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Lecture

Fracture Mechanics: Stress Intensity Factors

In course

MSE-424: Fracture of materials

This course covers elementary fracture mechanics and its application to the fracture of engineering materials. ...

Description

This lecture covers stress intensity factors in fracture mechanics, focusing on the concept of K as a fracture criterion. It explains the stress field around a crack tip, different crack opening modes, and situations where other modes may dominate. The instructor demonstrates the through-thickness crack in an infinite sheet and biaxial remote stress. The lecture also discusses the importance of mode I as a worst-case scenario for testing fracture properties. Various expressions for stress intensity factors and their implications are explored, including the relationship between K and G. The lecture concludes with a discussion on the thickness dependency of stress near the crack tip and the implications for fracture behavior.

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Instructors (4)

Andreas Mortensen

Andreas Mortensen is currently Professor and Director of the Institute of Materials at the Swiss Federal Institute of Technology in Lausanne (EPFL), where he heads the Laboratory for Mechanical Metallurgy. He joined the faculty of EPFL 1997 after ten years, from 1986 to 1996, as a member of the faculty of the Department of Materials Science and Engineering at the Massachusetts Institute of Technology, where he held the successive titles of ALCOA Assistant Professor, Associate Professor, and Professor. His research is focussed on the processing, microstructural development and mechanical behavior of advanced metallic materials with particular focus on metal matrix composites and metal foams, on infiltration processing and capillarity, and on damage and fracture in metallic materials. He is author or co-author of two monographs, around one hundred and eighty scientific or technical publications and twelve patents. Born in San Francisco in 1957, of dual (Danish and US) nationality, Andreas Mortensen graduated in 1980 from the Ecole Nationale Supérieure des Mines de Paris with a Diplôme dIngénieur Civil, and earned his Ph.D. in the Department of Materials Science and Engineering at MIT in 1986. Besides his academic employment, he was a postdoctoral researcher at Nippon Steel during part of 1986, and was invited professor at the Ecole des Mines in Paris during the academic year 1995 to 1996. He is a member of the editorial committee of International Materials Reviews and has co-edited four books. He is a Fellow of ASM, a recipient of the Howe Medal and the Grossman Award of the American Society of Metals, was awarded the Péchiney Prize by the French Academy of Sciences and the Res Metallica Chair from the Katholieke Universiteit Leuven, received three EPFL teaching awards, is one of ISIs Highly Cited authors for Materials Science since 2002 and was awarded an ERC advanced grant in 2012.

Jean-Marie Drezet

1992-1996: PhD work at Laboratoire de Métallurgie Physique under the supervision of Prof. Michel Rappaz (cf : http://library.epfl.ch/theses/?display=detail&nr=1509) 1997-2000: EMPACT project (European Modelling Programme for Aluminium Casting Technologies) 2001-2004: VIRCAST project (European Virtual Casting) 2005-2006: Study of the sawing process of rolling sheet al. ingots (Alcan Fonds) 2005-2006: WelAIR project (Welding of Airframes, EADS) 2005-2008: study of the electron beam welding of Cu-Cr-Zr alloys (CEA, France) 2006-2008: study of the laser beam welding of Al-Li alloys (EADS, France) 2008-2011: co-supervision with Prof. A. Nussbaumer of the PhD work of C. Acevedo on the influence of residual stresses on the fatigue design of tubular welded joints, http://library.epfl.ch/theses/?nr=5056 2007-2010: co-supervision with Prof. J.-F. Molinari of the PhD work of K. Shahim on the Normal Pressure Hydrocephalus (S. Momjian, HU-Genève et R. Sinkus, ESPCI-Paris), http://library.epfl.ch/theses/?nr=5191 2008-2012: co-supervision with Prof. M. Rappaz of the PhD work of M. Sistaninia on the simulation of solidification cracking using granular models (CCMX-MERU project) 2010-2014: supervision with Prof. M. Rappaz of the PhD work of N. Chobaut on the modelling of stresses during quenching of thick heat treatable aluminium parts (CCMX-MERU project) 2011-2015: supervision with Prof. H. Van Swygenhoven-Moens of the PhD work of P. Schloth on precipitation during quenching of thick heat treatable aluminium parts (CCMX-MERU project)

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Related concepts (32)

Fracture mechanics

Fracture mechanics is the field of mechanics concerned with the study of the propagation of cracks in materials. It uses methods of analytical solid mechanics to calculate the driving force on a crack and those of experimental solid mechanics to characterize the material's resistance to fracture. Theoretically, the stress ahead of a sharp crack tip becomes infinite and cannot be used to describe the state around a crack. Fracture mechanics is used to characterise the loads on a crack, typically using a single parameter to describe the complete loading state at the crack tip.

