A Mathematical Model of Interdendritic Thermometallurgical Strain for Dendritic Solidification Processes
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INTERDENDRITIC
strain,[1–5] when it generates sufficiently through the dendritic solid during the interdendritic coherent region in the mushy zone, is an unlikely phenomenon in the casting processes because sufficient interdendritic strain increases the possibility of casting defects formation, such as interdendritic cracking phenomena,[1] a high positive segregation,[2,3] and residuals stresses.[6] Depending on the generation of this strain and its pattern, it can affect the frequency and severity of casting defects by different mechanisms. These complex mechanisms can affect the quality of cast products and become time consuming and costly.[7] At the present time, the interdendritic strain can be classified into four main types generated from different sources.[8–10] Theses types are elastic, thermometallurgical, mechanical, and creep that generate through the dendritic solid within the interdendritic coherent region in the mushy zone. For these reasons, the derivation of the constitutive interdendritic strain equation is fundamentally important to explain the causes, sources, and means of minimization interdendritic strain, which leads to zero defects casting practice. Several authors previously have attempted to predict the magnitude and rate of interdendritic strain.[11–18] In these studies, the mathematical models describing the thermomechanical behavior of the mushy zone as a function of temperature and steel composition have
M.O. EL-BEALY, Chair Professor of Materials Processing & Technology, is with the Companies Chair of Swedish Iron Masters Association, S-100 44 Stockholm, Sweden. Contact email: moelbealy@ hotmail.com Manuscript submitted August 4, 2009. Article published online July 22, 2011. 1280—VOLUME 42B, DECEMBER 2011
been developed. These thermomechanical models essentially are required, which can explain both the experimental values of critical strain and the fracture stress criteria of interdendritic internal crack based on the changes in the strength and ductility behaviors as a result of solidification phenomena close to the solid front in the mushy zone. In the viewpoint of the experimental approach, the studies pointed out that the thermomechanical behavior of mushy zone is sensitive to the strain rate not only because the strain rate hardening of steel is considerable but also because creep cannot be distinguished from plastic strain.[19] In the view point of a numerical approach and beside mechanical deformation, other mechanisms of stress development such as thermal contraction and phase transformation influence the stress development close to the solid front in the mushy zone.[8,20] However, much effort has been put earlier into the understanding of interdendritic strain generated from different solidification phenomena, and several interdendritic strain formation theories from different sources have been proposed. These theories focused on the accumulated strain within the so-called vulnerable part of the solidification interval and the roles of interdendritic strain generation.[21,22] The solidificati
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