An engineering model for propagation of small cracks in fatigue

Abstract The propagation of small cracks in fatigue has received considerable attention over the past decade. Microstructurally and even mechanically small cracks have been shown to consistently exhibit higher crack growth rates than predicted using standard threshold and Paris growth law concepts, based on linear elastic fracture mechanics (LEFM) applied to mechanically long cracks. This has been commonly attributed to several factors, including the influence of microstructure, the breakdown of LEFM parameters for representation of the crack tip field, and the transient development of plasticity-induced closure towards some steady-state value associated with long crack behavior. Other mechanisms related to microstructural effects such as roughness-induced closure and crack face bridging/interference are also potential contributors. Quantitative attempts to explain the fatigue propagation of small cracks in terms of plasticity-induced closure, along with adoption of an additional component of the driving force (e.g. crack tip opening displacement) to reflect the contribution of cyclic plastic strain have met with some success in correlation of the so-called “anomalous” propagation behavior, including crack deceleration and acceleration transients. However, these models rely on the adoption of highly idealized assumptions regarding the self-similarity of crack growth, neglect of local anisotropy and heterogeneity associated with microstructure, etc.; in spite of these compromises, they still involve a considerable degree of complexity. Here, we adopt the viewpoint that multiple, microstructure interactions and closure effects may simultaneously influence the propagation of small cracks; moreover, driving force parameters based on self-similar crack growth arguments of elastic-plastic fracture mechanics (EPFM) for mechanically long cracks, such as the cyclic J -integral or crack tip opening displacement, may apply in principle, but not rigorously, as the driving force for small cracks. As an engineering approach, we consider a recent extension of the multiaxial microcrack propagation model first proposed by McDowell and Berard[1,2] for the growth of microstructurally small and mechanically small fatigue cracks[3] in multiaxial fatigue. Integrated between initial and final crack lengths, the model is fully consistent with standard strain-life laws of fatigue crack initiation mechanics under various states of stress, [1,2] and therefore bridges the mechanics of classical initiation and LEFM/EPFM to some extent. The existence of a fatigue limit (nonpropagating crack limit) is neglected in this particular work. It is shown for uniaxial loading of both 1045 steel and Inconel 718 that the model is able to describe, to first order, the anomalous high propagation rates of small cracks and convergence with long crack d a/ d N - ΔK data as the crack transitions from small to mechanically long scales. The limits of validity of engineering schemes based on decomposition of total fatigue life into “initiation” and propagation phases that rely on strainlife and long crack propagation laws are discussed[4]. Moreover, it is shown that the model essentially reflects a closure transient in the context of a cyclic J -integral approach, similar to the EPFM plasticity-induced closure modeling concepts set forth by Newman[5] and McClung et al. [6] for small cracks in fatigue. However, the present model implicitly reflects multiple forms of crack tip shielding effects, not just plasticity-induced closure. Finally, the model is shown to provide realistic treatment of cumulative damage in two level loading sequences, as reflected by comparison with the damage curve approach of Manson and Halford[7].