考虑界面相的单向复合材料力学性能预报研究
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摘要
碳纤维增强树脂基复合材料(CFRP)由于其诸多卓越的力学性能在工程领域得到广泛应用。复合材料的宏观性能是由其特殊的细观结构决定的,为了更加充分地发挥其力学潜能,需要深入了解其宏观现象的细观本质。随着实验技术的发展,人们对复合材料界面相的认识逐渐深入,从改变界面相性能角度优化复合材料是目前的一个研究热点。在这样的背景下,建立含有界面相的单向复合材料力学性能预报具有重要的工程和学术意义。为了在理论上清晰描述本论文的研究思路,将复合材料整体上等效为一个黑匣子,其细观和宏观参数分别作为黑匣子的输入和输出部分,性能预报研究的主要任务就是揭开黑匣子的秘密,建立该输入输出之间的定量关系,为复合材料的优化设计、性能评价提供理论指导。
本文针对单向CFRP,在考虑界面相的前提下,从刚度性能、热弹性性能、强度性能三个角度建立一套基于细观力学的性能预报方法,在预报宏观性能的同时揭示细观弹性应力状态直至损伤和破坏过程机理。本文所建立的性能预报模型在考虑纤维和基体等组分的同时,充分考虑了界面相的力学性能,并详细分析了界面相参数的影响规律。综合来讲,本文主要研究内容如下:
1.刚度性能预报:本文通过解析法和有限元法预报单向CFRP的五个独立弹性常数。解析法是基于Eshelby等效夹杂原理,应用Mori-Tanaka方法进行两步等效,第一步将界面相和碳纤维等效为新的等效纤维,第二步将上一步得到的等效纤维与树脂基体进行等效得出整体刚度性能,从而预报出复合材料宏观刚度矩阵。有限元法将复合材料简化为一个代表性体积元(RVE),附上组分材料属性并施加周期性边界条件,施加各个方向载荷并经过线弹性分析得出刚度矩阵中的五个独立参数。这两种方法的预报结果得到宏观实验数据的对比验证,在此基础上应用Mori-Tanaka方法分析了界面相参数的影响规律。
2.热弹性性能预报:热弹性性能预报主要包括热残余应力分析和宏观等效热膨胀系数(CTE)预报,后者依赖于前者准确的细观力学分析模型。针对由于细观组分材料的CTE不匹配引起的热残余应力,将复合材料简化为含有纤维、界面相、基体的轴对称圆柱体,建立弹性力学基本方程并结合边界条件得到残余应力场,其结果与有限元数值结果几乎完全一致。在此基础上,提出增量法用以分析树脂性能随温度变化的特点,其分析结果得到了碳纤维单丝电阻法实验验证;针对宏观等效CTE预报,在前面的热残余应力分析模型基础上预报复合材料的宏观等效CTE,并得到宏观实验数据的验证,最后分析了界面相参数对其影响规律。
3.强度性能预报:本文主要分析复合材料纵向拉伸强度和横向拉压强度。根据碳纤维纵向拉伸强度呈随机分布的特点,本文分别采用不同方法预报纵向拉伸强度和横向拉压强度。针对纵向拉伸载荷,采用基于蒙特卡洛的渐进损伤分析模型,从热残余应力、纤维间应力传递、纤维单丝的逐渐断裂三个层次不断循环计算,直到所有纤维断裂为止,从而预报出复合材料的纵向拉伸强度,结果得到宏观纵向拉伸实验数据验证;针对横向拉压载荷,界面脱粘或树脂开裂是其主要破坏模式,本文采用显式有限元方法分析其渐进损伤过程。通过SEM照片或碰撞模型得到纤维随机分布的几何微结构,在Abaqus中建立该微结构几何模型,通过渐进损伤分析得到横向拉压载荷下的损伤破坏过程,从而预报出横向拉压强度,并通过SEM原位实验和宏观横向拉压实验数据验证,确定模型的合理性以后分析了界面相等细观参数的影响规律。
本文所建立的一整套性能预报方法同样适用于其它复合材料,通过这些理论可以揭示复合材料细观与宏观之间的关联关系。
Carbon fiber reinforced plastic composites (CFRP) has been widely used in many kinds of structures due to their excellent mechanical performances. These excellent macro performances are mainly controlled by the mechanical properties of micro components. Thus, it is especially important to understand the micro mechanical properties of composite detailly for fully inspiring its macro mechanical properties. With the development of experimental techniques, interphase existing between fiber and matrix has been deeply understood gradually. Recently, it appears a new research area in which composite is optimized by considering the effect of variation of the interphase properties. Based on this background, it has an important significance to establish model to valuate the mechanical properties of composites with interphase for composites optimization.
