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非均质材料磨损和弹塑性的多尺度建模和数值模拟

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目录

声明

摘要

Abstract

Contents

Chapter 1 Introduction

1.1 Brief introduction to composites materials

1.2 Composites for tribological applications

1.2.1 Engineering composite materials

1.2.2 Natural composite materials

1.2.3 Evaluation of the wear of composites

1.3 Numerical simulation of wear

1.3.1 Application of wear simulation

1.3.2 Simulation of wear by numerical methods

1.3.3 Wear laws adopted in numerical application

1.4 Objective and organization

Chapter 2 Analytical estimates of the wear of fiber-reinforced composites

2.1 Introduction

2.2 A micromechanical approach for determining the effective wear

2.3 Estimations for the effective wear of fiber-reinforced composites

2.3.1 Estimation of the load ratios under uniform strain

2.3.2 Estimation of the load ratios under uniform stress

2.3.3 Estimation of the load ratios under uniform frictional stress

2.3.4 Effect of Poisson’s ratio on effective wear compliance

2.3.5 Comparison of effective wear compliances

2.4 Numerical applications and discussions

2.5 Wear estimates of fiber reinforced viscoelastic composites

2.5.1 Constitutive law of fiber and matrix

2.5.2 Numerical example of PTFE-GF composite

2.5.3 Numerical example of biocomposites

2.6 Closing Remarks

Chapter 3 Numerical analysis of the wear of fiber-reinforced composites

3.1 Introduction

3.2 Wear simulation by numerical analysis

3.2.1 Finite element contact model

3.2.2 Wear at nodes of model

3.2.3 Material properties of fiber and matrix phases

3.2.4 Wear of fiber and matrix phases

3.3 Determination of a Representative Surface Element(RSE)

3.3.1 RSE under normal loading

3.3.2 RSE in the case of frictional loading

3.4 Verification of the assumption of theoretical estimates

3.4.1 Load proportion under the normal loading and the sliding with friction

3.4.2 Discrepancy of strain and stress distribution of two phases

3.4.3 Composite wear without variation of contact surface

3.4.4 Composite wear after the variation of contact surface

3.5 Wear analysis of composites reinforced with oblique fibers

3.5.1 Load proportion

3.5.2 Wear volume and wear compliance

3.6 Closed remarks

Chapter 4 Homogenization of elastoplastic particle-reinforced composites

4.1 Introduction

4.2 Constitutive laws for the particle and matrix phases

4.2.1 Elastic properties of the matrix and particles

4.2.2 Mohr-Coulomb and Drucker-Prager yield criteria for the matrix phase

4.2.3 Non-associated flow rule

4.3 Effective elastoplastic behavior of particulate composites under isotropic loading

4.3.1 Micromechanical model

4.3.2 General results

4.3.3 Loading modes

4.4 Porous media under external and internal hydrostatic loading

4.4.1 Constitutive law of matrix

4.4.2 General results

4.5 Numerical applications and discussions

4.5.1 Elastoplastic behavior of particle-reinforced composites or porous mediaunder isotropic loading

4.5.2 Porous media subjected to the extemal and intemal hydrostatic loading

4.6 Concluding remarks

Chapter 5 Homogenization of elastoplastic the fiber-reinfoced composite under radial loading

5.1 Introduction

5.2 Local constitutive laws

5.3 Micromechanical model

5.4 General results

5.4.1 Initial plastification

5.4.2 Elastoplastic stage

5.4.3 Total plastification

5.5 Elastoplastic behavior of composite with von Mises matrix

5.6 Numerical examples

5.7 Closing remarks

Chapter 6 Wear estimates of the fiber-reinforced composite with elsatoplastic matrix

