Dislocation theory based short crack model and its application for aircraft aluminum alloys
Introduction
Currently, one of major research thrusts at the Institute for Aerospace Research of the National Research Council Canada (IAR/NRC) is Life Cycle Management Technologies, which is aiming to develop the Holistic Structural Integrity Process (HOLSIP) for Defence Research and Development of Canada (DRDC). The Holistic Structural Integrity Process (HOLSIP) augments and enhances traditional safe-life and damage tolerance paradigms in both the design and sustainment stages. In HOLSIP, the life of a component is divided into four distinct phases: nucleation (L1), short crack (L2), long crack (L3), and final instability (L4). The current project is focused on research in the short/small crack growth (L2) regime. In the future, IAR/NRC plans to pursue research in the nucleation (L1) regime by taking advantage of the results from the current projects.
A literature review has been carried out on short or small crack research, and a brief summary is presented in [1]. Up to now, some common observations on short or small cracks are:
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they grow faster than predicted by linear elastic fracture mechanics (LEFM) using large crack data;
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they can grow at ΔK levels well below the large crack threshold ΔKth;
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their growth can be decelerated or accelerated, arrested or coalesced, depending on the microstructure and stress level; and
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their growth rates have significantly greater scatter than those of large cracks.
On the modeling side, many limitations have been identified for applying the conventional LEFM for short crack modeling, such as:
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the small yield zone assumption in LEFM is no longer valid for a short crack, neither is the similitude concept used in LEFM [7];
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continuum mechanics concepts, which LEFM is based on, are no longer valid. The non-continuum and non-uniform microstructural effects are more pronounced in the short crack region; and
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elastic stress fields cannot accurately describe the high strain fields at the tips of small discontinuities in highly stressed materials.
Two types of models have drawn some attention: the first one is the modified LEFM-based model such as the Newman crack closure model [2], [3]. The second one is the dislocation theory based model, such as the crack tip sliding displacement (CTSD) or crack tip opening displacement (CTOD) models developed by Tanaka–Mura, as well as Navarro–de los Rios [4], [5], [6]. The limitations and merits of LEFM for short crack modeling were documented and discussed in contrast with the dislocation theory based models in [1]. It was recommended to investigate both LEFM and dislocation theory based models for short cracks.
In the previous report [1], a modified LEFM model was developed using some NRC coupon test data on 2024-T351, and the model was enhanced with probabilistic techniques to estimate the life distribution. This paper presents the short crack modeling work based on the dislocation theory based CTOD model.
Section snippets
Dislocation theory based short crack CTOD model
Due to the complexity of fatigue damage accumulation in polycrystalline solids, the physics based fatigue nucleation and short crack growth models have not been established in a quantitative and applicable manner. However, a lot of fundamental, qualitative studies on the fatigue mechanisms were carried out, especially after scanning electron microscopy (SEM) and transmission scanning microscopy (TEM) were used for this research. Extensive experimental observation using SEM and TEM have shown
Modified CTOD model
Based on the Tanaka model [4], [5], a modified CTOD model was developed to enhance the modeling capability in the following aspects:
- (1)
Additional CTOD solutions were developed for the global plasticity case, such as the case of low cyclic fatigue where the whole specimen can be in plasticity.
- (2)
Material initial discontinuity state (IDS) was used as a random variable for small crack analysis (in addition to grain size, friction stress, and critical microscopic ).
- (3)
A non-linear numerical program was
Application for short crack growth analysis
Since the AGARD program [28] generated a very large short crack growth database for 2024-T351 unclad sheet (0.0906″/2.3 mm), the modified CTOD model was used to simulate the short crack growth for the AGARD specimens. A single edge notch tension (SENT) specimen was used in the AGARD program, and many short surface cracks at the notch were collected. Fig. 4 presents the location of the short surface crack at the notch, as well as the parameters used in the modified CTOD model.
Fig. 5 presents the
Discussions
Compared to the conventional fracture mechanics models, the dislocation based model has the advantage of simulating the important physical characteristics of crack nucleation and short crack growth. The effects of microstructures on short crack growth can be quantified using the dislocation based model, thus the model has the potential for use in the development of new material where a single or multiple microstructural features can be considered.
However, at present many challenges exist in
Conclusion remarks
The Tanaka–Mura CTOD model was modified with additional plastic contribution on CTOD and other random variables, i.e., crack-nucleating particle size, grain size, friction stress, and critical microscopic stress intensity factor. A unique, non-linear multivariate minimization program, was developed to identify the hard-to-measure micro-parameters (e.g., friction stress, and critical microscopic stress intensity factor), in association with some test data (e.g., crack-nucleating particle size,
Acknowledgements
This work was carried out with the financial support of Defence Research and Development Canada (DRDC) and National Research Council Canada (NRC), Projects “Short Crack Model Development”.
Part of the theoretical work was completed while the author visited the Federal Institute for Materials Research and Testing (BAM, Bundesanstalt für Materialforschung und – prüfung, Berlin, Germany) under the supervision of Dr. Bernard Fedelich.
Thanks to Larry Crichlow for typing in all the equations in
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