Rapid solidification of liquid alloy is an importantsubject in both fundamental research and practical applications. However,theideal theoretical descriptionsofcrystal growth kineticsduring this processhave been still...Rapid solidification of liquid alloy is an importantsubject in both fundamental research and practical applications. However,theideal theoretical descriptionsofcrystal growth kineticsduring this processhave been still lacked up to now. Although several theories have been setup by using traditional methematical physics methods,the experimental results reveal that they cannot be universally applicable for different experimental conditions. The LKT model[1 ] ,for example,is quite successful to describe dendrite growth during rapid solidification. But it has been confirmed bo be only useful within medium undercooling regime[2 ,3 ] . With the developing of the materials science in space,the undercooling up to 2 0 0 to 50 0 K can be obtained by modern experimenttechniques. Therefore,itis highly desirable to develop a more universal theoretical model which can depictrapid dendrite growth within any attainable undercooling regime. The artificial neural network (ANN) technique is an important research field in automatic control engineering and hasalso found many application in otherscientific areas. By using such a method,Sun and coworkers[4] successfully predicated the thermophysical properties of high temperature metallurgical melts. Li and Xu[5 ] acquired satisfactory results when they used ANN technique to study the CVD/Si C coating formation processof C/C composites.However,there is no reporton dendrite growth investigation during rapid solidification by ANN technique.The objective of this paperis to directsome efforts to thisrespect. Since rapid solidification is a typical complex nonlinear dynamic process characterized by some random elements,a stochastic fuzzy neural network(SFNN model) which incorporates random control into ANN technique is developed and applied. The SFNN model is schematically presented in Fig.1 . This is a forward neural network with multi- inputs and single output. It consists of one input layer,one output layer and two hidden layers. Input parameters mainly involve such independent variables as melt undercooling and alloy composition,while output resultis dendrite growth velocity. The relationship between the outputand inputis determined by the following equation. f(x) = ∑M l=1 y g′δg′exp - y g′- mg′δg′ 2 ∏n i=1 exp - (xi - m F′i) 2 σ2F′i +σ2x′i∑M l=1 1 δg′exp - y g′- mg′δg′ 2 ∏n i=1 exp - (xi - m F′ i) 2 σ2F′ i +σ2x′ i (1 ) The back propagation (BP) learning method is used to train the above SFNN model. The corresponding targetfunction is: E =1 2 [f (x) - yd] 2 (2 ) In order to minimize the error E,the weights during parameter learning are modified according to the following rule: w(k +1 ) =w(k) -α E wk -η E wk-1 (3)In Eqs. (1 )～ (3) ,y g′、mg′、σg′、m F′i、σF′i andσx′i are adjusting parameters,α∈ [0 ,1 ] is learning coefficient, andη∈ [0 ,1 ] is momentum factor. The selected alloy for investigation is Ni- 35% Fe and the experiment was done by glass fluxing technique. The composition of the denucleating agent is 80 .6% Si O2 +1 2 .8% B2 O3+3.6% Na2 O+2 .4% Al2 O3+0 .6% K2 O. The masteralloy was prepared in situ from 99.999% pure Fe and 99.998% Ni by RF induction melting.Each sample had a mass of1 g and the experiments were fulfilled under80 k Pa Ar atmosphere. Both the undercooling and dendrite growth velocity were measured by infrared detecting technique.The LKT model wasalso used to calculate thedendrite growth velocity forfurtheranalysis and comparison. Fig.2 presents the experimental and theoretical results.It can be seen that the maximum obtained undercooling of Ni- 35% Fe alloy melt is 31 0 K(0 .1 8TL) and the corresponding dendrite growth velocity was measured as 77m/ s. The LKT growth model is well consistentwith experimental results only when undercooling is smaller than 1 70 K. If the undercooling exceeds this value and is further enhanced,large deviation appears. In such a case,the dendrite growth velocity rises up infinitely although the temperature-展开更多
文摘Rapid solidification of liquid alloy is an importantsubject in both fundamental research and practical applications. However,theideal theoretical descriptionsofcrystal growth kineticsduring this processhave been still lacked up to now. Although several theories have been setup by using traditional methematical physics methods,the experimental results reveal that they cannot be universally applicable for different experimental conditions. The LKT model[1 ] ,for example,is quite successful to describe dendrite growth during rapid solidification. But it has been confirmed bo be only useful within medium undercooling regime[2 ,3 ] . With the developing of the materials science in space,the undercooling up to 2 0 0 to 50 0 K can be obtained by modern experimenttechniques. Therefore,itis highly desirable to develop a more universal theoretical model which can depictrapid dendrite growth within any attainable undercooling regime. The artificial neural network (ANN) technique is an important research field in automatic control engineering and hasalso found many application in otherscientific areas. By using such a method,Sun and coworkers[4] successfully predicated the thermophysical properties of high temperature metallurgical melts. Li and Xu[5 ] acquired satisfactory results when they used ANN technique to study the CVD/Si C coating formation processof C/C composites.However,there is no reporton dendrite growth investigation during rapid solidification by ANN technique.The objective of this paperis to directsome efforts to thisrespect. Since rapid solidification is a typical complex nonlinear dynamic process characterized by some random elements,a stochastic fuzzy neural network(SFNN model) which incorporates random control into ANN technique is developed and applied. The SFNN model is schematically presented in Fig.1 . This is a forward neural network with multi- inputs and single output. It consists of one input layer,one output layer and two hidden layers. Input parameters mainly involve such independent variables as melt undercooling and alloy composition,while output resultis dendrite growth velocity. The relationship between the outputand inputis determined by the following equation. f(x) = ∑M l=1 y g′δg′exp - y g′- mg′δg′ 2 ∏n i=1 exp - (xi - m F′i) 2 σ2F′i +σ2x′i∑M l=1 1 δg′exp - y g′- mg′δg′ 2 ∏n i=1 exp - (xi - m F′ i) 2 σ2F′ i +σ2x′ i (1 ) The back propagation (BP) learning method is used to train the above SFNN model. The corresponding targetfunction is: E =1 2 [f (x) - yd] 2 (2 ) In order to minimize the error E,the weights during parameter learning are modified according to the following rule: w(k +1 ) =w(k) -α E wk -η E wk-1 (3)In Eqs. (1 )～ (3) ,y g′、mg′、σg′、m F′i、σF′i andσx′i are adjusting parameters,α∈ [0 ,1 ] is learning coefficient, andη∈ [0 ,1 ] is momentum factor. The selected alloy for investigation is Ni- 35% Fe and the experiment was done by glass fluxing technique. The composition of the denucleating agent is 80 .6% Si O2 +1 2 .8% B2 O3+3.6% Na2 O+2 .4% Al2 O3+0 .6% K2 O. The masteralloy was prepared in situ from 99.999% pure Fe and 99.998% Ni by RF induction melting.Each sample had a mass of1 g and the experiments were fulfilled under80 k Pa Ar atmosphere. Both the undercooling and dendrite growth velocity were measured by infrared detecting technique.The LKT model wasalso used to calculate thedendrite growth velocity forfurtheranalysis and comparison. Fig.2 presents the experimental and theoretical results.It can be seen that the maximum obtained undercooling of Ni- 35% Fe alloy melt is 31 0 K(0 .1 8TL) and the corresponding dendrite growth velocity was measured as 77m/ s. The LKT growth model is well consistentwith experimental results only when undercooling is smaller than 1 70 K. If the undercooling exceeds this value and is further enhanced,large deviation appears. In such a case,the dendrite growth velocity rises up infinitely although the temperature-