Fracture

Fracture is the separation of an object or material into two or more pieces under the action of stress. The fracture of a solid usually occurs due to the development of certain displacement discontinuity surfaces within the solid. If a displacement develops perpendicular to the surface, it is called a normal tensile crack or simply a crack; if a displacement develops tangentially, it is called a shear crack, slip band or dislocation. Brittle fractures occur without any apparent deformation before fracture.

Fracture toughness

In materials science, fracture toughness is the critical stress intensity factor of a sharp crack where propagation of the crack suddenly becomes rapid and unlimited. A component's thickness affects the constraint conditions at the tip of a crack with thin components having plane stress conditions and thick components having plane strain conditions. Plane strain conditions give the lowest fracture toughness value which is a material property.

Stress–strain analysis

Stress–strain analysis (or stress analysis) is an engineering discipline that uses many methods to determine the stresses and strains in materials and structures subjected to forces. In continuum mechanics, stress is a physical quantity that expresses the internal forces that neighboring particles of a continuous material exert on each other, while strain is the measure of the deformation of the material. In simple terms we can define stress as the force of resistance per unit area, offered by a body against deformation.

Stress (mechanics)

In continuum mechanics, stress is a physical quantity that describes forces present during deformation. An object being pulled apart, such as a stretched elastic band, is subject to tensile stress and may undergo elongation. An object being pushed together, such as a crumpled sponge, is subject to compressive stress and may undergo shortening. The greater the force and the smaller the cross-sectional area of the body on which it acts, the greater the stress. Stress has units of force per area, such as newtons per square meter (N/m2) or pascal (Pa).

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John Christopher Plummer

ÉCOLE POLYTECHNIQUE FÉDÉRALE DE LAUSANNE (EPFL), Lausanne, Switzerland 1989- Collaborateur Scientifique/Chargé de Cours (Lecturer) (1998-) Privat Docent (1998) Laboratoire de Technologie des Composites et Polymères (LTC) (2000-) Laboratoire de Polymères (LP) (1998-2000) UNIVERSITY OF MICHIGAN (UMICH), Ann Arbor, MI, USA 1995-1996 Visiting Scientist, Department of Materials Science and Engineering (DMSE) UNIVERSITY OF CAMBRIDGE, Cambridge, UK 1986-1989 Research Assistant, Physics and Chemistry of Solids Group (PCS), Department of Physics UNIVERSITY OF CAMBRIDGE, Cambridge, UK, Department of Materials 1986 PhD, "Flux Pinning in Type-II Superconductors" UNIVERSITY OF CAMBRIDGE, Cambridge, UK, 1982 BA/MA Honours Degree in Natural Sciences Awards Prix R&R Haenny, 2007, DuPont Research Award, 2003, Commendation, British Polymer Group, Reading 1989 RECENT PUBLICATIONS Ramier J, Da Costa N, Plummer CJG, Leterrier Y, Manson JAE, Eckert R, Gaudiana R, Cohesion and adhesion of nanoporous TiO2 coatings on titanium wires for photovoltaic applications, Thin solid films, 516, 1913 (2008). Ramier J, Plummer CJG, Leterrier Y, Manson JAE, Eckert B, Gaudiana R, Mechanical integrity of dye-sensitized photovoltaic fibers, Renewable energy, 33, 314 (2008).

Houphouet-Boigny C, Plummer CJG, Wakeman MD, Manson JAE, Hybrid glass fiber-reinforced thermoplastic nanocomposites, J. Thermoplast. Comp. Mater., 21, 103 (2008).

