热固性树脂基复合材料的固化变形数值模拟
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摘要
纤维增强树脂基复合材料具有比强度和比模量高、可设计性强、抗疲劳性和耐腐蚀性好以及便于整体成型等优点,已广泛用于航空航天、建筑、汽车、舰船、体育器材等领域。复合材料制品的性能很大程度上依赖于其制造工艺。树脂传递模塑(Resin Transfer Molding, RTM)因其具有的独特优势成为纤维增强树脂基复合材料的主要制备技术之一。针对国家中长期科技发展规划中确立的大飞机重大专项,开展纤维复合材料的树脂传递模塑制备技术研究,实现高性能、低缺陷、低成本目标,具有重大的现实意义。
RTM工艺的固化阶段是影响制品质量的关键环节之一。在固化过程中,由复合材料内部温度场和固化度场分布的不均匀性而引起的热应力以及固化收缩应力对复合材料的力学性能、形状以及尺寸稳定性有着较大的影响,可能导致复合材料层合板发生翘曲、基体开裂以及分层等现象。因此,复合材料的固化过程成为人们的研究重点之一
在固化过程中,复合材料的物理力学性能和内应力在时空间的分布具有非均匀、非稳态、强耦合的特点,需要揭示其演变规律,进而发展复合材料固化变形的调控机制。因此,本文以RTM工艺中热固性树脂的固化过程为研究对象,应用交联反应动力学理论、高分子交联反应统计理论、高聚物结构与性能理论、复合材料热-弹性理论、复合材料本构理论、数值传热学和有限元模拟方法等学科知识,开展树脂固化反应-交联结构-力学性能的集成研究。在此基础上分析复合材料的固化收缩应力和热应力的形成机制,数值模拟内应力的演变过程以及复合材料结构件的固化变形。然后分析各种工艺因素和结构因素对内应力和固化变形的影响方式和影响规律。引入局部灵敏度分析方法,定量分析复合材料制备过程中各种工艺因素和结构因素对固化变形的影响程度及规律。根据固化变形对其影响因素的局部灵敏度分析结果提出固化变形的调控方法。
主要工作与结论如下：
复合材料固化过程中形成的热应力主要是由复合材料的温度场控制的,而固化收缩应力主要是由复合材料的固化度场控制的。要掌握复合材料固化过程中产生的热应力和固化收缩应力,对复合材料温度场和固化度场的准确模拟是关键。本文根据热-化学模型和固化动力学模型的耦合计算,求解了复合材料的温度场和固化度场,分析了影响温度场和固化度场的影响因素,如固化工艺温度、对流换热系数、热传导系数、升温速率、材料厚度和纤维体积分数等。
在模拟温度场和固化度场的过程中,通过分析温度-时间-固化度之间的关系,发现在等固化条件下固化温度和固化时间的对数之间存在近似的线性关系。通过数据拟合,提出了一种简化固化动力学模型的新方法。在此基础上得到了时间-温度-固化度三者之间较为简单的关系式,简化了原先较为复杂的固化动力学方程。简化后的方程能够方便地用于工程实际,避免了繁琐的求解。
时间-温度-转变(Time-Temperature-Transformation, TTT)图是分析和设计固化过程的有用工具,具有重要的研究价值。大多数的TTT图都是通过分析大量的实验数据得出的,既费时又费力,而且还存在较大的系统误差。本文以一种具体的树脂体系为研究对象,通过数值模拟的方法预测得到了TTT图,大大节省了时间和成本。
复合材料的使用性能取决于其物理性能和力学性能,而材料结构是实现所需物理性能和力学性能的基础。从理论上来说,总可以找到某种材料结构来满足材料的某些性能需求。从应用的角度看,必须知道用于形成某种材料结构的加工工艺条件。同时,必须建立材料结构与材料性能之间的定量关系,从而既能够根据材料结构来定量地预测材料性能,又能够根据对材料性能的具体要求来确定材料结构。因此,进行材料的加工工艺—微观结构—宏观力学性能的集成研究,分析在具体的加工工艺条件下树脂结构、力学性能的演变过程,对于材料的开发、加工工艺的优化等方面都具有重要意义。本文结合高分子交联统计理论、树脂固化动力学、数值传热学等理论知识,建立了树脂固化过程的温度场、化学反应程度场和交联结构场的基本方程,分析了在固化反应过程中温度、固化反应程度、交联结构和力学性能等物理量的基本变化规律,实现了固化工艺-交联结构-力学性能之间诸多场量的集成研究。
分析了固化过程中复合材料的热物理性能变化,给出在固化过程中复合材料的模量、密度、热膨胀系数、比热、热传导系数等参数的计算方法及变化规律；然后结合一个具体的算例对比分析了在不同的固化工艺温度下,树脂及复合材料的弹性模量和剪切模量、收缩应变等物理量随时间的变化规律,并分析了在固化过程中复合材料内应力的形成及发展过程。
分析了影响复合材料结构件固化变形的工艺因素及结构因素,这些因素包括固化工艺温度、降温速率、对流换热系数、纤维体积分数、铺层方式、固化反应放热、固化收缩、层间纯树脂和树脂的粘弹效应等。任何一种树脂材料都或多或少具有粘弹效应,只是程度不同而已。在我们的研究中,由于计算机资源的限制和出于对计算时间的考虑,我们大多采用了线弹性模型。而在分析树脂的粘弹效应对固化变形的影响时,我们设计了几组对比算例,对比分析了线弹性模型和粘弹性模型的差异。研究发现,在复合材料纤维体积分数比较高、树脂固化收缩率比较低的情况下,采用线弹性和粘弹性两种模型计算的固化变形量差别不大,因为这时树脂的粘弹效应不显著。
在分析了各种工艺因素及结构因素对固化残余应力和固化变形的影响规律之后,为了研究工艺及结构参数对复合材料固化变形的影响程度,引入了局部灵敏度分析方法,量化了这些因素对固化变形的影响程度。结果表明：纤维体积分数、固化收缩率、铺层方式和固化工艺温度都对复合材料固化变形有着显著的影响。在采用局部灵敏度分析方法研究了各因素对固化变形的影响程度之后,根据局部灵敏度分析结果,着重针对对固化变形影响程度比较大的因素提出了调控固化变形的方法。
