Fracture mechanics and fatigue of structures

This course gives researchers and engineers the theory and tools to predict fracture and fatigue failure in structures, with a particular focus on metals and welded components. It combines fracture mechanics, numerical methods, fatigue design and statistical analysis of test data, so that students can assess both the integrity of cracked components and the fatigue life of structural details.

The course opens with the fundamentals of fracture mechanics: its history and fields of application, fracture mechanisms in metals (ductile, brittle and the ductile-to-brittle transition in steels), and stress concentration and the effect of flaws. Griffith's energy balance and Irwin's crack driving force G form the theoretical basis.

Linear elastic fracture mechanics (LEFM) is then developed in depth. Students derive the stress and displacement fields around a crack, link the stress intensity factor K to G through compliance, and use solutions for classical 2D cases and cracks at holes. They extend these to 3D through elliptical crack solutions, and to welded joints through superposition. Crack tip plasticity, K as a similitude parameter and fracture toughness testing define the scope and limits of LEFM. Stress intensity factors are also computed numerically with finite element models, using displacement extrapolation, the domain J-integral and the virtual crack closure technique.

The course then addresses fatigue crack initiation and propagation in metals. Students compute crack growth and the remaining life of structural elements with the Paris law, account for crack closure, and learn how crack growth tests are conducted and analysed. The failure assessment diagram is introduced to evaluate flaw acceptability, distinguishing brittle fracture from plastic collapse.

The last part of the course is devoted to fatigue design with resistance curves. Students apply the detail classification method (from the IIW recommendations and the Eurocodes), as well as the hot-spot and notch stress approaches. They study the factors that govern fatigue life, including size effects, residual stresses and post-weld treatments. Variable amplitude loading is treated with Miner's rule, the relative Miner rule, Gassner curves and damage limit concepts. A key theme here is statistical inference: students quantify scatter and derive fatigue strength curves and their safety parameters from test data using linear regression and the maximum likelihood method.

A large part of the exercises use Jupyter notebooks (non-exhaustive list) to study different computation methods for the stress intensity factor K, to compare with analytical solutions, to compute fatigue crack growth and fatigue lives, to evaluate flaw acceptability, to perform statistical inference.

Format: It is a bloc course delivered in hybrid mode over 7 weeks: Feb 15 to April 9. It is given at both TU/e (Eindhoven) and EPFL (Lausanne), so students from those universities attend onsite in videoconferencing-equipped classrooms, while EuroTeQ students participate online in real time. The course consists of weekly 90-minute hybrid sessions (except during the Easter break). Learning materials are provided through the course platform and include recorded videos, exercises, course materials, and an online discussion forum.

• Develop long-term competencies in applied fracture mechanics (applicable to different materials).
• Understand the bases and limits of linear elastic fracture mechanics (LEFM).
• Develop long-term competencies in fracture mechanics numerical methods.
• Evaluate Stress Intensity Factors (SIF) by various methods.
• Understand the links between LEFM and fatigue strength curves.
• Analyse fatigue test data using standard and more advanced methods.
• Conduct engineering critical assessment of flaws in metallic structures using the failure assessment diagram.
• Understand the principles and the outcomes of standard and advanced fatigue and fracture testing.

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The course is accessible to any student in material science, mechanical, civil, building, aeronautical engineering who has completed a University Bachelor’s program.

The learning prerequisites for the course are:

• Continuum mechanics.
• Structural mechanics.
• Mechanics of materials.
• Finite element method.
• Probability and statistics.
• Programming skills, preferably in Python.

• Janssen, M., J. Zuidema, and R. Wanhill. 2024. Fracture Mechanics. An Engineering Primer. TU Delft OPEN Publishing. Delft, The Netherlands: TU Delft OPEN Publishing. https://books.open.tudelft.nl/home/catalog/book/173