Fracture of materials

MSE-424

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General

Co-taught between Jean-François Molinari (JFM) for about 2/3 classes, and Jean-Marie Drezet (JMD), for 1/3 of classes.

TA, Gaëtan Cortes (LSMS PhD student) : gaetan.cortes@epfl.ch (GC A2 495) and Allegra Magnetti.

Course is offered to MX, GC, and GM MS students.

Reference book: T.L. Anderson, "Fracture mechanics: fundamentals and applications".

Final exam: written exam. Two parts:

Part 1) 1/3 final grade. Class questions (theory) without notes.

Part 2) 2/3 final grade. Practical questions, with access to a formula sheet.

Outline.

Week 1 (JFM, JMD): Introduction of instructors and course objectives. Refresher of Continuum Mechanics and Mechanics of solids with dynamics. Wave equation in 1D bars. (Course book, J.D. Achenbach, "Wave propagation in solids", 1973.)

Week 2 (JFM): Dispersion relation, limit of continuum model; 3D wave propagation.

Week 3 (JFM): Helmholtz decomposition; Reflection and refraction of planar waves; Rayleigh waves.

Week 4 (JFM): Introduction to fracture mechanics; Introduction to LEFM; theoretical strength of materials; Inglis solution to elliptical cracks.

Week 5 (JFM): Griffith energy criterion (global approach); energy release rate; R-curve.

Week 6 (JFM): Local approach; fracture modes and stresses at a crack tip; stress intensity factor.

Week 7 (JFM): Relation between local and global approach; crack tip plasticity; K-controlled rupture and limit of LEFM.

Week 8 (JFM): Mixed-mode rupture; crack propagation; J-integral.

Week 9 (JFM): Dynamic crack propagation; How fast cracks can grow. Examples: explosions/dynamic fragmentation and earthquakes.

Week 10 (JMD): Fracture of brittle materials; Weibull statistics.

Week 11 (JMD): Fracture of polymers.

Week 12 (JMD): Fracture of metals.

Week 13 (JMD): Fracture of heterogeneous materials (example of concrete; composites)

Week 14 (JFM, JMD): Course summary and opening on research questions (fracture of metamaterials; numerical simulations and ML driven fracture); Q&A for exam.

Week 1 : Introduction and wave equation in 1D bars

Week 2 : 1D waves and Buckingham-Pi theorem

Week 3 : Wave propagation and energy

Week 4 : 3D transverse and longitudinal waves

Week 5 : Griffith energy criterion

Week 6 : Energy release rate and R-curve

Week 7 : Westergaard, Irwin and stress concentration

Week 8 : K-G relation, crack-tip plasticity, K-controlled rupture

Week 9 : Ceramics, Weibull statistics

Week 10 : Mixed-mode fracture, J-integral

The exercise 3 of Assignment 10 will be done during next week exercise session (Week 11).

Week 11 : Numerical simulations, fragmentation

This week, you will have the occasion to try a bit of numerical simulation through a streamlit app. Please don't enter too extrem values (High number of elements, high forces, etc...) or you might crash the app, forcing a reload for everyone connected.