Fiber reinforced resin matrix composites have varieties of applications in aerospace, automobile, architecture and sports equipment industries because of their notable performances, such as high specific strength and modulus, easy to design, good fatigue resistance and good corrosion resistance. The performances of this kind of composite are highly reliable on molding processes. Resin Transfer Molding (RTM) is one of the advanced manufacturing techniques and attracts more and more attention owing to its unique advantages. Aimed at the large aircraft development projects established by country mid-long-term scientific and technological development plan, research on the preparation technical of fiber composites by RTM technology to achieve high performance, low-defect, low-cost objectives is of great practical significance.
The numerical simulation of the curing stage during RTM process is of significant importance in improving the product quality and reducing the cost. During curing process, because of the uneven distribution of the temperature field and cure degree field, the internal stress including thermal stress and chemical stress, can be induced, which can influence mechanical properties, shape and dimensional stability of composites, and may result in the composite plate warping, matrix cracking and matrix delimitation. Therefore, curing process attracts more and more attention and becomes one of the most important research priorities.
During the curing process, the time-space distributions of the physical and mechanical properties and internal stress of composites show the characteristics of non-uniform, non-steady state and strong coupling, so we need to reveal their evolution laws, and develop the curing deformation control mechanism of the composites. Therefore, making the curing process of thermosetting resin as the study project, using polymer crosslinking reaction kinetic theory, polymer crosslinking reaction statistical theory, composite thermoelastic theory, composite constitutive theory, numerical heat transfer theory and finite element simulation method, the project attempts to carry out the integration research about the resin curing reaction-crosslinked structure-mechanical properties. On this basis, we aimed to explore the formation mechanism of curing shrinkage stress and thermal stress in composites, simulate the evolution of its internal stress and curing deformation and analyze the effects of the processing parameters and structural parameters on the curing deformation. In order to qualitatively and quantitatively explore the effects of processing parameters, structural parameters and material performance parameters on the internal stress and curing deformation, the local sensitivity analysis method is introduced and quantitatively analyze the evolutions and influencing degrees of processing parameters, structural parameters and material performance parameters during the curing process on the internal stress and curing deformation in the composites. On the basis of the local sensitivity analysis, the regulation mechanism of composite curing deformation during the composite preparation process can be proposed and realized.
