基于应变梯度塑性理论的微纳米尺度材料力学行为研究
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摘要
微纳米尺度下,材料力学行为是尺度相关的。材料中各种内界面对变形的约束是导致微尺度效应的主要来源之一。当内界面约束导致的非均匀变形场的“特征波长”和材料的“内禀长度”在同一量级时,微尺度效应不可忽略。内界面约束行为及其尺度效应机理是当前微塑性力学领域关注的重点之一,具有重要的理论价值。
一方面,应变梯度理论可以很好地捕捉变形场非均匀性对材料力学行为的“附加强化”效应,但对材料中各种内界面约束的处理一直不理想,将它们用于研究由材料内界面约束导致的微尺度效应时存在局限。因此,有必要针对材料不同的内界面,在高阶应变梯度框架下发展相应的界面模型,以合理地刻画与内界面有关的材料变形行为及其微尺度机理。
另一方面,现有的应变塑性梯度理论多是唯象的,缺乏对材料塑性变形时微结构演化和微观变形机制的深入考虑,理论模型中非常重要的内禀材料长度和微观应力平衡条件往往缺乏明确的物理意义。基于塑性变形的位错机制,发展新的高阶应变梯度理论一直是学术界的热点,也是难点。
针对上述两个方面的问题,本文开展了一些积极的探索,主要研究内容和取得的创新性成果如下：
1、针对微纳米材料的变形特点,在高阶应变梯度塑性框架下,提出了三种内界面模型。单晶微柱压缩变形时,塑性滑移层先后屈服,内界面是处于不同变形状态的薄层之间的过渡面。双晶微柱中晶界作为阻碍位错运动的内界面,在应变梯度框架中赋予其界面能,从而有自己独立的屈服准则。纳米多晶材料,晶界体积分数占较大比例,因此作为单独的材料相进行处理,有自己独立的平衡方程和本构关系。
2、基于应变梯度微柱薄层模型,分析了单晶微柱压缩中出现的“应变陡增”现象。研究表明：高阶应力在相邻塑性薄层界面处是连续的,但在弹性薄层与塑性薄层问的界面处是不连续的；因此,在先后屈服的相邻薄层界面处高阶应力存在跳跃,由此导致了微柱压缩应力-应变曲线上“应变陡增”台阶的出现。另一方面,单品微柱压缩实验应力-应变曲线有较大的分散性,本文的应变梯度微柱薄层模型合理地预测了应力-应变曲线的上下界。
3、在高阶应变梯度框架下,将晶界作为材料内部的不连续面并被赋予晶界能,提出了具有界面能特性的内界面梯度理论模型。通过对双晶微柱压缩力学行为的分析,结果表明：该界面模型不仅能给出与实验符合良好的微柱压缩应力-应变曲线,而且还发现应力-应变曲线中“两个拐点”分别对应于晶粒和晶界屈服,从而从内在物理机理上对应力-应变曲线三阶段特征进行了解释。
4、针对纳米多晶材料,将晶界作为与晶粒内部同等地位的“材料相”,提出了考虑有限厚度内界面的梯度理论模型。在该模型中,品界相不仅可以是多晶材料塑性变形的障碍,也可以是塑性变形的通道。通过对多晶材料行为的分析,结果表明：有限厚度的内界面梯度模型不仅较好地描述了纳米多晶材料Hall-Petch和反Hall-Petch效应,而且还给出了从Hall-Petch效应过渡到反Hall-Petch效应时的临界品粒尺寸。
5、基于位错自能和相互作用能,在热力学框架下建立了功共轭的高阶应变梯度晶体塑性模型。通过简单的位错环构型,建立了镜像力、自力与位错自能演化,以及背应力与位错相互作用能演化之间的内在关系。基于虚功原理,建立了滑移系微观应力平衡方程,较好地捕捉晶体滑移时的流动准则。与现有高阶梯度本构理论相比,本文模型中的“内禀材料长度”被赋予了更加明确的物理意义；同时,它还能与三维离散位错动力学(3D-DDD)以及Evers-Bayley非功共轭的应变梯度晶体塑性框架建立起内在联系。
The mechanic behavior of micro/nano-sized material is size-dependent; one dominant source is the interface constraint which results in the non-uniform deformation filed, the size-dependent phenomena displays when the characteristic wavelength of the non-uniform deformation field is the same order as the intrinsic material length. The interface constraint and its corresponding size-dependent mechanism are the important research concerns in the field of micro/nano-plasticity mechanics, and have theoretical importance.
