A geometric analysis technique for crystal growth and microstructure development in single-crystal welds had been previously developed.And the effect of welding conditions on the tendency of stray grains formation during solidification was researched.In the present work,these analytical methods were further extended.Combined with an original vectorization method,a 3D Rosenthal solution was used to determine thermal conditions of the welds.Afterward,the dendrite growth orientation,the dendrite growth velocity and the thermal gradient along dendrite direction were calculated and lively plotted.Finally,the tendency of stray grains formation in the solidification front was forecasted and its distribution was presented with a 3D plot.The results indicate that substrate orientation has some impacts on the crystal growth pattern,dendrite growth velocity,distribution of thermal gradient and stray grain.Based on the research methods proposed in this work,any substrate crystallographic orientation can be studied,and predicted stray grains distribution can be visualized.
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