Quantitative Binary And Multi-phase Phase Field Modle Of Entire Solidification Process And Hot Cracking Susceptibility Of Al-Cu Alloy

Solidification hot cracking is the main defect in alloy solidification process.The study of microstructure evolution during solidification is helpful to analyze the mechanism of hot cracking defects and provide some principles for the design of production technology and product structure.As an important simulation method of microstructure evolution,phase field method has unique advantages in the study of interface dynamics.In the process of phase field simulation,the microstructure evolution information close to the actual solidification process can be obtained by coupling the external field such as temperature field and solute field correctly and efficiently.Based on this,the solidification path information can be extracted as the input data of the hot cracking susceptibility prediction model.Therefore,in this paper,a reasonable prediction of the hot cracking susceptibility of Al-Cu alloy was expected to achieve by constructing a binary polyphase and polycrystal quantitative phase field model that can calculate the accurate solidification path,combined with the hot cracking susceptibility evaluation model.A quantitative phase field model was established to simulate the whole process of solution solidification of binary multiphase（multisolid）alloys under non-isothermal conditions,including multiphase nucleation,free growth of multiphase dendrite and interdendrite condensation.At the same time,the expressions of temperature dependent thin interface limit condition and thermal noise are given.The grain boundary energy and interface dynamics coefficient can be tuned by the phase field model.The grain boundary energy range isγ_gb/γ_sl∈（2,5）.In addition,the thermal noise term equations related to temperature,adjusting the local coupling coefficient（inversely proportional to the nucleation barrier）to simulate the heterogeneous nucleation inoculants,dynamically and randomly allocated the heterogeneous nucleation points in the phase field model were proposed to coupling the nucleation process to phase field model,which enable to achieve the quantitative simulation of the entire process of binary multi-phase solidification.Based on this model,the nucleation and growth of the second phase between dendrites during directional solidification of Al-Cu alloy were simulated.The results show that when the second phase is generated,the growth of the second phase not only inhibits the growth of the interdendrite liquid tank,but also keeps the width of the liquid tank sufficiently,which is conducive to the replenation of the liquid phase.Therefore,the growth of the second phase in the interdendrite is beneficial to reduce the sensitivity of the thermal crack.Aiming at the important effect of grain boundary energy on the intergrain coalescence process,a quantitative phase field model of binary dilute solution polycrystalline solidification was established to quantitatively simulate the dendrite free growth and grain coalescence process.The proposed model can be used to regulate the grain boundary energies of three different types of grain boundaries（attractive,neutral and repulsive）,and the range of grain boundary energy regulation isγ_gb/γ_sl∈（0,5）.nn this basis,the simulation studies of grain boundary coalescence behaviors under three grain boundary energy conditions are carried out.The results show that the coalescence behavior characteristics of different grain boundaries in phase field simulation are consistent with that of sharp interface model.The coalescence temperature decreases with the rise of grain boundary energy.The interface instability of attractive grain boundary appears during the process of coalescence.With the decrease of the diffusion coefficient of solid phase solute,the coalescence temperature decreases.In addition,by comparision of the results between one-dimensional and two-dimensional phase field simulations,it is found that the effect of back diffusion on the solidification process is very limited due to the rapid diffusion of solute in the liquid channel between dendrites,which indicates that the dilute binary quantitative phase field model for solidification constructed in this paper can be used to quantitatively simulate the coalescence process of polycrystalline system.The solidification paths calculated by Scheil model and quantitative phase field model are compared and analyzed.The results show that the solidification path calculated by Scheil modelconstruced for one-dimensional directional solidification process is different from that calculated by quantitative phase field model,especially at the end of solidification,so it is not suitable to be used as the input data of thermal crack evaluation model.Meanwhile,two hot cracking susceptibility evaluation models（RDG and HCI index）are compared and analysized.The results show that the predictions by HCI index,proposed on the basis of the RDG model,are not consistent with the predictions of the RDG model by use the solidification path calculated by the quantitative phase field calculation.Therefore,combination of the quantitative multi-crystal phase field model and RDG model were proposed to predict the hot cracking susceptibility.The polycrystalline quantitative phase field model was used to simulate the growth of Al-Cu twin crystals under quantitative solidification condition.The effects of grain boundary energy,intergrain angle,grain arrangement and thermal noise on crack tendency of solidification heat were studied by extracting the solidification path information.The results show that the tendency of hot crack tendency of Al-Cu alloy is"Λ"with the change of concentration,which is consistent with the experimental result.With the increase of grain boundary energy,the concentration corresponding to the peak of hot crack tendency decreases gradually.The corresponding concentration of the highest peak of hot crack tendency in divergent grain arrangement is higher than that in accumulated grain arrangement.For the grain boundary with large angle,the pressure drop decreases with the grain boundary angle increasing.The pressure drop calculated by RDG model,based on the solidification path calculated by quantitative phase field model,and the theoretical cracking stress of liquid phase are compared and analyzed.The results show that the maximum pressure drop increases with the grain boundary energy increasing.Whenγ_gb/γ_sl≥1,the maximum pressure drop is higher than 10 MPa.The maximum pressure drop is higher than 600 MPa when the grain boundary is repulsive and grains growth condition is convergent,indicating that the hot cracking usually occurs at the large angle grain boundary（repulsive grain boundary）.In addition,the solute concentration range with pressure drop over 10 MPa at different grain boundary energies was statistically analyzed,and it was found that the concentration range of solute where hot cracks could occur was 0.50-3.25 wt.%,which is consistent with most of experimental results.Therefore,the quantitative phase field model and RDG model for the whole solidification process constructed in this paper can not only predict the tendency of hot cracking,but also predict the initiation of hot cracking,which also can instruct the development of materials and procedure.