A Simplified Hot-Tearing Criterion for Shape Castings Based on Temperature-Field Simulation
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Dt
½1
where k1-2 is the shrinkage rate from T1 to T2, and Dt is the time taken to cool from T1 to T2. k1-2 is determined by the alloy composition. For an alloy with known chemical composition, k1-2 is only determined by T1 and T2. Dt is determined by the cooling rate R: Dt ¼
T1 T2 ; R12
eO;12
½3
eO;12 ¼ D12 R12 :
½4
½5
If all of the deformation due to shrinkage concentrates at position O, the deformation rate ef due to the free shrinkage can be written as: ef ¼ LD12 R12 :
½6
When there are constraints at both ends, the alloy cannot shrink freely. If there is no crack nucleation, the deformation rate along the length direction es should be equal to the free shrinkage rate of ef, i.e.: es ¼ ef ¼ LD12 R12 :
½7
es
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