A numerically efficient phase‐field model for fatigue fracture – 1D analysis. Issue 1 (17th December 2018)

• Record Type: Journal Article
• Authors: Seiler, Martha; Hantschke, Peter; Brosius, Alexander; Kästner, Markus
• Other Names: Müller G. guestEditor.; Ulbrich M. guestEditor.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 18:Issue 1(2018)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2018-12-17
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201800207
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: 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 elasto‐plastic 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.