6.1 Introduction

6.2 Local constitutive laws

6.3 Preliminary results

6.3.1 Elastic stage

6.3.2 Elastoplastic stage

6.3.3 Total plastification

6.4 Numerical application

6.5 Closing remarks

Conclusion

Acknowledgements

Appendix

Reference

攻读学位期间发表的学术论文

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摘要

随着仿生学的蓬勃发展和3D打印技术的出现,颗粒和纤维增强非均质材料所具有的优异力学和摩擦学特性在多个尺度上得到表征,并受到力学、材料学和摩擦学等领域学者的进一步关注。现有研究多集中在单一尺度定性描述材料的磨损特性,难以获取宏观尺度磨损性能与微观几何结构和组分材料特性的相互关系。为了优化具有跨尺度结构的仿生复合材料的摩擦学设计,本论文第一部分拟采用细观力学方法对复合材料的磨损特性进行跨尺度建模和数值模拟,目的是建立复合材料宏观磨损系数与微观几何特征和材料特性的定量描述,分析复合材料各组分的弹性、粘弹性及弹塑性对宏观磨损性能的影响。此外,由于部分复合材料基体的塑性行为通常与静水压力相关,如高分子和岩土材料,论文第二部分探讨了颗粒和纤维增强复合材料的基体服从与静水压力相关的屈服条件时,其弹塑性行为对材料宏观有效性能的影响规律。论文的主要创新点如下:
  (1)运用细观力学方法估算纤维增强复合材料的宏观磨损系数:在均匀边界条件下,建立纤维增强复合材料宏观有效磨损系数与各组分材料特性和磨损系数的定量关系;阐明复合材料组分的弹性、粘弹性和弹塑性特征对其宏观磨损的影响;
  (2)建立模拟纤维复合材料的磨损过程的有限元模型:基于包含纤维复合材料几何特征的有限元模型,对磨损过程中的接触面进行受力分析和磨损计算,提取滑动过程中纤维复合材料的宏观和各组分的磨损系数的变化规律,通过更改表面单元节点坐标的方式获得磨损形貌的渐变特征;
  (3)考虑基体的塑性行为与静水压力相关的情况,扩展复合材料弹塑性行为的均匀化方法:使用Drucker-Prager及Mohr-Coulomb两种屈服条件及非关联流动准则,分析颗粒和纤维复合材料的等效弹塑性行为。
  主要研究结论如下:
  (1)在各组分材料磨损特性符合Archard磨损定律的情况下,纤维复合材料的宏观磨损系数决定于两相材料的磨损特性和应力分布;通过细观力学模型,可获得均匀应力、应变、摩擦力和线磨损率条件下纤维复合材料的有效磨损系数;其中均匀应变边界情况所得的宏观磨损系数具有较广泛的适用范围;
  (2)当材料本构关系为线性(弹性和粘弹性),纤维复合材料的宏观磨损系数仅与组分的材料特性和磨损系数相关,基体的粘弹性使得宏观磨损有减小的趋势;当考虑基体材料服从弹塑性本构关系的情况下,宏观磨损系数与边界条件相关,且随着塑性区域的扩展而增大;
  (3)数值结果中获取的有效磨损系数与均匀应变条件下的理论预估值具有较好的一致性;随着磨损循环的增加,具有较小磨损系数的纤维相承载比例增大,使得宏观有效磨损系数相比于“磨合期”较小;与垂直纤维相比,倾斜纤维使得宏观磨损系数与滑动方向和摩擦系数相关;
  (4)Mohr-Coulomb屈服条件的静水压力系数影响颗粒增强复合材料在各项同性加载下的弹塑性行为,非关联流动准则参数对多孔复合材料,即弹性颗粒为空穴情况下弹塑性行为的影响显著;对于基体服从Drucker-Prager屈服条件和非关联流动准的纤维增强复合材料,假设基体弹性和塑性不可压缩的情况下,其有效弹塑性特性的解析解存在。
  本论文第一部分对复合材料磨损的预测方法可丰富摩擦学设计的理论基础,并为磨损试验中对于材料粘弹性或弹塑性演变的定性观察提供理论依据;第二部分研究的结果可作为高分子或岩土材料等非均质材料的弹塑性有效特性研究的理论基准。

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