title: On kinetics of small fatigue crack growth
Creators: name: Li, Xu-Dong
Publisher: name: The Open University
Year: 1996

description: This work presents a systematic model which predicts the kinetics of small fatigue crack growth in polycrystalline materials. The dislocation-based micromechanical model covers die entire process of small crack propagation from Stage I growth, Stage I to Stage II crack growth transition, Stage II growth, to the convergence into long cracks. Two fatigue thresholds that specifically relate to small fatigue crack propagation are also modelled.<br><br>Beginning with a detailed review of the historic development of small crack research, this work aims to (1) seek a unified parameter that can kinetically correlate small fatigue crack growth and then a unified small crack growth rate law; (2) establish a coherent micro-macro mechanical relationship that connects microscopic cracking in solids with bulk fatigue properties; and (3) predict fatigue crack growth thresholds on the basis of physical phenomena rather then any crack closure argument; (4) achieve overall <i>da/dN</i> predictions. <br><br>Typical 7xxx series aluminium alloys plus a 8090 aluminium-lithium alloy were the materials selected for testing. Small fatigue crack growth and low-cycle fatigue tests were carried out to investigate small crack behaviour, typical crack growth characteristics, cyclic stress-strain responses and low-cyclic fatigue properties. Fatigue damage mechanisms for both alloys were also studied using SEM and TEM for proper simulation of microstructure.<br><br>By proposing a microstructurally-affected-zone, this work considers a polycrystalline material to be build up of microstructurally-affected-zones. The local microstructure affecting crack front advancing is interpreted in terms of slip band orientation and crack tip orientation. The local microstructural effect is characterised by the microstructurally-affected-zone size p*. By defining a process zone at the advancing small crack front, it is found that the process zone size d* is a novel unified physical parameter that can be used to kinetically correlate small fatigue crack growth rates. Further, a micro-macro mechanical relationship associated with growth of small fatigue cracks is established that describes the coherent connection of microscopic plastic deformation to local microstructure. The Stage I to Stage II crack growth transition is modelled to be due to the severe blockage to small fatigue crack growth caused by barriers. By using a pile-up simulation of continuous dislocations, the blockage is modelled as dislocations against grain boundaries. The transition crack size 2<i>a</i><sub>o</sub> is thus determined using the function 2<i>a</i><sub>o</sub> = f(ϕ, ɸ, σ, <i>l0</i>). As a result, a unified dislocation-based micro-mechanical model is established that predicts kinetics of overall small fatigue crack growth whose notable advantage is that the microscopic small crack growth can be directly predicted using macroscopic bulk fatigue properties without tedious fatigue tests for each load level.<br><br>Modelled are two fatigue threshold parameters, K*<sub>max</sub> and ɅK*<sub>th</sub>, that are coherently related to fatigue limit and describe fatigue threshold behaviour at any load ratio without invoking crack closure. The fatigue limit is determined in terms of a critical condition at which a fictitious microcrack associated with dislocation pile-up just begins to propagate. These two fatigue threshold parameters constitute two novel fatigue criteria that demarcate safety zones and predict fundamental fatigue threshold curves at any load ratio. Microstructure is incorporated into the model to account for its effect on fatigue threshold behaviour. Quantitative assessment of the two fatigue criteria requires only knowledge of the conventional material properties. The convergence of small fatigue crack growth into long fatigue crack growth is also modelled in terms of Lankford's criteria by using a simulation where the controlling microstructural dimension p* rather than the grain size controls small to long crack growth transition. All model predictions in this work are in good agreement with experimental results. Generally, a series of computer-assisted simulations for predicting realistic small crack growth are developed which lays a foundation for fatigue lifetime predictions that are based on fatigue crack growth tolerance techniques.