For unidirectional CFRP with interphase, this paper establishs a set of performances prediction methods, such as stiffness, CTE and strength etc. Meanwhile, the elastic and damage until failure modes of the composites are given with the increase of external load. The effects of interphase are considered in detail in the micromechanical models. Overall, the main contents of this paper are provided as follows:
1. Stiffness prediction. Stiffness properties of the composites are predicted by the analytical and finite element methods. Unidirectional fibrous reinforced composites are considered as transverse isotropic materials, which have five independent parameters in the stiffness matrix. The analytical and finite element methods were applied to predict these five independent parameters. In the analytical method, the Mori-Tanaka method based on Eshelby equivalent inclusion theory was used twice to evaluate the stiffness of the composites. In the finite element method, composite was simplified to a representative volume element (RVE). Then, five independent parameters were obtained after linear elastic analysis. The result was verified by experimental results. At last, the Mori-Tanaka method was used to analyze the influence of interphase parameters.
2. Thermal elastic properties prediction. In this paper, thermal elastic analysis includes thermal residual stress analysis and the prediction of macro equivalent coefficient of thermal expansion. Fiber composite is simplified as an axisymmetric cylinder model containing three phases: fiber, interphase and matrix. Elastic equations with boundary conditions were established to get the residual stresses. The analytical results are well agreement with the finite element results. The sub-increment method was used to overcome the fact that epoxy properties change with temperature, and it was verified by single carbon fiber resistance experiment. Based on the cylinder model, macro equivalent CTEs of the composites were predicted and verified by experiments. Then, the influence of interphase parameters on macro CTEs was analyzed.
3. Strength prediction. This paper mainly discusses the composite longitudinal tensile strength and transverse strength. According to discrete distribution of carbon fiber tensile strength, different methods were used to predict the longitudinal and transverse strength. In longitudinal direction, the Monte Carlo method was applied to conduct progressive damage analysis. There are three factors, including residual stress, stress transfer and fiber breakage, which are required to be considered in the model. The analysis was conducted iteratively until all fibers were broken, and the longitudinal tensile strength was obtained. The result was verified by macro experiments. In transverse direction, interphase debonding and matrix crack are the main failure modes. The explicit finite element was used to analyze the progressive damage process until ultimate failure. The geometric microstructure obtained by SEM or elastic collision model was imported into Abaqus. The transverse tensile or compressive strength was obtained by the progressive damage analysis. The result was also verified by experiment as well. At last, the influence of the interphase parameters on macro strength was analyzed.
These mechanical performance prediction methods in this paper can also be applied to analyze for many other composites to establish the relationship between the micro component parameters and macro performances.
本文针对单向CFRP,在考虑界面相的前提下,从刚度性能、热弹性性能、强度性能三个角度建立一套基于细观力学的性能预报方法,在预报宏观性能的同时揭示细观弹性应力状态直至损伤和破坏过程机理。本文所建立的性能预报模型在考虑纤维和基体等组分的同时,充分考虑了界面相的力学性能,并详细分析了界面相参数的影响规律。综合来讲,本文主要研究内容如下:
1.刚度性能预报:本文通过解析法和有限元法预报单向CFRP的五个独立弹性常数。解析法是基于Eshelby等效夹杂原理,应用Mori-Tanaka方法进行两步等效,第一步将界面相和碳纤维等效为新的等效纤维,第二步将上一步得到的等效纤维与树脂基体进行等效得出整体刚度性能,从而预报出复合材料宏观刚度矩阵。有限元法将复合材料简化为一个代表性体积元(RVE),附上组分材料属性并施加周期性边界条件,施加各个方向载荷并经过线弹性分析得出刚度矩阵中的五个独立参数。这两种方法的预报结果得到宏观实验数据的对比验证,在此基础上应用Mori-Tanaka方法分析了界面相参数的影响规律。
2.热弹性性能预报:热弹性性能预报主要包括热残余应力分析和宏观等效热膨胀系数(CTE)预报,后者依赖于前者准确的细观力学分析模型。针对由于细观组分材料的CTE不匹配引起的热残余应力,将复合材料简化为含有纤维、界面相、基体的轴对称圆柱体,建立弹性力学基本方程并结合边界条件得到残余应力场,其结果与有限元数值结果几乎完全一致。在此基础上,提出增量法用以分析树脂性能随温度变化的特点,其分析结果得到了碳纤维单丝电阻法实验验证;针对宏观等效CTE预报,在前面的热残余应力分析模型基础上预报复合材料的宏观等效CTE,并得到宏观实验数据的验证,最后分析了界面相参数对其影响规律。
3.强度性能预报:本文主要分析复合材料纵向拉伸强度和横向拉压强度。根据碳纤维纵向拉伸强度呈随机分布的特点,本文分别采用不同方法预报纵向拉伸强度和横向拉压强度。针对纵向拉伸载荷,采用基于蒙特卡洛的渐进损伤分析模型,从热残余应力、纤维间应力传递、纤维单丝的逐渐断裂三个层次不断循环计算,直到所有纤维断裂为止,从而预报出复合材料的纵向拉伸强度,结果得到宏观纵向拉伸实验数据验证;针对横向拉压载荷,界面脱粘或树脂开裂是其主要破坏模式,本文采用显式有限元方法分析其渐进损伤过程。通过SEM照片或碰撞模型得到纤维随机分布的几何微结构,在Abaqus中建立该微结构几何模型,通过渐进损伤分析得到横向拉压载荷下的损伤破坏过程,从而预报出横向拉压强度,并通过SEM原位实验和宏观横向拉压实验数据验证,确定模型的合理性以后分析了界面相等细观参数的影响规律。
