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TYC@imperial: A continuum theory for the fractures in brittle and ductile solids

Luca Cimbaro

Department of Physics

Monday 12th February 2018
Time: 12.00pm
Venue: Room G01, Royal School of Mines
Contact: Ms Hafiza Bibi
Tel: 02075947252

Abstract: In the physics of the fracture, brittle solids, such as glass, suddenly break when a sharp crack grows on the cleavage plane. In contrast, ductile solids, such as copper, are soft and resistant to cleavage. In the brittle solids, the elastic field of the medium determines the growth of the crack, while Griffith's equation expresses the thermodynamic condition at the point of the growth. However, in hard ductile materials, such as precipitation-hardened alloys, the plastic strains determine the sliding-off rupture. At the macroscopic scale, this fracture is similar to the cleavage fracture. When a small region at the tip of the crack contains the plastic strains, the Orowan-Irwin formula expresses the thermodynamic condition. The distinction between brittle and ductile solids does not reflect all the varieties of materials because there are intermediate solids where the features of the elastic fracture and those of the plastic rupture coexist. I will present a continuum theory of the fracture in solids, where the brittle and the ductile solids are the particular limits of the intermediate solids. For instance, in this theory, the stress field explains the type of the fracture, while the thermodynamic condition generalises Griffith's equation to include the shielding of the dislocations at the crack-tip. When only the plastic strains determine the fracture, this thermodynamic condition proves the Orowan-Irwin formula. Also, this theory has a versatile geometry, which can be used to solve applied problems, such as the embrittlement of the nickel-based superalloys at high temperatures.

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