The main contents and conclusions were as follows:
During the curing process, thermal stress is mainly controlled by the temperature field, and chemical stress is mainly controlled by the cure degree field. In order to understand the evolution of thermal stress and chemical stress during the curing process, accurately simulating the temperature and cure degree fields is an important procedure. According to coupling the heat transfer model and cure kinetic model, temperature and cure degree fields are simulated. The influencing factors of temperature and cure degree fields are analyzed, including cure temperature, convective heat transfer coefficient, thermal conductivity, heating rate, material thickness and fiber volume fraction.
When simulating the temperature and cure degree fields, by analyzing the relationship among the temperature, time and degree of cure, we find that there is a linear relationship between the curing temperature and the logarithm of curing time under the iso-conversional conditions. By means of data fitting method, we propose a new simplified method of cure kinetic model. On the basis of this simplified method, the relatively simple relationships among time-temperature-cure degree are obtained, which simplify the original complex cure kinetic equation and can be easily used in engineering practice to avoid the cumbersome solution process.
Time-Temperature-Transformation (TTT) diagram is a useful tool for analyzing and designing the curing process, and it has important research value. Most of the TTT diagrams are drawn through analyzing a large number of experimental data, which is time-consuming and laborious. There are also large systematic errors in experimental method. In this paper, we obtained the TTT diagram of a specific resin by numerical simulation method, which saves time greatly.
On one hand, from the viewpoint of basic research, certain material structures could be designed to meet specific material performance requirements. Therefore, the research on the formation mechanism and evolution characteristics of material structures attracts more and more attention. On the other hand, from the viewpoint of industrial production, the appropriate processing conditions must be designed in order to obtain the specific material structures. In a word, it is important for both basic research and industrial production to understand the quantitative relationship among thermosetting resin curing processes, crosslink structures and mechanical properties. In this paper, using such disciplines as the polymer crosslinking reaction statistical theory, resin cure kinetic, heat transfer theory and so on, the basis equations of temperature field, cure degree field and crosslink structure field are established; the evolutions of temperature, degree of cure, crosslink structure and mechanical properties are analyzed; and the integrated research of resin curing processes, crosslink structures and mechanical properties are realized.
We analyze the evolution of the thermal and physical properties of the composites during the curing process, and indicate the computing method and evolution of modulus, density and thermal expansion coefficient, specific heat and thermal conductivity. After that, aiming at a specific example, we analyze comparatively evolution of the elasticity modulus, shear modulus and shrinkage strain of resin and composites. Finally, we analyze the formation and development processes of the internal stress during the curing process.
The processing parameters and structural parameters which influence the curing deformation are analyzed. These factors include cure temperature, cooling rate, convective heat transfer coefficient, the fiber volume fraction, lay-up styles, the curing reaction heat, curing shrinkage, viscoelastic effect of the resin and so on. All kinds of resin materials are more or less viscoelastic. Otherwise, in our paper, due to the computer resource constraints and saving the computing time, we choose the linear elastic model in most examples. While in the analysis of resin viscoelastic effect on curing deformation, we design several groups of comparison cases to analyze the difference between the linear elastic model and the viscoelastic model. We find out that the difference between the results which are calculated by the two models respectively is not significant when the fiber volume fraction is relatively high and the resin curing shrinkage is relatively low. That means the resin viscoelastic effect is not significant.
