1991
DOI: 10.1115/1.2897699
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On the Calculation of Deformations and Stresses During Axially Symmetric Solidification

Abstract: In this paper finite element modeling of the deformation and stress development in solidifying bodies is presented. Emphasis is given to axially symmetric problems and especially to the accurate implementation of thermal and mechanical phenomena occurring at the freezing front. More specifically, the interface velocity and location are treated as primary variables of the heat transfer analysis, and the isostatic stress condition at the front is utilized as an initial condition in the stress analysis. A hypoela… Show more

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Cited by 27 publications
(9 citation statements)
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“…Studies have been carried out using numerical modelling to explore the underlying mechanisms of the physical phenomena described above (Rubinsky et al 1980;Thom et al 1983;Lin et al 1990;Zabaras et al 1991;Pegg 1996;Rabin & Steif 1996, 1998Kandra & Devireddy 2008;Trelea et al 2009;Zhmakin 2009). It has been demonstrated that mathematical models can be used to correlate thermophysical phenomena and biological outcomes to optimize experimental methods (Bischof 2006;Song et al 2009).…”
Section: Introductionmentioning
confidence: 99%
“…Studies have been carried out using numerical modelling to explore the underlying mechanisms of the physical phenomena described above (Rubinsky et al 1980;Thom et al 1983;Lin et al 1990;Zabaras et al 1991;Pegg 1996;Rabin & Steif 1996, 1998Kandra & Devireddy 2008;Trelea et al 2009;Zhmakin 2009). It has been demonstrated that mathematical models can be used to correlate thermophysical phenomena and biological outcomes to optimize experimental methods (Bischof 2006;Song et al 2009).…”
Section: Introductionmentioning
confidence: 99%
“…The hyperbolic-sine constitutive law was used to describe the creep behavior of the casting. This constitutive law was used successfully in previous research for modeling pure aluminum casting in continuous casting [29]. The constitutive equation is given in the next section.…”
Section: Materials Modelmentioning
confidence: 99%
“…Zabras et al [29] built a finite element model to be used in simulating continuous or ingot casting process of pure aluminum. This model is limited to castings of axial symmetry or plain strain casting conditions.…”
Section: Thermal Stressesmentioning
confidence: 99%
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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%