基于化学流变学的树脂传递模塑工艺过程的数值模拟及灵敏度分析
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摘要
近些年来,树脂传递模塑工艺(Resin Transfer Molding, RTM)是一种发展很快的复合材料制备工艺。它是指先把按性能和结构要求设计好的增强纤维材料预制体制件置放在模具型腔内,然后使用注射设备在一定压力下,将低粘度树脂体系注入模具型腔中,树脂固化后成型为有纤维预制件支撑的产品工件。由于具有低成本和高生产效率等优势,RTM工艺在很多领域的应用在日益扩大,如航空航天、舰船、汽车、建筑等。
树脂充填过程是RTM工艺成型过程中的关键环节,模具结构、纤维与树脂的材料性质、加热方式、边缘效应、树脂固化反应现象、工艺参数等都会影响产品的性能和质量。因此,综合考虑各种影响因素,深入研究树脂浸润机理以及动力学过程,将有助于建立复合材料制品制造的缺陷控制体系,从而提高产品质量、降低生产成本。
本文以RTM工艺树脂流体的充填过程为研究对象,应用多门类学科知识,建立并分析在复杂外场条件下材料体系、工艺条件、材料结构形成与充填行为之间的数学函数关系；耦合求解不同的化学与物理场量方程；自主开发等温和非等温条件下树脂充流动过程的数值模拟核心程序；引入灵敏度分析方法,定量分析工艺及材料性能参数对树脂流场的影响程度及规律。
主要工作与结论如下：
针对纤维预制体具有双级多孔介质的特点,采用局部体积平均化理论推导了预制体内树脂的流动控制方程,此动量方程考虑了树脂流体惯性力与粘性力的作用,比一般学者使用的Darcy定律的应用范围更广；基于矩形截面通道的完全发展流动控制方程以及等效渗透率的数学表达式,改进了标准Navier-Stokes方程,获得了边缘区域内树脂的流动控制方程,此模型考虑了模腔厚度对树脂流场的影响；根据大分子链的递归性质,应用全概率理论,推导了逐步聚合反应和链式聚合反应时树脂体系重均分子量的数值计算式。上述方程结合树脂固化反应动力学模型以及化学流变场的基本控制方程,便可实现树脂浸润过程的数学建模。
为了减少计算复杂性,采用单区域方法,树脂在纤维预制体内和边缘区域内的流动采用一组通用控制方程描述,此方法可避免显式列出这两个区域界面处的边界条件；考虑树脂相与空气相之间的相互作用,流体流动采用两相(树脂相和空气相)流动模型来处理,此方法可避免显式列出树脂流动前沿处的边界条件；应用有限体积法推导了相关场量控制方程的离散表达式；引入SIMPLE算法以及交错网格技术,便可实现压力场与速度场的耦合求解；采用直接积分法或向后差分方法,实现了固化反应动力学方程的离散；采用VOF/PLIC方法实时追踪充填过程中的树脂流动前沿的推进过程。上述方法为完整实施RTM工艺充填阶段的数值模拟提供关键技术支持。
编写了RTM工艺树脂充填过程的数值模拟核心程序；采用唯象模型和分子模型分别描述两种树脂体系材料(双马来酰亚胺树脂体系和环氧树脂体系)在充填过程中的化学流变行为；模拟分析了树脂固化反应程度、相对分子量、流体粘度、树脂流场随时间的演变规律,以及固化反应、流体温度、充填速度和渗透率对树脂流动前沿、模腔内化学—物理场量分布的影响,获得许多有意义的认识。
为了定性和定量地研究工艺及材料性能参数对RTM充填过程的影响,引入灵敏度分析方法,推导了相关流场物理量的灵敏度方程以及数学计算式,建立了树脂流动前沿形状的灵敏度表达式,确定了灵敏度方程与树脂流场控制方程的耦合求解方法；数值分析了在恒压和恒流速入口边界条件下,树脂温度、流体速度、注射压力、纤维预制体渗透率及边缘区域渗透率对充填时间和树脂流动前沿影响规律和程度,为提高充填效率与产品质量提出了有价值的建议。
分析了RTM工艺充模过程中温度场与树脂流场之间的关系特点,考虑厚度方向上的热传导现象,建立了二维流场/三维温度场的耦合求解方法,推导了三维能量方程在空间域和时间域上的离散形式,编写了非等温充填过程数值模拟核心程序；模拟分析了空间节点温度、树脂固化反应程度及粘度随时间的演变规律,探讨了边缘效应以及热传导系数对相关物理量空间分布的影响规律。结果表明,边缘效应会加剧模腔内相关物理场量的不均匀分布。
Recently, Resin Transfer Molding(RTM) is a fast developing technology for manufacturing fiber reinforced composite, which involves that the controlled fabrics are preplaced in the mold cavity, and then the resin with low viscosity is injected under a proper injection pressure, following by a curing stage. As advantages of low cost and high production efficiency, RTM Processes has been applied more and more extensively in many fields, such as aerospace, automotive and architecture industries.
