Low-temperature nitriding of steel or iron can produce an expanded austenite phase,which is a solid solution of a large amount of nitrogen dissolved interstitially in fcc lattice.It is characteristic that the nitogen ...Low-temperature nitriding of steel or iron can produce an expanded austenite phase,which is a solid solution of a large amount of nitrogen dissolved interstitially in fcc lattice.It is characteristic that the nitogen depth profiles in expanded austenite exhibit plateau-type shapes.Such behavior cannot be considered with a standard analytic solution for diffusion in a semi-infinite solid and a new approach is necessary.We formulate a model of interdiffusion in viscoelastic solid(Maxwellmodel)during the nitriding process.It combines themass conservation and Vegard’s rule with the Darken bi-velocity method.The model is formulated in any dimension,i.e.,a mixture is included in R^(n),n=1,2,3.For the system in one dimension,n=1,we transform a differential-algebraic system of 5 equations to a differential system of 2 equations only,which is better to study numerically and analytically.Such modification allows the formulation of effective mixed-type boundary conditions.The resulting nonlinear strongly coupled parabolic-elliptic differential initial-boundary Stefan type problem is solved numerically and a series of simulations is made.展开更多
基金the National Science Center(Poland)Decision No.UMO-2013/11/B/ST8/03758the Faculty of Applied Mathematics AGH UST statutory tasks within subsidy of Ministry of Science and Higher Education(Grant No.16.16.420.054).
文摘Low-temperature nitriding of steel or iron can produce an expanded austenite phase,which is a solid solution of a large amount of nitrogen dissolved interstitially in fcc lattice.It is characteristic that the nitogen depth profiles in expanded austenite exhibit plateau-type shapes.Such behavior cannot be considered with a standard analytic solution for diffusion in a semi-infinite solid and a new approach is necessary.We formulate a model of interdiffusion in viscoelastic solid(Maxwellmodel)during the nitriding process.It combines themass conservation and Vegard’s rule with the Darken bi-velocity method.The model is formulated in any dimension,i.e.,a mixture is included in R^(n),n=1,2,3.For the system in one dimension,n=1,we transform a differential-algebraic system of 5 equations to a differential system of 2 equations only,which is better to study numerically and analytically.Such modification allows the formulation of effective mixed-type boundary conditions.The resulting nonlinear strongly coupled parabolic-elliptic differential initial-boundary Stefan type problem is solved numerically and a series of simulations is made.
