脆性材料的细观损伤理论和损伤结构的安定分析
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摘要
材料的宏细观破坏理论是当前固体力学和材料科学研究的一个重要课题。
本文在对脆性和韧性材料的连续损伤理论和细观损伤理论进行评述的基础上，
研究了弹脆性材料的细观损伤和断裂问题以及含损伤的弹塑性结构的安定问
题。
本文建立了一套完整的脆性材料细观损伤模型──微裂纹扩展区模型，用
以分析材料在三轴拉伸和压缩情况下从初始无损状态到最终宏观裂纹形成的各
个阶段的细观损伤和本构关系。建议用微裂纹扩展区的概念来描述脆性材料的
各向异性损伤状态，从而方便地解决了复杂加载路径下材料的细观损伤演化和
宏观本构关系问题。将材料的本构关系分成包括线弹性、非线性强化、应力突
然跌落和应变软化的四个阶段，分别讨论了各个阶段的细观损伤机制，指出应
力跌落和应变软化是从连续分布损伤到损伤局部化过渡的结果。在拉伸和压缩
情况下微裂纹损伤机制和材料破坏模式都不相同，本文对张开微裂纹的自相似
扩展和闭合微裂纹的摩擦滑移、自相似扩展、弯折扩展进行了详细的研究，分
别给出了它们对材料的宏观力学性质的影响。并提出了一种柔度等效的损伤测
量方法，用以确定脆性材料中各向异性的微裂纹损伤状态。
本文研究了脆性材料中Ⅰ型宏观裂纹尖端的损伤和断裂行为。对于用微裂
纹扩展区模型描述的含损伤饱和段的材料，采用基于细观损伤力学的等效弹性
介质方法研究了宏观裂纹尖端的微裂纹屏蔽效应，得到了裂纹尖端的应力和应
变场。提出了一种修正J积分的方法，用以计算微裂纹损伤的屏蔽比，并将计
算结果与以往的J积分守恒方法进行了比较。指出由于应力跌落和应变软化的
原因，在脆性材料的宏观裂纹尖端将产生损伤局部化，并给出了损伤局部化带
长度的计算方法。
本文还发展了弹塑性损伤结构的安定理论。揭示了材料损伤和结构安定性
之间的联系，建议采用延性损伤因子作为弹塑性结构在变载作用下的失效准则
的控制参数，建立了理想弹塑性结构和应变强化结构在安定过程中损伤因子的
上限以及安全载荷范围的下限的数学规划方法。
The macro-and micro-failure theory of materials is a very important research subject of solid mechanics and material science. In the thesis, both phenomenological and micromechanical damage models for brittle and ductile materials are reviewed. Attention is focused on the micro-damage and fracture of brittle materials as well as the shakedown of elastic-plastic structures with damage.
A rather complete micromechanical damage model for quasi-brittle materials is established, which is called the damage mode of domain of microcrack growth (DMG) and can be used to analyze the micro-damage and constitutive response in all stages from the initial undamaged state to the ultimate macro-failure of brittle materials subjected to triaxial tension or triaxial compression. The domain of microcrack growth is defined and used to describe the damage state of microcrack-weakened brittle materials. Based on this concept, the problems of micro-damage evolution and macro-constitutive response can be solved easily. The constitutive relation of brittle materials is classified into four stages: namely linear elasticity, pre-peak nonlinear hardening, rapid stress drop and strain softening. The microscopic damage mechanisms in all these stages are investigated. The rapid stress drop reflects the transition from continuous distributed damage to damage localization. The damage and failure modes of brittle materials under tension and compression are different. The self-similar growth of open microcracks under tension, the frictional sliding, mode-n self-similar growth and kinking of closed microcracks under compression and their influences on the mechanical properties of materials are studied in detail. Moreover, an experimental method based on the equivalence of compliance is proposed to determine the anisotropic damage state in brittle materials.
The damage and fracture behaviors at the tip of a mode- I macroscopic
crack in brittle materials are studied. For a class of brittle materials with a stage of damage saturation, the stress shielding effect by microcracking at the tip of a mode- I crack is analyzed by using the effective elastic media method based on the micromechanical damage model of DMG. The stress and strain fields near the crack tip are obtained. A new method of modified J-integral is presented to calculate the shielding ratio by microcracking and its numerical result is compared with that obtained by the previous method of J-integral conservation. It is pointed out that due to the stress drop and strain softening of brittle material damage localization will occur ahead of a macroscopic crack under external loads. The method of calculating the length of damage localization band is given.
The shakedown theory of structures with damage is developed also in this thesis. The close relationship between damage of materials and shakedown of structures is revealed. The ductile damage factor is adopted as the control parameter of the failure criterion of elastic-plastic structures subjected to variable loads. A mathematical programming method is presented to calculate the lower bound of safety load domain and the upper bound of damage factor in either elastic-perfectly plastic or strain hardening structures at shakedown.
