基于内聚力模型的复合材料拉伸性能细观有限元分析
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摘要
现如今，无论从航空航天技术和核设备工程到微电子或者结构工程应用，复合材料都发挥着重要的作用。考虑到这一现实以及数值试验在结构和工业生产过程设计中的作用越来越大，计算力学研究和发展方向的最重要的内容之一就是要能够对这些材料进行精确模拟。现代复合材料计算力学通过不同的科学领域，从实验材料科学到先进计算技术和应用数学，遵从许多不同的研究方法。基于有限元方法的商业计算机程序(例如ABAQUS、ANSYS等)现在能够进行可视化多场、多相和非稳态物理和力学问题的研究，甚至可以使用随机变量把不确定性引入到计算机模拟之中。本论文基于细观力学理论，用有限元方法分析了两种典型复合材料(纤维增强单向复合材料和纳米化不锈钢层合轧压复合材料)的力学性能与其内在组分材料之间的关系，进行了如下几个方面的研究工作：
1．对纤维增强单向复合材料的横向SEM图像进行了数字化处理，得到了纤维在横截面内的几何微结构特征属性,包括面积、离心率、空间分布、方位角等。然后，编写了方便ABAQUS软件调用的Python语言脚本程序。该程序实现了两种纤维随机分布的RVE模型的生成方法：一种是用于较低体积含量的硬核算法，另一种是用于较高体积含量的RVE模型生成的双扰动算法。本文利用双扰动算法生成的RVE模型，对纤维增强单向复合材料进行了横向刚度分析和极限承载力的分析。
2．在考虑界面相情况下，对纤维增强单向复合材料横截面内单向拉伸时的力学行为进行了数值模拟，其中，界面相单元采用服从线性应力—分离演化规律的内聚力单元来表示。讨论了界面相厚度、模量、泊松比和强度对于复合材料整体横向性能的影响。研究结果表明：界面相厚度越小，界面相对刚度的影响越弱，而对泊松比ν的影响越大；界面相模量越大，复合材料的等效模量越大；复合材料整体横向拉伸强度随着界面相强度的增加而增加。
3．联合使用ABAQUS中的子程序USDFLD和UMAT，模拟了单纤维复合材料体系的纵向拉伸损伤过程。其中，用内聚力单元来实现纤维与基体界面的脱粘过程。研究发现：对于此类模拟，退化因子d=0.01是足够而有效的；各个组分材料的强度对材料的失效都有明显的影响。
4．通过在有限元网格中间插入内聚力单元，建立了纳米化不锈钢层合轧压结构复合材料的内聚有限元模型。分别研究了纳米晶层材料和粗晶基体材料的内聚强度与能量释放率对复合材料整体失效应变的影响，总结了拉伸过程中，微裂纹个数与损伤耗散能的变化规律。此外，纳米晶层体积含量在两种不同分布形式下，对复合材料整体失效应变的影响也做了初步研究。
综上所述，本文建立了两种典型复合材料的有限元模型，研究了这些材料在拉伸载荷下的力学响应，希望本文的结果能够为更进一步的研究与复合材料的设计及工程应用提供一定的参考和帮助。
Nowadays composites play a very important role in engineering from aerospacetechnology and nuclear devices to microelectronics or structural engineering applications.Considering this fact and the growing role of numerical experiments in the designing ofstructures and industrial processes, one of the most important purposes of computationalmechanics research and direction of progress appeared to be precise numerical modelling ofthese materials. Modern computational mechanics of composite materials follows manyvarious ways through different science domains from experimental materials science toadvanced computational techniques and applied mathematics. Commercial computerprograms (such as ABAQUS and ANSYS) based on the Finite Element Method enable nowvisualisation of the multifield, multiphase and non-stationary physical and mechanicalproblems and even introducing uncertainty into computer simulation using random variables.Based on mesomechanics, the mechanical properties and relationship between the constitutematerials of two typical composites (unidirectional fiber reinforced composite and nano rolledstainless steel laminated composites) have been analysed. The following aspects have beenresearched in detail:
1. In order to obtain the geometric properties of micro-structural of the fiber (such asarea, eccentricity, spatial distribution and orientation) in the cross section, the transverse SEMpicture of unidirectional fiber reinforced composites is digital processed. Then, script isdeveloped using Python language, which will be called by ABAQUS comfortably. Two typesof fiber random distribution RVE generation method are carried out in the script. One is hardcore algorithm which will be used for low volume content, and the other is two disturbingalgorithm which will be used for high volume content. The transverse stiffness and ultimateload of unidirectional fiber reinforced composites is analysed by using the RVE modelgenerated using two disturbing algorithm.
2. The mechanical behaviors of unidirectional fiber reinforced composites consideringinterphase under tensile load are simulated. The interphase is represented by cohesive elementwhich obeys the linear traction-separation law. The effect of thickness, modulus, Poisson rateand strength of interphase on transverse properties of composites is discussed. The resultsindicate that with the decrease of the interphase thickness, the effect of interphase on stiffnessis weak while the effect of interphase on Poisson rateν is strong. The larger the interphasemodulus is, the larger the overall modulus of composites is. The transverse strengt h ofcomposites increases with the increase of interphase strength.
3. The tensile damage process of single fiber composite system is simulated bycombination of subroutine USDFLD and UMAT in ABAQUS. Cohesive element is used fordebonding process between fiber and matrix. The results indicate that degradation factor d=0.01is efficient for this type simulation. The effects of constituent materials on the failureof material are significant.