After the analysis of the effects of processing parameters and structural parameters on internal stress and curing deformation, in order to explore the effects of processing parameters and structural parameters on curing deformation, the local sensitivity analysis method is introduced. The results indicate that fiber volume fraction, curing shrinkage, lay-up styles and cure temperature have significant influence on curing deformation. After the analysis of the influencing degree of several factors by the local sensitivity analysis method, we propose the advices of controlling the curing deformation focusing on the most important factors of curing deformation.
RTM工艺的固化阶段是影响制品质量的关键环节之一。在固化过程中,由复合材料内部温度场和固化度场分布的不均匀性而引起的热应力以及固化收缩应力对复合材料的力学性能、形状以及尺寸稳定性有着较大的影响,可能导致复合材料层合板发生翘曲、基体开裂以及分层等现象。因此,复合材料的固化过程成为人们的研究重点之一
在固化过程中,复合材料的物理力学性能和内应力在时空间的分布具有非均匀、非稳态、强耦合的特点,需要揭示其演变规律,进而发展复合材料固化变形的调控机制。因此,本文以RTM工艺中热固性树脂的固化过程为研究对象,应用交联反应动力学理论、高分子交联反应统计理论、高聚物结构与性能理论、复合材料热-弹性理论、复合材料本构理论、数值传热学和有限元模拟方法等学科知识,开展树脂固化反应-交联结构-力学性能的集成研究。在此基础上分析复合材料的固化收缩应力和热应力的形成机制,数值模拟内应力的演变过程以及复合材料结构件的固化变形。然后分析各种工艺因素和结构因素对内应力和固化变形的影响方式和影响规律。引入局部灵敏度分析方法,定量分析复合材料制备过程中各种工艺因素和结构因素对固化变形的影响程度及规律。根据固化变形对其影响因素的局部灵敏度分析结果提出固化变形的调控方法。
主要工作与结论如下：
复合材料固化过程中形成的热应力主要是由复合材料的温度场控制的,而固化收缩应力主要是由复合材料的固化度场控制的。要掌握复合材料固化过程中产生的热应力和固化收缩应力,对复合材料温度场和固化度场的准确模拟是关键。本文根据热-化学模型和固化动力学模型的耦合计算,求解了复合材料的温度场和固化度场,分析了影响温度场和固化度场的影响因素,如固化工艺温度、对流换热系数、热传导系数、升温速率、材料厚度和纤维体积分数等。
在模拟温度场和固化度场的过程中,通过分析温度-时间-固化度之间的关系,发现在等固化条件下固化温度和固化时间的对数之间存在近似的线性关系。通过数据拟合,提出了一种简化固化动力学模型的新方法。在此基础上得到了时间-温度-固化度三者之间较为简单的关系式,简化了原先较为复杂的固化动力学方程。简化后的方程能够方便地用于工程实际,避免了繁琐的求解。
时间-温度-转变(Time-Temperature-Transformation, TTT)图是分析和设计固化过程的有用工具,具有重要的研究价值。大多数的TTT图都是通过分析大量的实验数据得出的,既费时又费力,而且还存在较大的系统误差。本文以一种具体的树脂体系为研究对象,通过数值模拟的方法预测得到了TTT图,大大节省了时间和成本。
复合材料的使用性能取决于其物理性能和力学性能,而材料结构是实现所需物理性能和力学性能的基础。从理论上来说,总可以找到某种材料结构来满足材料的某些性能需求。从应用的角度看,必须知道用于形成某种材料结构的加工工艺条件。同时,必须建立材料结构与材料性能之间的定量关系,从而既能够根据材料结构来定量地预测材料性能,又能够根据对材料性能的具体要求来确定材料结构。因此,进行材料的加工工艺—微观结构—宏观力学性能的集成研究,分析在具体的加工工艺条件下树脂结构、力学性能的演变过程,对于材料的开发、加工工艺的优化等方面都具有重要意义。本文结合高分子交联统计理论、树脂固化动力学、数值传热学等理论知识,建立了树脂固化过程的温度场、化学反应程度场和交联结构场的基本方程,分析了在固化反应过程中温度、固化反应程度、交联结构和力学性能等物理量的基本变化规律,实现了固化工艺-交联结构-力学性能之间诸多场量的集成研究。
分析了固化过程中复合材料的热物理性能变化,给出在固化过程中复合材料的模量、密度、热膨胀系数、比热、热传导系数等参数的计算方法及变化规律；然后结合一个具体的算例对比分析了在不同的固化工艺温度下,树脂及复合材料的弹性模量和剪切模量、收缩应变等物理量随时间的变化规律,并分析了在固化过程中复合材料内应力的形成及发展过程。
分析了影响复合材料结构件固化变形的工艺因素及结构因素,这些因素包括固化工艺温度、降温速率、对流换热系数、纤维体积分数、铺层方式、固化反应放热、固化收缩、层间纯树脂和树脂的粘弹效应等。任何一种树脂材料都或多或少具有粘弹效应,只是程度不同而已。在我们的研究中,由于计算机资源的限制和出于对计算时间的考虑,我们大多采用了线弹性模型。而在分析树脂的粘弹效应对固化变形的影响时,我们设计了几组对比算例,对比分析了线弹性模型和粘弹性模型的差异。研究发现,在复合材料纤维体积分数比较高、树脂固化收缩率比较低的情况下,采用线弹性和粘弹性两种模型计算的固化变形量差别不大,因为这时树脂的粘弹效应不显著。
在分析了各种工艺因素及结构因素对固化残余应力和固化变形的影响规律之后,为了研究工艺及结构参数对复合材料固化变形的影响程度,引入了局部灵敏度分析方法,量化了这些因素对固化变形的影响程度。结果表明：纤维体积分数、固化收缩率、铺层方式和固化工艺温度都对复合材料固化变形有着显著的影响。在采用局部灵敏度分析方法研究了各因素对固化变形的影响程度之后,根据局部灵敏度分析结果,着重针对对固化变形影响程度比较大的因素提出了调控固化变形的方法。