Feng Xiqiao (Solid Mechanics) Directed by Professor Yu Shouwen
本文在对脆性和韧性材料的连续损伤理论和细观损伤理论进行评述的基础上，
研究了弹脆性材料的细观损伤和断裂问题以及含损伤的弹塑性结构的安定问
题。
本文建立了一套完整的脆性材料细观损伤模型──微裂纹扩展区模型，用
以分析材料在三轴拉伸和压缩情况下从初始无损状态到最终宏观裂纹形成的各
个阶段的细观损伤和本构关系。建议用微裂纹扩展区的概念来描述脆性材料的
各向异性损伤状态，从而方便地解决了复杂加载路径下材料的细观损伤演化和
宏观本构关系问题。将材料的本构关系分成包括线弹性、非线性强化、应力突
然跌落和应变软化的四个阶段，分别讨论了各个阶段的细观损伤机制，指出应
力跌落和应变软化是从连续分布损伤到损伤局部化过渡的结果。在拉伸和压缩
情况下微裂纹损伤机制和材料破坏模式都不相同，本文对张开微裂纹的自相似
扩展和闭合微裂纹的摩擦滑移、自相似扩展、弯折扩展进行了详细的研究，分
别给出了它们对材料的宏观力学性质的影响。并提出了一种柔度等效的损伤测
量方法，用以确定脆性材料中各向异性的微裂纹损伤状态。
本文研究了脆性材料中Ⅰ型宏观裂纹尖端的损伤和断裂行为。对于用微裂
纹扩展区模型描述的含损伤饱和段的材料，采用基于细观损伤力学的等效弹性
介质方法研究了宏观裂纹尖端的微裂纹屏蔽效应，得到了裂纹尖端的应力和应
变场。提出了一种修正J积分的方法，用以计算微裂纹损伤的屏蔽比，并将计
算结果与以往的J积分守恒方法进行了比较。指出由于应力跌落和应变软化的
原因，在脆性材料的宏观裂纹尖端将产生损伤局部化，并给出了损伤局部化带
长度的计算方法。
本文还发展了弹塑性损伤结构的安定理论。揭示了材料损伤和结构安定性
之间的联系，建议采用延性损伤因子作为弹塑性结构在变载作用下的失效准则
的控制参数，建立了理想弹塑性结构和应变强化结构在安定过程中损伤因子的
上限以及安全载荷范围的下限的数学规划方法。
The macro-and micro-failure theory of materials is a very important research subject of solid mechanics and material science. In the thesis, both phenomenological and micromechanical damage models for brittle and ductile materials are reviewed. Attention is focused on the micro-damage and fracture of brittle materials as well as the shakedown of elastic-plastic structures with damage.
A rather complete micromechanical damage model for quasi-brittle materials is established, which is called the damage mode of domain of microcrack growth (DMG) and can be used to analyze the micro-damage and constitutive response in all stages from the initial undamaged state to the ultimate macro-failure of brittle materials subjected to triaxial tension or triaxial compression. The domain of microcrack growth is defined and used to describe the damage state of microcrack-weakened brittle materials. Based on this concept, the problems of micro-damage evolution and macro-constitutive response can be solved easily. The constitutive relation of brittle materials is classified into four stages: namely linear elasticity, pre-peak nonlinear hardening, rapid stress drop and strain softening. The microscopic damage mechanisms in all these stages are investigated. The rapid stress drop reflects the transition from continuous distributed damage to damage localization. The damage and failure modes of brittle materials under tension and compression are different. The self-similar growth of open microcracks under tension, the frictional sliding, mode-n self-similar growth and kinking of closed microcracks under compression and their influences on the mechanical properties of materials are studied in detail. Moreover, an experimental method based on the equivalence of compliance is proposed to determine the anisotropic damage state in brittle materials.
The damage and fracture behaviors at the tip of a mode- I macroscopic
crack in brittle materials are studied. For a class of brittle materials with a stage of damage saturation, the stress shielding effect by microcracking at the tip of a mode- I crack is analyzed by using the effective elastic media method based on the micromechanical damage model of DMG. The stress and strain fields near the crack tip are obtained. A new method of modified J-integral is presented to calculate the shielding ratio by microcracking and its numerical result is compared with that obtained by the previous method of J-integral conservation. It is pointed out that due to the stress drop and strain softening of brittle material damage localization will occur ahead of a macroscopic crack under external loads. The method of calculating the length of damage localization band is given.
The shakedown theory of structures with damage is developed also in this thesis. The close relationship between damage of materials and shakedown of structures is revealed. The ductile damage factor is adopted as the control parameter of the failure criterion of elastic-plastic structures subjected to variable loads. A mathematical programming method is presented to calculate the lower bound of safety load domain and the upper bound of damage factor in either elastic-perfectly plastic or strain hardening structures at shakedown.
Feng Xiqiao (Solid Mechanics) Directed by Professor Yu Shouwen
引文
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