Lecture

Probabilistic Fracture: Weibull Model

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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 explores the Weibull model for probabilistic fracture in brittle solids, discussing the concepts of global fracture criteria, stress distribution, and the reliability of materials. The instructor covers the application of the Weibull distribution in testing materials and the implications of different m values on material reliability.

Instructors (4)

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)

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).

Official source

Related concepts (32)

Weibull distribution

In probability theory and statistics, the Weibull distribution ˈwaɪbʊl is a continuous probability distribution. It models a broad range of random variables, largely in the nature of a time to failure or time between events. Examples are maximum one-day rainfalls and the time a user spends on a web page. The distribution is named after Swedish mathematician Waloddi Weibull, who described it in detail in 1939, although it was first identified by Maurice René Fréchet and first applied by to describe a particle size distribution.

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.

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).

Gumbel distribution

In probability theory and statistics, the Gumbel distribution (also known as the type-I generalized extreme value distribution) is used to model the distribution of the maximum (or the minimum) of a number of samples of various distributions. This distribution might be used to represent the distribution of the maximum level of a river in a particular year if there was a list of maximum values for the past ten years. It is useful in predicting the chance that an extreme earthquake, flood or other natural disaster will occur.

Reliability engineering

Reliability engineering is a sub-discipline of systems engineering that emphasizes the ability of equipment to function without failure. Reliability describes the ability of a system or component to function under stated conditions for a specified period of time. Reliability is closely related to availability, which is typically described as the ability of a component or system to function at a specified moment or interval of time. The reliability function is theoretically defined as the probability of success at time t, which is denoted R(t).

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