本文所建立的一整套性能预报方法同样适用于其它复合材料,通过这些理论可以揭示复合材料细观与宏观之间的关联关系。
Carbon fiber reinforced plastic composites (CFRP) has been widely used in many kinds of structures due to their excellent mechanical performances. These excellent macro performances are mainly controlled by the mechanical properties of micro components. Thus, it is especially important to understand the micro mechanical properties of composite detailly for fully inspiring its macro mechanical properties. With the development of experimental techniques, interphase existing between fiber and matrix has been deeply understood gradually. Recently, it appears a new research area in which composite is optimized by considering the effect of variation of the interphase properties. Based on this background, it has an important significance to establish model to valuate the mechanical properties of composites with interphase for composites optimization.
For unidirectional CFRP with interphase, this paper establishs a set of performances prediction methods, such as stiffness, CTE and strength etc. Meanwhile, the elastic and damage until failure modes of the composites are given with the increase of external load. The effects of interphase are considered in detail in the micromechanical models. Overall, the main contents of this paper are provided as follows:
1. Stiffness prediction. Stiffness properties of the composites are predicted by the analytical and finite element methods. Unidirectional fibrous reinforced composites are considered as transverse isotropic materials, which have five independent parameters in the stiffness matrix. The analytical and finite element methods were applied to predict these five independent parameters. In the analytical method, the Mori-Tanaka method based on Eshelby equivalent inclusion theory was used twice to evaluate the stiffness of the composites. In the finite element method, composite was simplified to a representative volume element (RVE). Then, five independent parameters were obtained after linear elastic analysis. The result was verified by experimental results. At last, the Mori-Tanaka method was used to analyze the influence of interphase parameters.
2. Thermal elastic properties prediction. In this paper, thermal elastic analysis includes thermal residual stress analysis and the prediction of macro equivalent coefficient of thermal expansion. Fiber composite is simplified as an axisymmetric cylinder model containing three phases: fiber, interphase and matrix. Elastic equations with boundary conditions were established to get the residual stresses. The analytical results are well agreement with the finite element results. The sub-increment method was used to overcome the fact that epoxy properties change with temperature, and it was verified by single carbon fiber resistance experiment. Based on the cylinder model, macro equivalent CTEs of the composites were predicted and verified by experiments. Then, the influence of interphase parameters on macro CTEs was analyzed.
3. Strength prediction. This paper mainly discusses the composite longitudinal tensile strength and transverse strength. According to discrete distribution of carbon fiber tensile strength, different methods were used to predict the longitudinal and transverse strength. In longitudinal direction, the Monte Carlo method was applied to conduct progressive damage analysis. There are three factors, including residual stress, stress transfer and fiber breakage, which are required to be considered in the model. The analysis was conducted iteratively until all fibers were broken, and the longitudinal tensile strength was obtained. The result was verified by macro experiments. In transverse direction, interphase debonding and matrix crack are the main failure modes. The explicit finite element was used to analyze the progressive damage process until ultimate failure. The geometric microstructure obtained by SEM or elastic collision model was imported into Abaqus. The transverse tensile or compressive strength was obtained by the progressive damage analysis. The result was also verified by experiment as well. At last, the influence of the interphase parameters on macro strength was analyzed.
These mechanical performance prediction methods in this paper can also be applied to analyze for many other composites to establish the relationship between the micro component parameters and macro performances.
引文
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