loading path and instead requires only one increment per load cycle at most.We combine the phase-field method for brittle fracture with a classic fatigue concept for lifetime calculation of components, which is applied to the material point here. A local lifetime variable is obtained, which we use to modify the material resistance incrementally in order to consider the progressive weakening of the material. Since we make use of an elastoplastic revaluation technique, a linear-elastic material model is sufficient in the simulations. Furthermore, the phase-field method allows to describe fatigue crack initiation as well as propagation.In this contribution we describe the method's framework including the mentioned lifetime concept, followed by a proposal for a simulation scheme. Finally, results -for now limited to the one-dimensional case and constant load amplitudes -are discussed.

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