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Thesis defences

PhD Oral Exam - Navid Mortazavi, Mechanical Engineering

Driving force computation for fatigue crack growth based on the integration of fracture mechanics with artificial neural networks

Wednesday, September 20, 2023
3 p.m. – 5 p.m.

This event is free


School of Graduate Studies


Thesis Office


Engineering, Computer Science and Visual Arts Integrated Complex
1515 St. Catherine W.
Room EV 3.309



When studying for a doctoral degree (PhD), candidates submit a thesis that provides a critical review of the current state of knowledge of the thesis subject as well as the student’s own contributions to the subject. The distinguishing criterion of doctoral graduate research is a significant and original contribution to knowledge.

Once accepted, the candidate presents the thesis orally. This oral exam is open to the public.


Fracture mechanics principles play a crucial role in characterizing fatigue crack growth (FCG) rates based on the concept of driving force. Two well-known and promising driving forces in fracture mechanics are the stress intensity factor range (∆K) and cyclic J-integral (∆J). While ∆K is a linear elastic fracture mechanics (LEFM) parameter, ∆J is an elasto-plastic fracture mechanics (EPFM) parameter. However, both driving forces have limitations when it comes to FCG characterization. ∆K fails to account for relatively large-scale plasticity, rendering it inadequate for describing the short crack (SC) regime. On the other hand, ∆J inherently has the potential to consider large-scale plasticity, but its application on real engineering problems is challenging. The difficulty arises from the need to perform complex and time-consuming elasto-plastic analyses to compute the actual elasto-plastic stress, strain, and displacement fields near the crack tip for the calculation of ∆J. This study explores the integration of artificial neural networks (ANNs) with fracture mechanics principles to overcome these challenges. The research is carried out in three phases:

Phase 1 focuses on integrating ANN with ∆K as a LEFM parameter. Unlike ∆K-based models that solely formulate FCG rate based on the maximum stress intensity factor (Kmax) and ∆K, this approach incorporates other controlling parameters. FCG rate is considered as a function of ∆K and stress ratio (R) in the long crack (LC) regime, and as a function of stress level (σ) in addition to ∆K and R in the SC regime. ANNs are developed to reveal these non-linear and complex functions in both regimes, using experimental FCG data sets from Ti-6Al-4V titanium alloy, 2024-T3, and 7075-T6 aluminum alloys for training and verification. Although this phase shows potential, the reliance on limited FCG data sets due to costly procedures remains a challenge. Moreover, ∆K as a LEFM parameter inherently cannot handle large-scale plasticity in the SC regime.

To address these issues, a novel approach is suggested and investigated in Phases 2 and 3. Phases 2 and 3 propose replacing ∆K with ∆J as a promising EPFM driving force and combining finite element (FE) analyses with ANN algorithms. Firstly, the implementation of FE models provides ample datasets for training the ANNs. Secondly, this integration allows for the determination of ∆J through a linear elastic solution rather than complex elasto-plastic analyses.

Phase 2 involves FE analyses to determine stress, strain, and displacement fields under elastic and elasto-plastic states near a crack tip for a notched specimen made of stainless steel (SS304) under monotonic loading. Hypothetical elastic stress, strain, and displacement fields around the crack tip are used as input data for the developed ANNs. The corresponding actual elasto-plastic stress, strain, and displacement fields are the output of the ANNs. Well-trained ANNs successfully establish relationships between the elastic and elasto-plastic fields, enabling predictions of elasto-plastic stress, strain, and displacement based on hypothetical elastic data. An in-house model based on the equivalent domain integral (EDI) method is developed to determine J-integral as a function of stress, strain, and displacement fields around the crack tip. This model can be served as a post-processing step after elasto-plastic FE analyses. In addition, it can be employed to determine J-integral based on ANN predictions. The accuracy of the in-house model is verified by the J-integral data in the literature. ANN predicted elasto-plastic stress, strain, and displacement fields are compared and verified with those obtained from elasto-plastic FE analyses. The proposed method demonstrates significant accuracy in determining J-integral values.

Phase 3 extends the approach to cyclic loading conditions. The developed ANNs are trained on cyclic stress, strain, and displacement fields. The in-house model is upgraded to determine ∆J under cyclic loading. The accuracy of cyclic ANN-predicted elasto-plastic stress, strain, and displacement fields is compared with those obtained from elasto-plastic FE models, resulting in significant agreement. The in-house model is verified by the ∆J data in the literature. Moreover, ∆J values predicted by the proposed model are comparable to those directly determined by elasto-plastic FE analyses.

The integration of artificial neural networks with fracture mechanics principles provides valuable insights into overcoming traditional driving force limitations in FCG characterization. This research offers a promising avenue for future research and practical applications in the field of fatigue crack growth analysis.

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