Outline

3 ECTS / 30h / 10 sessions of 3 hours

Courses : 13h

Exercices : 13h

Practice : 4h

Team

Coord. Bruno Fayolle (bruno.fayolle@ensam.eu, ENSAM Paris)

Etienne Barthel (etienne.barthel@espci.psl.eu, ESPCI Paris)

Karine Lavernhe, (karine.lavernhe@ens-paris-saclay.fr, ENS Paris-Saclay)

Ricardo Gatti (riccardo.gatti@onera.fr, ONERA)

Jean-Michel Scherer (jean-michel.scherer@minesparis.psl.eu, Mines Paris)

Sylvie Pommier (sylvie.pommier@universite-paris-saclay.fr, ENS Paris-Saclay)

Objectives

This teaching unit aims at clarifying the relationships between the structure of materials and their mechanical properties. In materials science, multiscale modelling is developing rapidly and requires an in-depth understanding of the physical basis of materials behaviour so that for instance new materials with optimal properties can be created. Therefore it is aimed at relating the desired properties of a material to the structure of the material from the atomic scale (10-10m) to the scale of the microstructure (10-4 m). From this point of view, the field is at the intersection between mechanics and physics. In this teaching unit, metallic materials, polymers and material that possess and internal length scale such as nano-structured materials, metallic foams or bones will be specifically considered..

Targets

A solid knowledge in material science becomes essential when working within the field of processin of existing or new materials, and of structural design, in particular when complex, non-linear material behaviours are encountered. In industry, this is mainly relevant for the material selection when a new system is designed, for the choice of the best process to obtain optimized properties for a given application, and for the development of new materials and processes for emerging applications. The relevant industrials sectors are diverse, ranging from transportation, energy production, construction to electronics or health !

Topics

• Polymers : 3 sessions
• Metals : 4 sessions
• Nano-Materials and biological materials : 2 sessions
• One session for practice (numerical or experimental).

References

• D. François, A.Pineau, A. Zaoui, (1993), Comportement mécanique des materiaux, tomes 1 et 2, Hermes, Paris
• J. Friedel, (1964), Dislocations, Pergamon, Oxford.
• J.P. Hirth, J.Lothe, (1968), Theory of dislocations, Mac Graw Hill.
• D. Jaoul, (1965), Etude de la plasticité et application aux métaux, Dunod, Paris.
• D. Hull, J. Bacon, (1984), Introduction to dislocations, International series on materials science and technologie, Pergamon, Oxford.
• H. H. Kausch et col.(2001), Matériaux Polymères. Propriétés Mécaniques et Physiques, Traité des Matériaux vol. 14. Presses Polytechniques et Universitaires Romande Lausanne.
• G. Kostortz et col. (2001), Phase Transformations in Materials, Wiley-VCH, Weinheim.

Content

Session 1 : Polymers, course

Introduction to polymers and macromolecules . Molecular architecture and classification of polymers. Applications. Relationships between microstructure and mechanical and optical properties.

Session 2 : Polymers, course and Exercise

Time-temperature equivalence, linear viscoelasticity and rubber elasticity. Effect of temperature on the mechanical properties of polymers.

Session 3 : Polymères, TD

Plasticity and fracture mechanisms of polymers. Case study : observation of damage mechanisms, crazes and shear bands

Session 4 : Metals, course and exercise

Stresses : crystalline metal behaviour – Crystal plasticity: slip systems, resolved shear stress, Schmid law, Non-Schmid effects. Case of polycrystals and role of the texture - Exercises : Yied surface for single crystal in tensile-torsion loadings, Effect of crystal orientation, application to textured polycrystal

Session 5 : Metals, course and exercise

Dislocations : The theoretical critical shear stress, edge and screw dislocations, Burgers vector, stress field of a straight dislocation, Strain energy of a dislocation - Exercices : Forces between dislocations and consequences...

Session 6 : Metals, course and exercise

Structural and work hardening – Multiplication of dislocations by Franck-Read sources, Interaction between dislocations and point defects/precipitates (cutting and Orowan mechanisms - Exercices : Single-crystal work hardening.

Session 7 : Metals, course and exercise

Strain rate – Kinematics of the single crystal : single and multiple slips, Additional deformation mechanisms : geometrically necessary dislocations, climb, cross slip, twinning and others… - Exercices : Dissociation of perfect dislocations, Suzuki effect, Applications to industrial alloys

Session 8 : Scale effects in materials, nanostructured materials, course

Nano-structured materials and nono-objects. Evolution law of the dislocation density with plastic strain. Grain size effects in polycrystals the Hall Petch law and the deviations to this law for nano-crystalline materials.

Session 9 : Scale effects in materials, nanostructured materials, course and exercise

Exercice: Geometrically necessary dislocations and second gradient models. Image force associated to a free surface and its effect on the flow of dislocations in nano-objects. Course: The behaviour of organics or metallics foams (bone, biological materials, and new metallic materials) How the internal structure of a material modifies its macroscopic behaviour.

Session 9 : Scale effects in materials, nanostructured materials, show

Numerical simulation of the dynamics of dislocations in nanostructured materials / Numerical simulation of the behaviour of a collection of grains (polycristal) and using a crystal plasticity formulation.