One side, the strain gradient theories succeeded in describing the effect of non-uniform deformation fields on the mechanical response of the micro/nano sized materials, however, the reasonable considerations of interface constraint within the strain gradient framework are still not satisfying, thus there are still some limitations in explaining the size-dependent mechanical behavior resulting from the interface constraint. It's necessary to develop a strain gradient model within the strain gradient plasticity framework by treating the interface in different ways with the detailed interface deformation characteristics and mechanisms.
On the other side, the strain gradient theories are mostly phenomenological, and didn't give a careful and deep consideration for the microstructure evolution and underlying deformation mechanism related with the plastic deformation; meanwhile, there are no clear physical meanings to be endowed to intrinsic material length scales and microscopic stress balance equation. It's an open issue to establish a new strain gradient plasticity theory which should be physically reasonable and enriched with underlying consideration of microstructure related deformation mechanisms.
In the present dissertation, we address the above two sides of strain gradient plasticity research. The main research contents and results are summarized as follows:
1、Three different interface models are proposed within the strain gradient theory framework depending on the deformation characteristics of the micro/nano-szied materials. In the compressed single crystalline micropillar, the interfaces lie between the slip layers which are in different deformation status due to asynchronous plastic yielding in the micropillar and play a role as the transition interfaces. In the compressed bi-crystalline micropillar, the grain boundary play a role as barrier to the movement of dislocations, and the interface energy is endowed to the grain boundary within the strain gradient plasticity framework, then the interfacial yielding rules are developed. In nanocrystalline solids, grain boundaries occupy significant volume fraction of the material, thus are treated as a separate phase endowed with balance equations and constitutive equations.
2、Based on the strain gradient multilayer model, the "strain bursts" phenomena observed in single crystalline micropillar compression experiments are investigated. The higher-order stress, which is discontinuous at the interface between a plastic layer and its neighboring elastic layer but continuous when two neighboring layers begin deforming plastically, is the underlying mechanism responsible for the strain burst. The transition from discontinuity to continuity of the higher-order stress across the internal boundary between two neighboring layers results in the strain burst. Furthermore, the stress-strain response of the single crystal micropillar is dispersed; the strain gradient multilayer model could also capture the upper and lower bounds of the stress-strain curves.
3、The compression behavior of the bi-crystalline micropillar is interpreted by considering the interface energy term in the grain plasticity framework. Grain boundary is the interface where higher order stress experiences a jump, thus it is modeled using interface energy, an "interfacial" yield criterion is deduced to describe the yielding behavior of grain boundary as a result. The tri-linear stress-strain curves obtained from the theory fit in well with experimental data of bi-crystal micropillars, and display two distinct "knee" at whichthe grain and grain boundary begin to yield.
4、The mechanical behavior of the nanocrystalline is analyzed using the strain gradient model treating grain boundaries as a separate phase with a finite thickness. Grain boundary phase and grain phase interchange their role to accommodate deformation as the grain size varies from microsclae to nanoscale. Grain boundary phases could be either the obstacles or passage of the plastic deformation depending on the ratio of grain boundary thickness to the grain size. The "normal" to "abnormal" Hall-Petch transition is successfully captured by the present model; the critical grain size at which this transition occurs is also predicted with good agreement with the experiments.
5、Based on the dislocation self-energy and interaction energy, a thermodynamics consistent work-conjugated higher-order strain gradient crystal plasticity theory is developed. The evolution of self energy based on rectangular dislocation loop is related with the image stress and self stress, and the interaction energy enables the back stress to be deduced. The final microscopic stress balance equation derived from virtual power principle describes the plastic flow of the crystalline material in separate slip system. It should be noted that the multiple intrinsic length scales introduced in present model are related with the characteristic sizes of micro structures in the material, so have specific physical meanings. Furthermore, the present dislocation energy based work-conjugated strain gradient theory is compared with Zbib's three-dimensional discrete dislocation dynamics (3D-DDD) framework and Evers-Bayley models of non-work-conjugated type, and correspondence between them are revealed.
