结构钢韧性损伤模型研究
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摘要
结构钢是多相材料,且在成形加工工艺中,其内部会留存一定量非金属夹杂物。在加载变形过程中,微空洞会围绕这些二相粒子和非金属夹杂物萌生、扩展、汇合,直至材料发生韧性损伤断裂。韧性损伤对结构钢力学性能的劣化影响非常大,因此一直是固体力学和结构工程研究的热点。曾有许多研究工作者致力于建立结构钢韧性损伤宏观、细观模型,这些模型各有特点。本文共五章,分别从物理、几何角度入手,建立三种结构钢韧性损伤模型。
第一种是考虑材料硬化与韧性损伤耦合作用的有限变形率本构模型。该模型采用基于细观机制的唯象方法,把韧性损伤作为物理缺陷,将其对材料力学性能的劣化影响体现在本构方程中。创新之处在于模型中考虑了有限变形引起的几何非线性影响,分别在初始构形和即时构形中定义应力张量、应变张量以及它们的增量和变化率,并分别在两个构形中引入考虑韧性损伤的屈服条件;其次模型中考虑了材料硬化与韧性损伤之间的线性耦合作用,将比自由能定义为弹性自由能、塑性耗散势和弹塑性损伤耗散势三部分之和,其中塑性损伤耗散势分别为两个构形中累积塑性变形和损伤度量的函数。模型推导过程遵循不可逆热力学基本理论;状态变量与内变量满足正交法则。其结果说明不能简单将结构钢小变形韧性损伤本构模型作形式上的推广而得到有限变形情况下的韧性损伤本构模型,有限变形引起的几何非线性效应并不能忽略。
第二种是结构钢韧性损伤变形非协调模型。该模型从韧性损伤微观实质——几何缺陷入手,考虑韧性损伤引起的变形非协调性,并将非协调的基本几何法则与平衡方程、线性物理方程一起得到以位移为未知量的平衡微分方程。本文分别由宏观连续损伤变量和细观几何量定义拟塑性应变张量描述结构钢内部微结构在变形过程中的变化,建立了不同情况的变形非协调模型,并通过算例来说明模型的应用。结构钢韧性损伤变形非协调模型从几何角度描述了韧性损伤对其力学性能的影响,是解决韧性损伤问题的一种新的尝试,它显著拓展了弹塑性模型的描述能
第三种是结构钢韧性损伤几何-拓扑模型。该模型以几何的改变为视角,应用几何.拓扑的方法建立结构钢韧性损伤微分流形,并讨论一般流形中含韧性损伤结构钢的力学状态。模型中以空间的弯曲描述韧性损伤对结构钢力学性能的劣化影响,将物理非线性问题转化为物理线性和空间弯曲之和。韧性损伤几何-拓扑模型有统一的形式,且可以不断延伸进而解决更复杂的非线性问题。
Structural steel is multiphase material in which there are some nonmetal extraments. The cavity will generate around these nonmetal extraments and second-phase particles. With deformation these cavities will growth and join while the structural steel has damaged. Ductile damage is always the focus of research because it has great effects on materials. There are many researches work discuss macro-models and micro-models of ductile damage. This paper has established three kinds of ductile damage models from physical and geometry angle respectively.
The first is rate constitutive model under finite deformation. This way is microscopic property-based phenomenological theory. In this model, ductile damage is physical defects which embodied in the damdge constitutive equation. The innovation first is geometrical non-linear is taken into account in the model. In the paper yielding condition is presented in initial configuration and updated configuration respectively. Second innovation is the coupling effect of hardening and damage has been taken into account. This model follows the thermodynamics and the state variable and the internal variable meet the orthogonal principle.
The second is ductile damage incompatible model of structural steel. This model take account the incompatible with a view of ductile damage essential- geometry defect. In this model, quasi-plastic strain is defined from continuous damage virable and micro-damage theory respectively, to describe the deterioration of mechanical performance of structural steel. This model is a new way to discuss the ductile damage from the geometry, and it extends the elastic-plastic model remarkably.
