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Mathematics of the portevin-le chatelier effect

1972; University of Toronto Press; Volume: 20; Issue: 10 Linguagem: Inglês

10.1016/0001-6160(72)90165-4

1878-0768

Paul Penning,

Rheology and Fluid Dynamics Studies

Abstract The Portevin-Le Chatelier effect is associated with an inhomogeneous plastic flow in the tensile specimen. It is shown mathematically that the strain rate at any point in the specimen must make jumps as a function of time, whenever the stress as a function of strain rate, for given strain, goes through a maximum and minimum. Two types of solutions are considered: the region, where appreciable deformation takes place, either moves continuously or hops through the specimen. Small strain rates in front of the moving band cause a strain gradient in the specimen. The deformation band moves in the direction of increasing strain.