The resin filling process is the main step in RTM processes. Many factors, such as mold structure, characteristics of fiber and resin, manner of heating, edge effect, resin curing reaction, the processing parameters and so on, will influence the performance and quality of products. As a result, considering the various influencing factors, the mechanism and the dynamic process of resin infiltration should be investigated deeply, and then the defect control system of the advanced composites is established. Consequently, the performance of advanced composites can be improved and the production cost is reduced.
In this paper, the resin flow process is researched, using multi-disciplines, the functional relationships among the materials systems, processing conditions, material microstructure and flow behavior are constructed and analyzed. The equations fulfilled by the different chemical and physical field variables were solved by an uncoupled algorithm. And then, the core programs for the numerical simulation of isothermal/non-isothermal RTM filling process is developed. The sensitivity analysis method is introduced, in the view of quantitatively analyzing the influencing law and degree of the processing parameters and materials properties on the resin flow patterns.
The main work and conclusion were as follows:
For the case of fiber preform that exhibit characteristics of dual-scale porous medium, the volume averaged method is introduced to deduce the governing equations in the preform, and the momentum equations contain the inertia and viscous terms, and its application is more extensive than that of the Darcy law. Based on the governing equations of fully developed flow in a rectangular duct and the formulation of the equivalent permeability, the modified Navier-Stokes equations are adopted to describe the resin flow in the edge channel, which considering the effect of the mold thickness on the flow patterns. Considering the different curing reaction mechanism, stepwise polymerizations and chain addition polymerizations, the weight-average molecular weight of resin is computed by employing the probability theory and the recursive nature of polymers. The above governing equations are integrated with the curing reaction kinetic equation and the chemorheological equation to model the resin infiltration process.
In order to reduce the computational complexity, the single approach is adopted, therefore, the resin flow behavior in preform/edge area can be described by one set of general governing equations, and it can avoid giving the explicit formulation of the boundary conditions at these two areas. Considering the interaction between resin fluid and air fluid, the fluid filling process are treated as two-phase flow, this method can avoid giving the explicit formulation of resin flow front. The finite volume method is applied to deduce the discrete expressions of the related governing equations. The staggered grid and the SIMPLE algorithm are introduced to compute the pressure and velocity coupling. The direct numerical integration and backward difference method are used to discretize the curing kinetic model. The Volume of Fluid/Piecewise Linear Interface Construction approach is implemented to track the resin flow front advancement during the resin flow process. The above method is the critical technique for applying the numerical simulation of the RTM filling process.
The core programs for the numerical simulation of RTM filling process is developed. The phenomenological model and a viscosity model based on the branching theory are used to describe the chemorheological behavior of BMI resin and Epoxy resin during the resin flow process, respectively. And then, the evolution of the curing degree, molecular weight, resin viscosity and flow patterns is simulated. And effects of curing reaction, fluid temperature, injection flow rate and permeability on flow patterns and distribution of curing degree and molecular weight in the mold cavity are analyzed. Some significant resluts are obtained.
In order to qualitative and quantitative explore the effect of processing parameters and material properties on the resin flow infiltration, the sensitivity analysis method is introduced, the mathematical models of sensitivity equations for the related physical quantities are deduced, the sensitivity equation of the resin flow front shape is established, and the coupling solution method for the sensitivity equations is determined. Numerical simulations of the resin flow process under constant flow rate injection condition and under constant pressure injection condition are carried out separately. And then the influencing law and degree of the resin temperature, flow rate, injection pressure, fiber permeability and the permeability in the edge area on the filling time and resin flow front are investigated. The simulated results provide valuable suggestions for improving the flow efficiency and products quality.
