Theory of thermal stresses and air-gap formation during the early stages of solidification in a rectangular mold

Richmond, O.; Tien, R. H.

doi:10.1016/0022-5096(71)90013-5

Cited by 58 publications

(16 citation statements)

References 5 publications

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“…ð2:42Þ which then gives Richmond & Tien (1971), that the lateral stress, i.e. s x , should vanish when the air gap forms; we continue to use that condition thereafter also.…”

Section: K1mentioning

confidence: 99%

“…A similar procedure using (3.20) and (3.35) gives While there is no doubt that S!0 when solidification begins, there is no guarantee that there is a solution for Z gap for all possible combinations of operating parameters; such a situation was found by Richmond & Tien (1971). For example, if _ Sð0; ZÞ!…”

Section: ð3:33þmentioning

confidence: 99%

“…In view of the detrimental effect that the air gap has on process efficiency, mathematical models of varying degrees of complexity have been derived to describe the phenomenon. Early analytical models for predicting the onset of air-gap formation, although not its evolution, were due to Savage (1962), Richmond & Tien (1971), Kristiansson (1982) and Tien & Richmond (1982). Most subsequent models have been numerical and have adopted different approaches for handling the thermomechanical interaction at the air gap.…”

Section: Introductionmentioning

confidence: 99%

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An asymptotic model for the formation and evolution of air gaps in vertical continuous casting

Vynnycky

2009

Proc. R. Soc. A.

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The formation of an air gap at the mould-metal interface in vertical continuous casting has long been known to have a detrimental effect on the efficiency of the process, and has therefore attracted attempts at mathematical modelling. While almost all current efforts consist of complex three-dimensional numerical simulations of the phenomenon, this paper considers instead an asymptotic model that captures the essential characteristics. The model is thermomechanical and is derived for a geometry, where the generalized plane strain approximation is appropriate. Although two-way coupling between the thermal and mechanical problems is accounted for, it is found that the problems decouple at leading order anyway, and that the thickness of the air gap does not depend on the constitutive relation used for describing the inelastic strains. Furthermore, a criterion for the onset of air-gap formation is derived in terms of the process operating parameters. Mathematically, we obtain a moving boundary problem for a parabolic partial differential equation with a degenerate initial condition and a non-standard Neumann-type boundary condition. Sample computations are performed using parameters for the continuous casting of the copper, and the results, qualitative trends and possible extensions are discussed.

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“…ð2:42Þ which then gives Richmond & Tien (1971), that the lateral stress, i.e. s x , should vanish when the air gap forms; we continue to use that condition thereafter also.…”

Section: K1mentioning

confidence: 99%

Section: ð3:33þmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An asymptotic model for the formation and evolution of air gaps in vertical continuous casting

Vynnycky

2009

Proc. R. Soc. A.

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“…The analysis of the deformation of a solidifying body is significantly different from that of a standard fixed body [6][7][8]. These efforts emphasize the need to incorporate both the initial stresses at the instant of solidification as well as the fact that the growing nature of a solidifying body leads to an incompatibility of the strain tensor.…”

Section: Introductionmentioning

confidence: 99%

A thermomechanical study of the effects of mold topography on the solidification of Aluminum alloys

Tan

Zabaras

2005

Materials Science and Engineering: A

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A thermomechanical study of the effects of mold topography on the solidification of aluminum alloys at early times is provided. The various coupling mechanisms between the solid-shell and mold deformation and heat transfer at the mold/solid-shell interface during the early stages of aluminum solidification on molds with uneven topographies are investigated. The air-gap nucleation time, the stress evolution and the solid-shell growth pattern are examined for different mold topographies to illustrate the potential control of aluminum cast surface morphologies during the early stages of solidification using proper design of mold topographies. The unstable shell growth pattern in the early solidification stages results mainly from the unevenness of the heat flux between the solid-shell and the mold surface. This heat flux is determined by the size of the air-gaps formed between the solidifying shell and mold surface or from the value of the contact pressure. Simulation results show that a sinusoidal mold surface with a smaller wavelength leads to nucleation of air-gaps at earlier times. In addition, the unevenness in the solid-shell growth pattern decreases faster for a smaller wavelength. Such studies can be used to tune mold surfaces for the control of cast surface morphologies.

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“…This is obtained from the assumption that there is no discontinuous change in the stress state of a particle as it passes from the liquid to the solid state. It therefore follows that the newly-solidified material is instantaneously in a state of hydrostatic compression [14].…”

Section: The Development Of Residual Stressmentioning

confidence: 99%

Thermoelastic instability in planar solidification

Barber

1991

International Journal of Mechanical Sciences

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Abstract--A linear perturbation method is used to examine the stability of a unidirectional solidification problem in which a liquid, initially at the melting temperature, becomes solidified by heat transfer across a pressure-dependent thermal contact resistance to a plane mold. The contact pressure will be influenced by thermal distortion in response to the instantaneous temperature field in the solidified shell. The heat transfer and thermal stress problems are therefore coupled through the boundary conditions.The temperature and stress fields are assumed to consist of a unidirectional component and a small spatially-sinusoidal perturbation which can vary with time. Analysis of the thermoelastic problem for the solidified shell leads to an ordinary differential equation relating the perturbation in heat flux at the mold/casting interface and the corresponding perturbation in contact pressure. A second equation relating the same two variables is obtained by linear perturbation of the relation for heat conduction across the thermal contact resistance. These are then reduced to a single equation which is solved numerically. The results show that a small initial perturbation will grow substantially during the solidification process if the thermal contact resistance is very sensitive to pressure.

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Theory of thermal stresses and air-gap formation during the early stages of solidification in a rectangular mold

Cited by 58 publications

References 5 publications

An asymptotic model for the formation and evolution of air gaps in vertical continuous casting

An asymptotic model for the formation and evolution of air gaps in vertical continuous casting

A thermomechanical study of the effects of mold topography on the solidification of Aluminum alloys

Thermoelastic instability in planar solidification

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