High and low cycle fatigue failure effects of metals predicted automatically from innovative elastoplastic equations wit
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O R I G I NA L A RT I C L E
Lin Zhan · Si-Yu Wang · Hui-Feng Xi · Heng Xiao
High and low cycle fatigue failure effects of metals predicted automatically from innovative elastoplastic equations with high-efficiency algorithms Professor Dr. Holm Altenbach on the occasion of his 65th birthday
Received: 13 July 2020 / Accepted: 21 October 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract New finite strain elastoplastic J2 -flow equations with no reference to the yield condition are proposed for the purpose of simultaneously simulating low-to-ultrahigh cycle failure effects of metals. As inherent response features of such new equations, the entire responses up to eventual failure under cyclic and non-cyclic loadings of constant and variable amplitudes are automatically predicted, in a direct sense without involving any additional damage-like variables and any ad hoc failure criteria. The thermodynamic consistency is ensured by demonstrating that the intrinsic dissipation is identically non-negative. Furthermore, a high-efficiency algorithm for integrating the elastoplastic rate equations is established toward bypassing very time-consuming numerical procedures in treating cyclic responses with high and even ultrahigh cycle number. With numerical examples, model predictions are shown to be in good agreement with fatigue failure data for low, high and very high cycle numbers, and the new algorithm is shown to be much faster and far more efficient than usual integration procedures. Keywords Metals · Fatigue failure · High cycle · Low cycle · Ealstoplastic equations · Unified simulation
1 Introduction The fatigue behavior of metals under repeated loading conditions is known to be mainly responsible for failure effects of various key metal components and parts, such as those in aircrafts, automobiles, turbine engines, nuclear engineering and offshore engineering, etc. For the purpose of effectively assessing reliability and safety issues concerning such components and parts, considerable efforts have been devoted to investigations into failure effects of metals under cyclic and non-cyclic loading conditions. In the past decades, different approaches have been established toward simulating metal fatigue failure effects from various standpoints. Details may be found in recent surveys, e.g., in [1] for certain typical topics in fracture and fatigue, in [2] for fatigue damage and crack growth, in [3] for the theory of critical distances, in [4] for failure criteria for mixed-mode fatigue crack growth, in [5] for fatigue behaviors of nano-crystalline metals, in [6] for microstructural mechanisms, and in [7] for recent developments in simulating damage effects and related failure mechanisms, as well as the references therein. Representative samples of recent studies with various approaches may be found, e.g., in [8–26]. Of them, fatigue effects were studied in [8–10,13,15,17–21] and damage effects were treated in [11,12,14,16], and, in particular, high cycle fatigue effects were investigated in [22–26]
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