【作者】 周力；

【导师】 侯华；

【作者基本信息】 中北大学 ， 材料加工工程， 2010， 硕士

【摘要】 微观组织数值模拟对金属材料的发展和应用有着重要意义，也是计算机应用于材料科学领域的主要发展方向之一。微观组织数值模拟的方法主要有：确定性方法、随机方法及相场法。其中相场法是一种用于描述在非平衡状态中复杂相界面演变强有力的工具，不需要跟踪复杂固液界面，就可实现模拟金属凝固过程中枝晶生长的复杂形貌，是目前凝固组织模拟的国际前沿研究领域。本文基于金兹堡－朗道相变理论，分别建立了一个以熵增原理的二元合金相场模型和自由能减小原理的纯物质相场模型，并在薄界面限制条件下，建立了相场参数与材料热物性参数的关系；采用基于均匀网格的有限差分离散控制方程，网格剖分采用了双重网格法。数值计算时，为了避免时间步长的限制，提高计算效率，相场和溶质场控制方程采用了用显式算法，即向前Euler法；温度控制方程则采用交替方向隐式法（ADI算法）。分析了各向异性对平衡形貌的影响，发现在界面各向异性系数变化中，这之间有一临界值，二维的临界值为0.067；建立了引入各向异性的二维相场模型，并对二维各向异性项进行了离散；分别对二维界面能各向异性进行了数值模拟，得到了模拟结果与理论分析结果基本相符；在大于临界值时，相场模型模拟出的结果出现了失真。在相场模型的基础上推导了噪声的数学模型，给出了相场噪声和温度场噪声的数学方程；从理论上分析了相场模型中噪声的引入，提出了三种噪声引入的方法；对噪声产生侧向分支进行了模拟，发现热噪声能够引发枝晶侧向不稳定,是侧向分支形成的主要起因。模拟了不同过冷度下纯镍凝固过程枝晶生长，发现温度场可解释过冷度对二次枝晶生长的影响的原因；低过冷度下枝晶半径随过冷度的增加而减少，与边缘稳定性理论和微观可解性理论一致。更多还原

【Abstract】 Numerical simulation of microstructure plays an important role on the development and application of metallic materials, and it is also one of the main development directions which a computer used in the field of materials science. There are some microstructure numerical simulation methods: deterministic methods, stochastic methods and phase field method. Phase-field methods can be used to describe the complicated morphologies of dendritic growth without explicitly tracking the complex phase boundaries. It is expected as a powerful tool to describe complex phase transitions in non-equilibrium state. It is the frontier domain of the numerical simulation during solidification processes at present.Based on the Ginzburg - Landau theory of phase transitions, respectively, it established a principle of entropy of binary alloy phase field model and the principle of freedom to reduce the phase-field model of pure substances , and in the thin interface limit condition, it established a relationship between phase-field parameters and thermal physical parameters. Using uniform grid based on finite difference equations to discrete control equation, mesh generation used a dual grid. Numerical calculations, in order to avoid time step constraints, and improving computational efficiency, phase field and solute field equations used an explicit algorithm, that is forward Euler method; temperature control equation is adopted alternating direction implicit method (ADI method) .We analyzed the impact of anisotropy on the equilibrium shape and found a critical value. The critical value is 0.067,also we established a two-dimensional anisotropic phase field model, and two-dimensional anisotropic discrete items; respectively, two-dimensional interface energy anisotropy of the numerical simulation results obtained the result was consistent with the theoretical analysis; In greater than the critical value, the phase field model to simulate came out with the distortion.In the phase field model based on the noise derived mathematical model of phase field and temperature field disturbance disturbance mathematical equation; from the theoretical analysis of the phase field model, the introduction of noise, making noise, the introduction of three ways; noise generated on the lateral branches were simulated and found that thermal noise can lead to dendritic lateral instability is the main cause of the formation of lateral branches.Simulation under different undercooling solidification process of pure nickel dendrite growth, found that could explain the undercooling temperature on the secondary branch growth of the reasons; low undercooling dendrite radius increases with the undercooling decrease and the result is consistent with the edge of stability theory and the microscopic solvability of the theory.更多还原