Ternat C, Ouali L, Sommer H, Fieber W, Velazco MI, Plummer CJG, Kreutzer G, Klok HA, Manson JAE, Herrmann, Investigation of the Release of Bioactive Volatiles from Amphiphilic Multiarm Star-Block Copolymers by Thermogravimetry and Dynamic Headspace Analysis, Macromolecules 41(19), 7079 (2008). Ruggerone, R., Plummer, C.J.G., Negrete Herrera, N., Bourgeat-Lami, E., Månson, J-EA, Mechanical properties of highly filled latex-based polystyrene/laponite nanocomposites, Solid State Phenomena Vol. 151, 30 (2009). Plummer, CJG, Dalle Vacche, S, Houphouët-Boigny, C, Michaud, V, Månson, JAE, Hybrid Glass Mat Reinforced Polypropylene-Montmorillonite Nanocomposites, Solid State Phenomena Vol. 151, 60 (2009). Ruggerone, R., Plummer, C.J.G., Negrete Herrera, N., Bourgeat-Lami, E., Månson, J-EA, Highly filled polystyrenelaponite nanocomposites prepared by emulsion polymerization, European Polm. J. 45, 621 (2009). Ruggerone, R., Plummer, C.J.G., Negrete Herrera, N., Bourgeat-Lami, E., Månson, J-EA, Fracture mechanisms in polystyrene/laponite nanocomposites prepared by emulsion polymerization, Engineering Fracture Mechanics 76, 2846 (2009) Clausen P., Andreoni W., Curioni A., Hughs E., Plummer C.J.G. Adsorption of low-molecular-weight molecules on the surface of a sodium smectite clay: an ab initio study, Journal of Physical Chemistry C 113, 12293 (2009). Clausen P., Andreoni W., Curioni A., Hughs E., Plummer C.J.G., Water adsorption on a sodium smectite clay surface: an ab initio study, Journal of Physical Chemistry C 113, 15218 (2009). Molberg, M, Leterrier, Y., Plummer, C.J.G., Walder, C., Löwe, C., Opris, D.M., Nüesch, F.A., Bauer, S., Månson, J.-A.E., Frequency dependent dielectric and mechanical behaviour of elastomers for actuator applications, J. Appl. Phys. 106, 054112 (2009) Clausen P., Signorelli M., Schreiber A., Hughes E., Plummer CJG, Fessas D., Schiraldi A., Månson E. J.-A., Equilibrium desorption isotherms of water, ethanol, ethyl acetate and toluene on a sodium smectite clay, Journal of Thermal Analysis and Calorimetry 98, 833 (2009) Micusik, M., Bonnefond, A., Reyes, Y., Bogner, A., Chazeau, L., Plummer, C.J.G., Paulis, M., Leiza, J.R., Morphology of Polymer/Clay Latex Particles Synthesized by Miniemulsion Polymerization: Modeling and Experimental Results Macromol. React. Eng. 2010, 4, 432 (2010). Houphouet-Boigny C., Plummer CJG, Vacche SD, Michaud V, Wakeman MD, Månson E. J.-A., Hybrid Glass Mat-reinforced Polypropylene-Montmorillonite Nanocomposites, J. Comp. Mater. 44, 1975 (2010). Delabarde, C., Plummer C.J.G., Bourban, P.-E., Månson E. J.-A., Solidification behavior of PLLA/nHA nanocomposites, Comp. Sci. & Tech. 70, 1813 (2010). Plummer C.J.G., Ruggerone R., Negrete-Herrera N., Bourgeat-Lami E., Månson J.-A.E., Small Strain Mechanical Properties of Latex-Based Nanocomposite Films, Macromol. Symp. 294, 1 (2010). Dalle Vacche, S., Plummer C.J.G., Houphouet-Boigny C., Månson E. J.-A., Morphology and mechanical properties of isotactic polypropylene glass mat thermoplastic composites modified with organophilic montmorillonite, J Mater Sci 46, 2112 (2011).

Related concepts (32)

Fracture mechanics

Fracture

Fracture toughness

Stress–strain analysis

Stress (mechanics)