Abstract
In this paper, a framework for the simulation of crack propagation in brittle and ductile materials is proposed. The framework is derived by extending the eigenerosion approach of Pandolfi and Ortiz (Int J Numer Methods Eng 92(8):694–714, 2012. https://doi.org/10.1002/nme.4352) to finite strains and by connecting it with a generalized energy-based, Griffith-type failure criterion for ductile fracture. To model the elasto-plastic response, a classical finite strain formulation is extended by viscous regularization to account for the shear band localization prior to fracture. The compression–tension asymmetry, which becomes particularly important during crack propagation under cyclic loading, is incorporated by splitting the strain energy density into a tensile and compression part. In a comparative study based on benchmark problems, it is shown that the unified approach is indeed able to represent brittle and ductile fracture at finite strains and to ensure converging, mesh-independent solutions. Furthermore, the proposed approach is analyzed for cyclic loading, and it is shown that classical Wöhler curves can be represented.
Highlights
Engineering structures often consist of various different materials exhibiting a brittle or ductile behavior
Whereas fracture at the macroscale has to be considered to evaluate potential failure of the tool, sub-critical crack propagation under cyclic loading is important at the microscale as it is mostly responsible for wear in terms of surface spalling
In order to show the performance of the proposed approach for the simulation of crack propagation at finite strains, several numerical calculations are analyzed which are based on rather classical benchmark problems
Summary
Engineering structures often consist of various different materials exhibiting a brittle or ductile behavior. Whereas fracture at the macroscale has to be considered to evaluate potential failure of the tool, sub-critical crack propagation under cyclic loading is important at the microscale as it is mostly responsible for wear in terms of surface spalling This is just a representative example for a variety of engineering applications where brittle and ductile fracture play a role. In the context of erosion algorithms, the first consistent nonlocal approach enabling mesh-independent calculations, the so-called “eigenerosion,” was proposed in [27], based on the variational eigenfracture formulation proposed in [34] This eigenerosion approach is based on the Griffith criterion for crack propagation and achieves its mesh independence from the regularization of the crack area by evaluating a defined spatial -neighborhood. This asymmetry is necessary for simulations in which the load direction changes, for example for the simulation of a specimen under cyclic loading, as it is essential for the calculation of the Wöhler curve
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