Analytical Study Of The Steady-state Solution Of Rod-like Eutectic Growth

It has been known for a long time that,within a certain range of value of the growth rate,the metal-metal rod eutectic and metal-gas rod eutectic materials are fabricated by using the directional solidification technique which exhibit many superior physical,chemical and mechanical properties.The properties of the eutectic materials are effect by the eutectic microstructure such as the eutectic spacing or the inter-pore spacing.Therefore,the analytical calculations of the process of the eutectic microstructure formation by using the mathematical methods are coming more and more important.In this paper,the mathematical model of the metal-metal rod eutectic and the metal-gas rod eutectic growth is established to study the influence of the process parameters on the rod eutectic microstructure.The contact angle at the triple phase junction is the small order or normal order.In the other words,the triple phase junction exits singularly perturbed phenomenon.The uniformly valid asymptotic solutions of the concentration filed and the interface function of the rod eutectic growth are obtained by using the asymptotic expansion method and the matching method for the contact angle at the triple phase junction being the small order or normal order.The relationship of the dimensional interface average undercooling with the rod eutectic spacing is obtained by the uniformly valid asymptotic solutions of the interface function and the concentration field.When the dimensional interface average undercooling arrive minimum value,the relationship of the rod eutectic critical spacing and the critical inter-pore spacing with the process factors are obtained.We also obtain the relationship of the solid-liquid interface shape and the pore morphology with process factors.Particularly,the effect of the process factors on the porosity is studied.The main content is summarized as following:(1)In the system of the metal-metal rod eutectic,the effect of thepulling velocity,the thermal gradient,the alloy initial concentration,thermal gradient and ? solid phase volume fraction on the rod eutectic critical spacing is studied.We also compare our theory result with the Jackson-Hunt result.The results show that the metal-metal rod eutectic critical spacing is independent of the thermal gradient,but dependent on the growth velocity,the initial concentration and the volume fraction of the solid phase.The increase in the growth velocity,the initial concentration and the volume fraction of the solid phase results in the decrease in the rod eutectic critical spacing.The amplitude of the concave liquid-solid interface in front of ? phase gradually increases with rising the pulling velocity.However,the increase in the pulling velocity results in the decrease in the amplitude of the convex liquid-solid interface in front of ? phase.A decrease in the thermal gradient brings an increase in the amplitude of the convex liquid-solid interface in front of ? phase.However,the amplitude of concave liquid-solid interface in front of ? phase increases with decreasing the thermal gradient.The critical rod eutectic spacing is smaller than Jackson-Hunt result.As the contact angle at the triple phase junction is tend to zero,our theory results are agreement with the one given by Jackson and Hunt.(2)In the system of the metal-gas rod eutectic,the influence of the growth velocity,the thermal gradient,the gas pressure and the hot zone temperature on the pore morphology and the critical inter-pore spacing is investigated.In addition,we compare our theory result with the experimental result.The results show that the porosity is independent of the growth velocity and the thermal gradient.The increase in the hot zone temperature brings the increase in the porosity.However,the increase in the gas pressure results in the decrease in the porosity.The pore shrink as the gas pressure and the pulling velocity increase.The pore shrinks as the hot zone temperature decreases.However,the pore morphology is effect by the thermal gradient.The increase in the gas pressure brings the decrease in the critical inter-pore spacing,and the critical inter-pore spacing decreases withincreasing the hot zone temperature.The predicted values of the critical inter-pore spacing are in good agreement with the experimental results.