The last is ductile damage geometry- topology model of structural steel. This model has established differential manifold of ductile damage with view of geometry, and discussed the mechanical state of structural steel in the manifold. In this model, damage is described with the curvature and a physical non-linear problem is taken into physical linear and the curve of space. ductile damage geometry- topology model has unified form and can be extended to discuss more complex defects.
第一种是考虑材料硬化与韧性损伤耦合作用的有限变形率本构模型。该模型采用基于细观机制的唯象方法,把韧性损伤作为物理缺陷,将其对材料力学性能的劣化影响体现在本构方程中。创新之处在于模型中考虑了有限变形引起的几何非线性影响,分别在初始构形和即时构形中定义应力张量、应变张量以及它们的增量和变化率,并分别在两个构形中引入考虑韧性损伤的屈服条件;其次模型中考虑了材料硬化与韧性损伤之间的线性耦合作用,将比自由能定义为弹性自由能、塑性耗散势和弹塑性损伤耗散势三部分之和,其中塑性损伤耗散势分别为两个构形中累积塑性变形和损伤度量的函数。模型推导过程遵循不可逆热力学基本理论;状态变量与内变量满足正交法则。其结果说明不能简单将结构钢小变形韧性损伤本构模型作形式上的推广而得到有限变形情况下的韧性损伤本构模型,有限变形引起的几何非线性效应并不能忽略。
第二种是结构钢韧性损伤变形非协调模型。该模型从韧性损伤微观实质——几何缺陷入手,考虑韧性损伤引起的变形非协调性,并将非协调的基本几何法则与平衡方程、线性物理方程一起得到以位移为未知量的平衡微分方程。本文分别由宏观连续损伤变量和细观几何量定义拟塑性应变张量描述结构钢内部微结构在变形过程中的变化,建立了不同情况的变形非协调模型,并通过算例来说明模型的应用。结构钢韧性损伤变形非协调模型从几何角度描述了韧性损伤对其力学性能的影响,是解决韧性损伤问题的一种新的尝试,它显著拓展了弹塑性模型的描述能
第三种是结构钢韧性损伤几何-拓扑模型。该模型以几何的改变为视角,应用几何.拓扑的方法建立结构钢韧性损伤微分流形,并讨论一般流形中含韧性损伤结构钢的力学状态。模型中以空间的弯曲描述韧性损伤对结构钢力学性能的劣化影响,将物理非线性问题转化为物理线性和空间弯曲之和。韧性损伤几何-拓扑模型有统一的形式,且可以不断延伸进而解决更复杂的非线性问题。
Structural steel is multiphase material in which there are some nonmetal extraments. The cavity will generate around these nonmetal extraments and second-phase particles. With deformation these cavities will growth and join while the structural steel has damaged. Ductile damage is always the focus of research because it has great effects on materials. There are many researches work discuss macro-models and micro-models of ductile damage. This paper has established three kinds of ductile damage models from physical and geometry angle respectively.
The first is rate constitutive model under finite deformation. This way is microscopic property-based phenomenological theory. In this model, ductile damage is physical defects which embodied in the damdge constitutive equation. The innovation first is geometrical non-linear is taken into account in the model. In the paper yielding condition is presented in initial configuration and updated configuration respectively. Second innovation is the coupling effect of hardening and damage has been taken into account. This model follows the thermodynamics and the state variable and the internal variable meet the orthogonal principle.
The second is ductile damage incompatible model of structural steel. This model take account the incompatible with a view of ductile damage essential- geometry defect. In this model, quasi-plastic strain is defined from continuous damage virable and micro-damage theory respectively, to describe the deterioration of mechanical performance of structural steel. This model is a new way to discuss the ductile damage from the geometry, and it extends the elastic-plastic model remarkably.
The last is ductile damage geometry- topology model of structural steel. This model has established differential manifold of ductile damage with view of geometry, and discussed the mechanical state of structural steel in the manifold. In this model, damage is described with the curvature and a physical non-linear problem is taken into physical linear and the curve of space. ductile damage geometry- topology model has unified form and can be extended to discuss more complex defects.
引文
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[7]Lemeitre J.A continuous damage mechanics model for ductile fracture[J].J.Eng.Mater.and Tech.198,107:83-89.
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