The teaching unit is mandatory.
The teaching unit is taught in English. 

Outline

3 ECTS / 30 h

 Courses : 15 h

 Exercises : 3 h

 Practice : 6 h

 Conferences : 6 h

Team

Coord. Thilo Mogeneyer (thilo.morgeneyer@mines-paristech.fr, Mines ParisTech)

 

Objectives

 

This teaching unit covers the broad topic of structural integrity which is founded on the mechanics of fracture, and is concerned with the reliability, durability and security of structural components of any scale, geometry or material. It is aimed at presenting and practising efficient and up-to-date engineering designs methods when defects or cracks are present (damage tolerance approaches) for various fracture mechanisms.

Targets

Fracture mechanics is employed in industrial applications when the failure of a component could have catastrophic consequences, such as losses of human lives or an ecologic disaster for instance. This is the case of mass transportation (trains or planes), energy production and in particular nuclear powerplants and the industries concerned with the production, the transportation or the recycling of toxics (oil industry, chemical industry). In these industrial fields, the risk of failure is not acceptable, therefore it should always be assumed that the existence of a defect is possible, even if its probability is very low, and determine at which conditions this defect can’t be at the origin of a catastrophic failure.

Topics

• Linear elastic fracture mechanics, mode I and mixed mode
• Non linear fracture mechanics
• Mécanisms of failure : ductile, brittle, fatigue and related models
• Numerical practice: Calculation of K, J and T, case study of real catastrophic failure events
• Experimental Practice: observation of stress fields in a cracked sample of PMMA (photoelasticimetry)

References

• Mécanique de la rupture fragile et ductile, Jean-Baptiste Leblond, Hermes Science Publications (2003), Etudes en mecanique materiaux
• Comportement mécanique des matériaux : viscoplasticité, endommagement, rupture, D. Francois, A. Pineau, Hermes Sciences Publication (1993)
• La simulation numérique de la propagation des fissures, S. Pommier, A. Gravouil, N. Moës, A. COmbescure, Hermes Sciences Publication (2009)
• Fatigue of Materials, S. Suresh , Cambridge University Press, (1998)

Content

Session 1 : introduction, linear elastic fracture mechanics (LEFM)

Introduction, Griffith's theory, elastic singularities, asymptotic development, linear elastic fracture mechanics (LEFM), KI, KII, KIII and T.

Session 2 : Exercises

Analysis of the results of a tensile test on a pre-cracked sample: KIC, case study of a real failure event. Notions of toughness and of potential energy release rate…

Session 3 : Numerical Practice. Determination of SIF

For the same sample geometry that will be used in the experimental practice session, computations of of stress intensity factors, displacements, stresses, J integral and interactions integrals.

Session 4 : LEFM for tridimensionnal probles (loading and geometry)

Mixed mode fracture, I, II and III. Bifurcation criteria in linear elastic fracture mechanics. Role of non-singular terms for the crack path stability. 3D cracks with curved crack front. Surface singularity (when a 3D crack front intersect a free surface), interface singularity.

Session 5 : Non-liear fracture mechanics

How plasticity modifies the loading conditions at crack tip, from a microscopic point of view (disclocation emission and shielding effect at crack tip) and from a macroscipic point of view (Irwin's plastic zone, J integral and HRR field)

Session 6 : Experimental practice

Observatiin using the scanning electron microscope of typical fracture surfaces (ductile, brittle and fatigue). Initiation and arrest toughness measurements, in mode I and Mixed mode conditions.

Session 7 : Mode I fatigue crack growth

Fatigue failure for complex loading conditions. Physical mechanisms of crack extent in fatigue. Paris law and domain of application. Application: prevision of the fatigue life of an aerospace component. Effect of variable amplitude loadinds, history effects. Design methods.

Session 8 : Mixed Mode fatigue crack growth

Ductile failure and fatigue crack growth under mixed mode loading concitions. Examples of torsion failures of contact fatigue failures. Effect of friction on fatigue crack growth.

Session 9 : Novel tools and concept for predictinig crack growth in brittle or ductile materials

Mesh size effect, fatigue and ductile fracture, non-local models, Levels sets and X-FEM.

Session 9 : Conference, ductile fracture

Ductile fracture and design rules for industrial components, global and local approaches of ductile fracture.