Time derivative equations for mode I fatigue crack growth in metals

Abstract : Predicting fatigue crack growth in metals remains a difficult task since the available models based on the Paris law are cycle-derivative equations (da/dN), while service loads are often far from being cyclic. This imposes a cycle-reconstruction of the load sequence, which significantly modifies the load history in the signal. The main objective of this paper is therefore to propose a set of time-defivative equations for fatigue crack growth in order to avoid any cycle reconstruction. The model is based on the thermodynamics of dissipative processes. Its main originality lies in the introduction of a supplementary state variable for the crack, which allows describing continuously the state of the crack throughout any complex load sequence. The state of the crack is considered to be fully characterized at the global scale by its length a, its plastic blunting p, and its elastic opening. In the equations, special attention is paid to the elastic energy stored inside the crack tip plastic zone, since, in practice, residual stresses at the crack tip are known to considerably influence fatigue crack growth. The model consists finally in two laws: a crack propagation law, which is a relationship between dp/dt and da/dt and which observes the inequality stemming from the inequality of Clausius Duhem, and an elastic-plastic constitutive behaviour for the cracked structure, which provides dp/dt versus load and which stems from the energy balance equation. The model was implemented and tested. It successfully reproduces the main features of fatigue crack growth as reported in the literature, such as the Paris law, the stress ratio effect, and the overload retardation effect
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Submitted on : Wednesday, November 15, 2006 - 2:08:34 PM
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Sylvie Pommier, M. Risbet. Time derivative equations for mode I fatigue crack growth in metals. International Journal of Fatigue, Elsevier, 2005, 27 (10-12), pp.1297-1306. ⟨10.1016/j.ijfatigue.2005.06.034⟩. ⟨hal-00114052⟩



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