一方面,应变梯度理论可以很好地捕捉变形场非均匀性对材料力学行为的“附加强化”效应,但对材料中各种内界面约束的处理一直不理想,将它们用于研究由材料内界面约束导致的微尺度效应时存在局限。因此,有必要针对材料不同的内界面,在高阶应变梯度框架下发展相应的界面模型,以合理地刻画与内界面有关的材料变形行为及其微尺度机理。
另一方面,现有的应变塑性梯度理论多是唯象的,缺乏对材料塑性变形时微结构演化和微观变形机制的深入考虑,理论模型中非常重要的内禀材料长度和微观应力平衡条件往往缺乏明确的物理意义。基于塑性变形的位错机制,发展新的高阶应变梯度理论一直是学术界的热点,也是难点。
针对上述两个方面的问题,本文开展了一些积极的探索,主要研究内容和取得的创新性成果如下：
1、针对微纳米材料的变形特点,在高阶应变梯度塑性框架下,提出了三种内界面模型。单晶微柱压缩变形时,塑性滑移层先后屈服,内界面是处于不同变形状态的薄层之间的过渡面。双晶微柱中晶界作为阻碍位错运动的内界面,在应变梯度框架中赋予其界面能,从而有自己独立的屈服准则。纳米多晶材料,晶界体积分数占较大比例,因此作为单独的材料相进行处理,有自己独立的平衡方程和本构关系。
2、基于应变梯度微柱薄层模型,分析了单晶微柱压缩中出现的“应变陡增”现象。研究表明：高阶应力在相邻塑性薄层界面处是连续的,但在弹性薄层与塑性薄层问的界面处是不连续的；因此,在先后屈服的相邻薄层界面处高阶应力存在跳跃,由此导致了微柱压缩应力-应变曲线上“应变陡增”台阶的出现。另一方面,单品微柱压缩实验应力-应变曲线有较大的分散性,本文的应变梯度微柱薄层模型合理地预测了应力-应变曲线的上下界。
3、在高阶应变梯度框架下,将晶界作为材料内部的不连续面并被赋予晶界能,提出了具有界面能特性的内界面梯度理论模型。通过对双晶微柱压缩力学行为的分析,结果表明：该界面模型不仅能给出与实验符合良好的微柱压缩应力-应变曲线,而且还发现应力-应变曲线中“两个拐点”分别对应于晶粒和晶界屈服,从而从内在物理机理上对应力-应变曲线三阶段特征进行了解释。
4、针对纳米多晶材料,将晶界作为与晶粒内部同等地位的“材料相”,提出了考虑有限厚度内界面的梯度理论模型。在该模型中,品界相不仅可以是多晶材料塑性变形的障碍,也可以是塑性变形的通道。通过对多晶材料行为的分析,结果表明：有限厚度的内界面梯度模型不仅较好地描述了纳米多晶材料Hall-Petch和反Hall-Petch效应,而且还给出了从Hall-Petch效应过渡到反Hall-Petch效应时的临界品粒尺寸。
5、基于位错自能和相互作用能,在热力学框架下建立了功共轭的高阶应变梯度晶体塑性模型。通过简单的位错环构型,建立了镜像力、自力与位错自能演化,以及背应力与位错相互作用能演化之间的内在关系。基于虚功原理,建立了滑移系微观应力平衡方程,较好地捕捉晶体滑移时的流动准则。与现有高阶梯度本构理论相比,本文模型中的“内禀材料长度”被赋予了更加明确的物理意义；同时,它还能与三维离散位错动力学(3D-DDD)以及Evers-Bayley非功共轭的应变梯度晶体塑性框架建立起内在联系。
The mechanic behavior of micro/nano-sized material is size-dependent; one dominant source is the interface constraint which results in the non-uniform deformation filed, the size-dependent phenomena displays when the characteristic wavelength of the non-uniform deformation field is the same order as the intrinsic material length. The interface constraint and its corresponding size-dependent mechanism are the important research concerns in the field of micro/nano-plasticity mechanics, and have theoretical importance.
