Fatigue damage in polycrystals – Part 2: Intrinsic scatter of fatigue life C.A. Rodopoulos a,b, * , G. Chliveros b a Department of Mechanical Engineering and Aeronautics, University of Patras, Rion-Patras 26500, Greece b Materials and Engineering Research Institute, Sheffield Hallam University, City Campus, S1 1WB, United Kingdom Available online 26 November 2007 Abstract Part 2 deals with the evolution of plastic flow resistance with crack growth from its minimum value (fatigue limit) towards its saturated bulk value (cyclic yield stress). The far-field stress level, the geometry of the crack and the grain size distribution of the material are those parameters that control the area of crack tip plasticity and hence the rate towards saturation. The implication of the far-field stress is held responsible for the violation of the similitude concept and the fail- ure of the stress intensity factor to describe conditions of short cracking. However, an engineering tool based on the stress intensity factor and being able to predict the fatigue life of short cracks can be constructed, considering that the distribu- tion of crack growth rates is intrinsically defined by the material itself. The above allows the development of a set of equa- tions able to construct the fatigue life scatter of the material. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Grain size distribution; Crack growth; Plastic zone; Crack geometry; Plastic flow resistance evolution; Fatigue life scatter 1. Introduction In Part 1, the Kitagawa–Takahashi diagram showed the conditions of variable plastic flow resis- tance. The early plateau corresponds to plastic flow resistance equating in value the fatigue limit. For longer crack lengths the plastic flow resistance will increase until saturation to its bulk or macro-scale value is achieved (cyclic yield stress). The point coincides with the long crack threshold. The rate towards saturation will depend on the shape of the crack, the grain size distribution of the material and the crystal structure. Hence, century old state- ments of the type ‘‘under cyclic loading, compo- nents can fail below their monotonic strength given enough loading cycles’’ [1,2] are flawed. In other words, during the early stages of fatigue dam- age the far-field stress will always be larger than the local plastic flow resistance. Such rationale has a great impact on our understanding of the stress-life or S–N curve. The representation of fatigue damage in terms of a single life point creates a misperception of an identical mechanism operating throughout the accumulation of cycles. Reality however is different. During the early stages of growth, the plastic flow resistance will increase with the area of crack tip plasticity. In this work, it will be demonstrated that 0167-8442/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.tafmec.2007.10.001 * Corresponding author. Address: Department of Mechanical Engineering and Aeronautics, University of Patras, Rion-Patras 26500, Greece. E-mail address: C.Rodopoulos@shu.ac.uk (C.A. Rodopoulos). Available online at www.sciencedirect.com Theoretical and Applied Fracture Mechanics 49 (2008) 77–97 www.elsevier.com/locate/tafmec