4. The cohesive finite element mode l of nano rolled stainless steel laminated compositesis generated by inserting cohesive element in the finite element mesh. The effects of cohesivestrength and energy release rate of nanocrystal material and coarse crystal material on thefailure strain of the composites are studied. The law of microcrack number and damagedisperse energy is realized. In addition, the effect of volume content of nanocrystal materialunder two distribution types on the overall failure of the composites is initially studied.
In conclusion, the finite models of two typical composites are generated in the paper.The mechanical response of these materials under tensile load is studied which hopefullywould provide useful reference to the study and design of composites and engineeringapp lication.
1．对纤维增强单向复合材料的横向SEM图像进行了数字化处理，得到了纤维在横截面内的几何微结构特征属性,包括面积、离心率、空间分布、方位角等。然后，编写了方便ABAQUS软件调用的Python语言脚本程序。该程序实现了两种纤维随机分布的RVE模型的生成方法：一种是用于较低体积含量的硬核算法，另一种是用于较高体积含量的RVE模型生成的双扰动算法。本文利用双扰动算法生成的RVE模型，对纤维增强单向复合材料进行了横向刚度分析和极限承载力的分析。
2．在考虑界面相情况下，对纤维增强单向复合材料横截面内单向拉伸时的力学行为进行了数值模拟，其中，界面相单元采用服从线性应力—分离演化规律的内聚力单元来表示。讨论了界面相厚度、模量、泊松比和强度对于复合材料整体横向性能的影响。研究结果表明：界面相厚度越小，界面相对刚度的影响越弱，而对泊松比ν的影响越大；界面相模量越大，复合材料的等效模量越大；复合材料整体横向拉伸强度随着界面相强度的增加而增加。
3．联合使用ABAQUS中的子程序USDFLD和UMAT，模拟了单纤维复合材料体系的纵向拉伸损伤过程。其中，用内聚力单元来实现纤维与基体界面的脱粘过程。研究发现：对于此类模拟，退化因子d=0.01是足够而有效的；各个组分材料的强度对材料的失效都有明显的影响。
4．通过在有限元网格中间插入内聚力单元，建立了纳米化不锈钢层合轧压结构复合材料的内聚有限元模型。分别研究了纳米晶层材料和粗晶基体材料的内聚强度与能量释放率对复合材料整体失效应变的影响，总结了拉伸过程中，微裂纹个数与损伤耗散能的变化规律。此外，纳米晶层体积含量在两种不同分布形式下，对复合材料整体失效应变的影响也做了初步研究。
综上所述，本文建立了两种典型复合材料的有限元模型，研究了这些材料在拉伸载荷下的力学响应，希望本文的结果能够为更进一步的研究与复合材料的设计及工程应用提供一定的参考和帮助。
Nowadays composites play a very important role in engineering from aerospacetechnology and nuclear devices to microelectronics or structural engineering applications.Considering this fact and the growing role of numerical experiments in the designing ofstructures and industrial processes, one of the most important purposes of computationalmechanics research and direction of progress appeared to be precise numerical modelling ofthese materials. Modern computational mechanics of composite materials follows manyvarious ways through different science domains from experimental materials science toadvanced computational techniques and applied mathematics. Commercial computerprograms (such as ABAQUS and ANSYS) based on the Finite Element Method enable nowvisualisation of the multifield, multiphase and non-stationary physical and mechanicalproblems and even introducing uncertainty into computer simulation using random variables.Based on mesomechanics, the mechanical properties and relationship between the constitutematerials of two typical composites (unidirectional fiber reinforced composite and nano rolledstainless steel laminated composites) have been analysed. The following aspects have beenresearched in detail:
1. In order to obtain the geometric properties of micro-structural of the fiber (such asarea, eccentricity, spatial distribution and orientation) in the cross section, the transverse SEMpicture of unidirectional fiber reinforced composites is digital processed. Then, script isdeveloped using Python language, which will be called by ABAQUS comfortably. Two typesof fiber random distribution RVE generation method are carried out in the script. One is hardcore algorithm which will be used for low volume content, and the other is two disturbingalgorithm which will be used for high volume content. The transverse stiffness and ultimateload of unidirectional fiber reinforced composites is analysed by using the RVE modelgenerated using two disturbing algorithm.
2. The mechanical behaviors of unidirectional fiber reinforced composites consideringinterphase under tensile load are simulated. The interphase is represented by cohesive elementwhich obeys the linear traction-separation law. The effect of thickness, modulus, Poisson rateand strength of interphase on transverse properties of composites is discussed. The resultsindicate that with the decrease of the interphase thickness, the effect of interphase on stiffnessis weak while the effect of interphase on Poisson rateν is strong. The larger the interphasemodulus is, the larger the overall modulus of composites is. The transverse strengt h ofcomposites increases with the increase of interphase strength.
3. The tensile damage process of single fiber composite system is simulated bycombination of subroutine USDFLD and UMAT in ABAQUS. Cohesive element is used fordebonding process between fiber and matrix. The results indicate that degradation factor d=0.01is efficient for this type simulation. The effects of constituent materials on the failureof material are significant.
4. The cohesive finite element mode l of nano rolled stainless steel laminated compositesis generated by inserting cohesive element in the finite element mesh. The effects of cohesivestrength and energy release rate of nanocrystal material and coarse crystal material on thefailure strain of the composites are studied. The law of microcrack number and damagedisperse energy is realized. In addition, the effect of volume content of nanocrystal materialunder two distribution types on the overall failure of the composites is initially studied.
In conclusion, the finite models of two typical composites are generated in the paper.The mechanical response of these materials under tensile load is studied which hopefullywould provide useful reference to the study and design of composites and engineeringapp lication.
引文
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