The relationship between the resin flow patterns and temperature field are analyzed. Considering the heat conduction in the thickness direction, the coupling resolution method is established for the 2-D flow field/3-D temperature field. The discrete expression of the 3-D energy equations in the time domain and space domain is deduced. And then the program codes for the non-isothermal resin flow process are complied. The evolution of temperature, curing degree and resin viscosity are analyzed, and the effects of edge effect and thermal conductivity on the distribution of related physical quantities are investigated. The studies show that the edge effect will aggravate a heterogeneous distribution of related physical quantities in the mold cavity.
树脂充填过程是RTM工艺成型过程中的关键环节,模具结构、纤维与树脂的材料性质、加热方式、边缘效应、树脂固化反应现象、工艺参数等都会影响产品的性能和质量。因此,综合考虑各种影响因素,深入研究树脂浸润机理以及动力学过程,将有助于建立复合材料制品制造的缺陷控制体系,从而提高产品质量、降低生产成本。
本文以RTM工艺树脂流体的充填过程为研究对象,应用多门类学科知识,建立并分析在复杂外场条件下材料体系、工艺条件、材料结构形成与充填行为之间的数学函数关系；耦合求解不同的化学与物理场量方程；自主开发等温和非等温条件下树脂充流动过程的数值模拟核心程序；引入灵敏度分析方法,定量分析工艺及材料性能参数对树脂流场的影响程度及规律。
主要工作与结论如下：
针对纤维预制体具有双级多孔介质的特点,采用局部体积平均化理论推导了预制体内树脂的流动控制方程,此动量方程考虑了树脂流体惯性力与粘性力的作用,比一般学者使用的Darcy定律的应用范围更广；基于矩形截面通道的完全发展流动控制方程以及等效渗透率的数学表达式,改进了标准Navier-Stokes方程,获得了边缘区域内树脂的流动控制方程,此模型考虑了模腔厚度对树脂流场的影响；根据大分子链的递归性质,应用全概率理论,推导了逐步聚合反应和链式聚合反应时树脂体系重均分子量的数值计算式。上述方程结合树脂固化反应动力学模型以及化学流变场的基本控制方程,便可实现树脂浸润过程的数学建模。
为了减少计算复杂性,采用单区域方法,树脂在纤维预制体内和边缘区域内的流动采用一组通用控制方程描述,此方法可避免显式列出这两个区域界面处的边界条件；考虑树脂相与空气相之间的相互作用,流体流动采用两相(树脂相和空气相)流动模型来处理,此方法可避免显式列出树脂流动前沿处的边界条件；应用有限体积法推导了相关场量控制方程的离散表达式；引入SIMPLE算法以及交错网格技术,便可实现压力场与速度场的耦合求解；采用直接积分法或向后差分方法,实现了固化反应动力学方程的离散；采用VOF/PLIC方法实时追踪充填过程中的树脂流动前沿的推进过程。上述方法为完整实施RTM工艺充填阶段的数值模拟提供关键技术支持。
编写了RTM工艺树脂充填过程的数值模拟核心程序；采用唯象模型和分子模型分别描述两种树脂体系材料(双马来酰亚胺树脂体系和环氧树脂体系)在充填过程中的化学流变行为；模拟分析了树脂固化反应程度、相对分子量、流体粘度、树脂流场随时间的演变规律,以及固化反应、流体温度、充填速度和渗透率对树脂流动前沿、模腔内化学—物理场量分布的影响,获得许多有意义的认识。
为了定性和定量地研究工艺及材料性能参数对RTM充填过程的影响,引入灵敏度分析方法,推导了相关流场物理量的灵敏度方程以及数学计算式,建立了树脂流动前沿形状的灵敏度表达式,确定了灵敏度方程与树脂流场控制方程的耦合求解方法；数值分析了在恒压和恒流速入口边界条件下,树脂温度、流体速度、注射压力、纤维预制体渗透率及边缘区域渗透率对充填时间和树脂流动前沿影响规律和程度,为提高充填效率与产品质量提出了有价值的建议。
分析了RTM工艺充模过程中温度场与树脂流场之间的关系特点,考虑厚度方向上的热传导现象,建立了二维流场/三维温度场的耦合求解方法,推导了三维能量方程在空间域和时间域上的离散形式,编写了非等温充填过程数值模拟核心程序；模拟分析了空间节点温度、树脂固化反应程度及粘度随时间的演变规律,探讨了边缘效应以及热传导系数对相关物理量空间分布的影响规律。结果表明,边缘效应会加剧模腔内相关物理场量的不均匀分布。
Recently, Resin Transfer Molding(RTM) is a fast developing technology for manufacturing fiber reinforced composite, which involves that the controlled fabrics are preplaced in the mold cavity, and then the resin with low viscosity is injected under a proper injection pressure, following by a curing stage. As advantages of low cost and high production efficiency, RTM Processes has been applied more and more extensively in many fields, such as aerospace, automotive and architecture industries.
