L'unité d'enseignement est obligatoire. 
Les cours sont dispensés en anglais 

Outline

3 ECTS / 30 h

Team

Coordinator : Federica Daghia (federica.daghia@ens-paris-saclay.fr, ENS Paris-Saclay)

Instructors :

Lucien Laiarinandrasana (lucien.laiarinandrasana@mines-paristech.fr, Mines ParisTech)

Sebastien Joannes (sebastien.joannes@mines-paristech.fr, Mines ParisTech)

Federica Daghia (federica.daghia@ens-paris-saclay.fr, ENS Paris-Saclay)

Cristian Ovalle Rodas (cristian.ovalle_rodas@mines-paristech.fr, Mines Paris-Tech)

Objectives

The aim of the course is to discover the damage and fracture mechanisms of polymers and polymer matrix composites at different scales, and to learn about the appropriate modelling approaches. Specific aspects developed in the course include the extension of fracture mechanics concepts to large and viscoplastic deformations, statistical approaches for fibres' characterization, the damage mesomodel for laminated composites, thermo-mechanical aspects and ageing of elastomers.

Targets

Polymers and polymer matrix composites occupy an increasing part of the market in different industrial applications, especially in the transportation industry. It is therefore important to understand, and to be able to predict, the degradation and failure of these materials. Due to their specificities (large deformations and viscosity for polymers, complex and hierarchical microstructure for composites), the study of these materials require specific tools, both from the point of view of characterization and of the appropriate modelling approaches, which often involve different scales of observation and scale transition techniques.

Topics

• Polymers : extension of classical fracture mechanics concepts to polymers (large deformations, viscosity), deformation and damage mechanisms in link with their microstructure.
• Polymer matrix composites : damage and fracture at different scales - fibre/matrix, ply/interface, laminate.
• Rubbers : damage and fracture behaviour under monotonic and fatigue loading, including thermal considerations.

References

• Mechanical Behaviour of Materials - François, D, Pineau, A, Zaoui, A, Springer (2012)
  • Volume I : Micro- and Macroscopic Constitutive Behaviour
    Series : Solid Mechanics and Its Applications, Vol. 180
  • Volume II : Fracture Mechanics and Damage
    Series : Solid Mechanics and Its Applications, Vol. 191, chapter 10
• John A. Nairn, Polymer Matrix Composites, Chapter 13, R. Talreja and J-A. Manson, eds., in press (2000) Volume 2 of Comprehensive Composite Materials, A. Kelly and C. Zweben, eds., Elsevier Science
   

Content

Each session lasts 3 hours, it can include classical course as well as exercise sessions.

Session 1 (Lucien Laiarinandrasana)
Fracture mechanics applied to polymers: limitations of linear elastic fracture mechanics due to large transformations, viscoelastic and viscoplastic behaviour and non-linearities.

Session 2 (Lucien Laiarinandrasana)
Deformation and damage mechanisms in polymers classes in link with their microstructure observed by fractography and 3D observations.

Session 3 (Lucien Laiarinandrasana)
Fracture mechanics concepts for polymers: essential work of fracture and effects of viscosity.

Sessions 4 (Sebastien Joannes)
Characterization of single fibres: failure mechanisms at the fibre's scale, statistical aspects, multi-scale models.

Sessions 5 (Sebastien Joannes)
The unidirectional ply with continuous aligned fibres: anisotropy, symmetry classes, failure mechanisms in the fibres and transverse directions.

Session 6 (Federica Daghia)
Notions on laminated composites: stacking sequence, modelling of the overall behaviour, couplings (normal/shear, membrane/bending).

Session 7 (Federica Daghia)
Damage mechanisms at the ply's and at the laminate's scale: load redistribution and final failure, multiple cracking, delamination.

Session 8 (Federica Daghia)
The damage mesomodel for laminates: ply and interface models, illustrations.

Session 9 (Cristian Ovalle Rodas)
Mechanical behaviour of elastomers: hyperelasticity. Influence of the manufacturing process.

Session 10 (Cristian Ovalle Rodas)
Fatigue behaviour of elastomers: Wohler's curves, damage initiation mechanisms, thermomechanical and ageing aspects.