Fiber reinforced resin matrix composites have varieties of applications in aerospace, automobile, architecture and sports equipment industries because of their notable performances, such as high specific strength and modulus, easy to design, good fatigue resistance and good corrosion resistance. The performances of this kind of composite are highly reliable on molding processes. Resin Transfer Molding (RTM) is one of the advanced manufacturing techniques and attracts more and more attention owing to its unique advantages. Aimed at the large aircraft development projects established by country mid-long-term scientific and technological development plan, research on the preparation technical of fiber composites by RTM technology to achieve high performance, low-defect, low-cost objectives is of great practical significance.
The numerical simulation of the curing stage during RTM process is of significant importance in improving the product quality and reducing the cost. During curing process, because of the uneven distribution of the temperature field and cure degree field, the internal stress including thermal stress and chemical stress, can be induced, which can influence mechanical properties, shape and dimensional stability of composites, and may result in the composite plate warping, matrix cracking and matrix delimitation. Therefore, curing process attracts more and more attention and becomes one of the most important research priorities.
During the curing process, the time-space distributions of the physical and mechanical properties and internal stress of composites show the characteristics of non-uniform, non-steady state and strong coupling, so we need to reveal their evolution laws, and develop the curing deformation control mechanism of the composites. Therefore, making the curing process of thermosetting resin as the study project, using polymer crosslinking reaction kinetic theory, polymer crosslinking reaction statistical theory, composite thermoelastic theory, composite constitutive theory, numerical heat transfer theory and finite element simulation method, the project attempts to carry out the integration research about the resin curing reaction-crosslinked structure-mechanical properties. On this basis, we aimed to explore the formation mechanism of curing shrinkage stress and thermal stress in composites, simulate the evolution of its internal stress and curing deformation and analyze the effects of the processing parameters and structural parameters on the curing deformation. In order to qualitatively and quantitatively explore the effects of processing parameters, structural parameters and material performance parameters on the internal stress and curing deformation, the local sensitivity analysis method is introduced and quantitatively analyze the evolutions and influencing degrees of processing parameters, structural parameters and material performance parameters during the curing process on the internal stress and curing deformation in the composites. On the basis of the local sensitivity analysis, the regulation mechanism of composite curing deformation during the composite preparation process can be proposed and realized.