The resin filling process is the main step in RTM processes. Many factors, such as mold structure, characteristics of fiber and resin, manner of heating, edge effect, resin curing reaction, the processing parameters and so on, will influence the performance and quality of products. As a result, considering the various influencing factors, the mechanism and the dynamic process of resin infiltration should be investigated deeply, and then the defect control system of the advanced composites is established. Consequently, the performance of advanced composites can be improved and the production cost is reduced.
In this paper, the resin flow process is researched, using multi-disciplines, the functional relationships among the materials systems, processing conditions, material microstructure and flow behavior are constructed and analyzed. The equations fulfilled by the different chemical and physical field variables were solved by an uncoupled algorithm. And then, the core programs for the numerical simulation of isothermal/non-isothermal RTM filling process is developed. The sensitivity analysis method is introduced, in the view of quantitatively analyzing the influencing law and degree of the processing parameters and materials properties on the resin flow patterns.
The main work and conclusion were as follows:
For the case of fiber preform that exhibit characteristics of dual-scale porous medium, the volume averaged method is introduced to deduce the governing equations in the preform, and the momentum equations contain the inertia and viscous terms, and its application is more extensive than that of the Darcy law. Based on the governing equations of fully developed flow in a rectangular duct and the formulation of the equivalent permeability, the modified Navier-Stokes equations are adopted to describe the resin flow in the edge channel, which considering the effect of the mold thickness on the flow patterns. Considering the different curing reaction mechanism, stepwise polymerizations and chain addition polymerizations, the weight-average molecular weight of resin is computed by employing the probability theory and the recursive nature of polymers. The above governing equations are integrated with the curing reaction kinetic equation and the chemorheological equation to model the resin infiltration process.
In order to reduce the computational complexity, the single approach is adopted, therefore, the resin flow behavior in preform/edge area can be described by one set of general governing equations, and it can avoid giving the explicit formulation of the boundary conditions at these two areas. Considering the interaction between resin fluid and air fluid, the fluid filling process are treated as two-phase flow, this method can avoid giving the explicit formulation of resin flow front. The finite volume method is applied to deduce the discrete expressions of the related governing equations. The staggered grid and the SIMPLE algorithm are introduced to compute the pressure and velocity coupling. The direct numerical integration and backward difference method are used to discretize the curing kinetic model. The Volume of Fluid/Piecewise Linear Interface Construction approach is implemented to track the resin flow front advancement during the resin flow process. The above method is the critical technique for applying the numerical simulation of the RTM filling process.
The core programs for the numerical simulation of RTM filling process is developed. The phenomenological model and a viscosity model based on the branching theory are used to describe the chemorheological behavior of BMI resin and Epoxy resin during the resin flow process, respectively. And then, the evolution of the curing degree, molecular weight, resin viscosity and flow patterns is simulated. And effects of curing reaction, fluid temperature, injection flow rate and permeability on flow patterns and distribution of curing degree and molecular weight in the mold cavity are analyzed. Some significant resluts are obtained.
In order to qualitative and quantitative explore the effect of processing parameters and material properties on the resin flow infiltration, the sensitivity analysis method is introduced, the mathematical models of sensitivity equations for the related physical quantities are deduced, the sensitivity equation of the resin flow front shape is established, and the coupling solution method for the sensitivity equations is determined. Numerical simulations of the resin flow process under constant flow rate injection condition and under constant pressure injection condition are carried out separately. And then the influencing law and degree of the resin temperature, flow rate, injection pressure, fiber permeability and the permeability in the edge area on the filling time and resin flow front are investigated. The simulated results provide valuable suggestions for improving the flow efficiency and products quality.
The relationship between the resin flow patterns and temperature field are analyzed. Considering the heat conduction in the thickness direction, the coupling resolution method is established for the 2-D flow field/3-D temperature field. The discrete expression of the 3-D energy equations in the time domain and space domain is deduced. And then the program codes for the non-isothermal resin flow process are complied. The evolution of temperature, curing degree and resin viscosity are analyzed, and the effects of edge effect and thermal conductivity on the distribution of related physical quantities are investigated. The studies show that the edge effect will aggravate a heterogeneous distribution of related physical quantities in the mold cavity.
引文
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