One side, the strain gradient theories succeeded in describing the effect of non-uniform deformation fields on the mechanical response of the micro/nano sized materials, however, the reasonable considerations of interface constraint within the strain gradient framework are still not satisfying, thus there are still some limitations in explaining the size-dependent mechanical behavior resulting from the interface constraint. It's necessary to develop a strain gradient model within the strain gradient plasticity framework by treating the interface in different ways with the detailed interface deformation characteristics and mechanisms.
On the other side, the strain gradient theories are mostly phenomenological, and didn't give a careful and deep consideration for the microstructure evolution and underlying deformation mechanism related with the plastic deformation; meanwhile, there are no clear physical meanings to be endowed to intrinsic material length scales and microscopic stress balance equation. It's an open issue to establish a new strain gradient plasticity theory which should be physically reasonable and enriched with underlying consideration of microstructure related deformation mechanisms.
In the present dissertation, we address the above two sides of strain gradient plasticity research. The main research contents and results are summarized as follows:
1、Three different interface models are proposed within the strain gradient theory framework depending on the deformation characteristics of the micro/nano-szied materials. In the compressed single crystalline micropillar, the interfaces lie between the slip layers which are in different deformation status due to asynchronous plastic yielding in the micropillar and play a role as the transition interfaces. In the compressed bi-crystalline micropillar, the grain boundary play a role as barrier to the movement of dislocations, and the interface energy is endowed to the grain boundary within the strain gradient plasticity framework, then the interfacial yielding rules are developed. In nanocrystalline solids, grain boundaries occupy significant volume fraction of the material, thus are treated as a separate phase endowed with balance equations and constitutive equations.
2、Based on the strain gradient multilayer model, the "strain bursts" phenomena observed in single crystalline micropillar compression experiments are investigated. The higher-order stress, which is discontinuous at the interface between a plastic layer and its neighboring elastic layer but continuous when two neighboring layers begin deforming plastically, is the underlying mechanism responsible for the strain burst. The transition from discontinuity to continuity of the higher-order stress across the internal boundary between two neighboring layers results in the strain burst. Furthermore, the stress-strain response of the single crystal micropillar is dispersed; the strain gradient multilayer model could also capture the upper and lower bounds of the stress-strain curves.
3、The compression behavior of the bi-crystalline micropillar is interpreted by considering the interface energy term in the grain plasticity framework. Grain boundary is the interface where higher order stress experiences a jump, thus it is modeled using interface energy, an "interfacial" yield criterion is deduced to describe the yielding behavior of grain boundary as a result. The tri-linear stress-strain curves obtained from the theory fit in well with experimental data of bi-crystal micropillars, and display two distinct "knee" at whichthe grain and grain boundary begin to yield.
4、The mechanical behavior of the nanocrystalline is analyzed using the strain gradient model treating grain boundaries as a separate phase with a finite thickness. Grain boundary phase and grain phase interchange their role to accommodate deformation as the grain size varies from microsclae to nanoscale. Grain boundary phases could be either the obstacles or passage of the plastic deformation depending on the ratio of grain boundary thickness to the grain size. The "normal" to "abnormal" Hall-Petch transition is successfully captured by the present model; the critical grain size at which this transition occurs is also predicted with good agreement with the experiments.
5、Based on the dislocation self-energy and interaction energy, a thermodynamics consistent work-conjugated higher-order strain gradient crystal plasticity theory is developed. The evolution of self energy based on rectangular dislocation loop is related with the image stress and self stress, and the interaction energy enables the back stress to be deduced. The final microscopic stress balance equation derived from virtual power principle describes the plastic flow of the crystalline material in separate slip system. It should be noted that the multiple intrinsic length scales introduced in present model are related with the characteristic sizes of micro structures in the material, so have specific physical meanings. Furthermore, the present dislocation energy based work-conjugated strain gradient theory is compared with Zbib's three-dimensional discrete dislocation dynamics (3D-DDD) framework and Evers-Bayley models of non-work-conjugated type, and correspondence between them are revealed.
引文
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