The main contents and conclusions were as follows:
During the curing process, thermal stress is mainly controlled by the temperature field, and chemical stress is mainly controlled by the cure degree field. In order to understand the evolution of thermal stress and chemical stress during the curing process, accurately simulating the temperature and cure degree fields is an important procedure. According to coupling the heat transfer model and cure kinetic model, temperature and cure degree fields are simulated. The influencing factors of temperature and cure degree fields are analyzed, including cure temperature, convective heat transfer coefficient, thermal conductivity, heating rate, material thickness and fiber volume fraction.
When simulating the temperature and cure degree fields, by analyzing the relationship among the temperature, time and degree of cure, we find that there is a linear relationship between the curing temperature and the logarithm of curing time under the iso-conversional conditions. By means of data fitting method, we propose a new simplified method of cure kinetic model. On the basis of this simplified method, the relatively simple relationships among time-temperature-cure degree are obtained, which simplify the original complex cure kinetic equation and can be easily used in engineering practice to avoid the cumbersome solution process.
Time-Temperature-Transformation (TTT) diagram is a useful tool for analyzing and designing the curing process, and it has important research value. Most of the TTT diagrams are drawn through analyzing a large number of experimental data, which is time-consuming and laborious. There are also large systematic errors in experimental method. In this paper, we obtained the TTT diagram of a specific resin by numerical simulation method, which saves time greatly.
On one hand, from the viewpoint of basic research, certain material structures could be designed to meet specific material performance requirements. Therefore, the research on the formation mechanism and evolution characteristics of material structures attracts more and more attention. On the other hand, from the viewpoint of industrial production, the appropriate processing conditions must be designed in order to obtain the specific material structures. In a word, it is important for both basic research and industrial production to understand the quantitative relationship among thermosetting resin curing processes, crosslink structures and mechanical properties. In this paper, using such disciplines as the polymer crosslinking reaction statistical theory, resin cure kinetic, heat transfer theory and so on, the basis equations of temperature field, cure degree field and crosslink structure field are established; the evolutions of temperature, degree of cure, crosslink structure and mechanical properties are analyzed; and the integrated research of resin curing processes, crosslink structures and mechanical properties are realized.
We analyze the evolution of the thermal and physical properties of the composites during the curing process, and indicate the computing method and evolution of modulus, density and thermal expansion coefficient, specific heat and thermal conductivity. After that, aiming at a specific example, we analyze comparatively evolution of the elasticity modulus, shear modulus and shrinkage strain of resin and composites. Finally, we analyze the formation and development processes of the internal stress during the curing process.
The processing parameters and structural parameters which influence the curing deformation are analyzed. These factors include cure temperature, cooling rate, convective heat transfer coefficient, the fiber volume fraction, lay-up styles, the curing reaction heat, curing shrinkage, viscoelastic effect of the resin and so on. All kinds of resin materials are more or less viscoelastic. Otherwise, in our paper, due to the computer resource constraints and saving the computing time, we choose the linear elastic model in most examples. While in the analysis of resin viscoelastic effect on curing deformation, we design several groups of comparison cases to analyze the difference between the linear elastic model and the viscoelastic model. We find out that the difference between the results which are calculated by the two models respectively is not significant when the fiber volume fraction is relatively high and the resin curing shrinkage is relatively low. That means the resin viscoelastic effect is not significant.
After the analysis of the effects of processing parameters and structural parameters on internal stress and curing deformation, in order to explore the effects of processing parameters and structural parameters on curing deformation, the local sensitivity analysis method is introduced. The results indicate that fiber volume fraction, curing shrinkage, lay-up styles and cure temperature have significant influence on curing deformation. After the analysis of the influencing degree of several factors by the local sensitivity analysis method, we propose the advices of controlling the curing deformation focusing on the most important factors of curing deformation.
引文
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