位错非均匀形核及与晶界作用研究
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摘要
微纳米尺度下，晶体材料表现出优良的力学性能（如高强度和高韧性）越来越受到关注。该尺度下晶体材料的缺陷主要包括位错与晶界，完美晶体内的位错的形核决定了材料的屈服性质，位错与晶界的相互作用影响着材料的塑性强化。本文以位错形核及与晶界的相互作用为主要研究内容开展了如下工作。
基于原子势的连续化方法，研究了晶体片的位错非均匀形核问题。采用Cauchy-Born准则描述其变形，推导了本构关系，得到了基于稳定性的位错非均匀形核准则。研究了六边形晶格结构的晶体片拉伸作用下的位错非均匀形核问题。通过应力-应变曲线和应变-准则曲线，预测了二维晶体片的位错形核应力和形核位置，结果表明晶体片的手性对位错形核应力具有周期性影响。
采用分子动力学方法研究了剪切作用下Cu（100）扭转晶界的强化机制问题，得到了剪切强度的临界角度，当扭转角度大于临界角度时，剪切强度随着扭转角度的增加而减小，屈服形式表现为晶界的滑动；当扭转角度小于临界角度时，剪切强度随着扭转角度的增加而增加，屈服形式表现为晶界处的位错形核与扩展。进一步研究了Cu（111）扭转晶界的强化机制，得到了扭转晶界存在拉伸和压缩强度的不对称性，拉伸屈服形式为偏位错的形核与扩展，偏位错相遇会形成新的偏位错形核；压缩屈服表现为位错环的发射，位错环相遇形成位错的交截；剪切屈服表现为位错切过晶界导致扭转晶界的增殖。
阐述了孪晶界的层间距与屈服强度之间的关系，模拟结果表明对于剪切强度和压缩强度存在临界间距d大约为1nm，当d大于1nm时，压缩和剪切强度随着d的增加而减小，当d小于1nm时，压缩和剪切强度随着d的增加而增加。拉伸和压缩作用下，晶界的屈服表现为晶界与自由表面位错形核与位错扩展，剪切作用下，屈服表现为晶界沿垂直剪切方向的运动。
最后将基于缺陷能的梯度塑性理论进行了有限元实现，针对四边形晶粒和六边形晶粒，系统研究了单向拉伸载荷作用下多晶薄膜的塑性硬化问题。在模拟中，晶界被处理为不可穿透晶界，揭示了滑移系对薄膜硬化特性影响的机制，给出了位错从自由表面逃逸导致薄膜软化，位错在晶界处的塞积作用导致了薄膜硬化，同时得到了晶界密度与薄膜屈服应力、硬化率的近似满足线性关系。
High strength and hard toughness of crystalline solid are intensively investigated atsub-micron and nano scales. The yield strength of perfect crystal depends on thedislocation nucleation. The interactions between dislocations and grain boundary affectthe plastic properties of crystal material. The research work is mainly focused on thedislocation nucleation and the interactions between dislocations and grain boundary.
Based on the atom potential method, the stability theory is developed, and thenonhomogeneous dislocation nucleation of crystal sheet is studied. The Cauchy-Bornrule is introduced to describe the deformation of2D hexagonal crystal sheet. Thenonhomegeneous dislocation nucleation criterion is deduced. The onset of dislocationnucleation and the criterion distribution map are illustrated. Furthermore, the loadingamplitude corresponding to the dislocation nucleation can be determined by comparisonbetween the stress-strain curve and criterion-strain curve easily. The results show thatthe dislocation nucleation stress is related to the crystal sheet orientation angles.
By using molecular dynamics method, yield strength of copper with (100) twistgrain boundary effect are investigated under shear loading. The critical twist angle isobtained, which mediates the hardening mechanism of twist grain boundary. When twistangle is lower than critical value, the yield strength increases with the increase of thetwist angle, and the yield form of twist grain boundary is the dislocations nucleation attwist grain boundary and dislocations piling-up in the grain interior. When twist angle isgreater than critical value, the yield strength decreases with increasing the twist angle,and the yield form of twist grain boundary is the grain boundary sliding instead ofdislocation nucleation. Furthermore, the hardening mechanism of copper with (111)twist grain boundary is illustrated also. The yield form of twist grain boundary fortensile stress is the partial dislocation nucleation and propagation. The yield form oftwist grain boundary for compression is emission and propagation of dislocation loops.When two dislocation loops meet, the intersection of dislocation loops occur. The yieldform of twist grain boundary for shear load is proliferation of the twist grain boundary.
The relationship between the twin boundary spacing and yield strength is obtained.The critical twin boundary spacing is founded for shear strength and compression strength. When the twin boundary spacing is lower than the critical value about1nm,the compression strength and shear strength increase with increase of the twin boundaryspacing. When the twin boundary spacing is greater than the critical value1nm, thecompression strength and shear strength decreases with increasing the twin boundaryspacing. The tensile and compression yielding forms are the dislocation nucleation andpropagation from the section of free surface and twin boundary. The shear yielding formis the twin boundary motion perpendicular to the direction of shear load.
Based on the gradient plastic theory of defect energy, the implementation finiteelement is illustrated. Considering rectangular and hexagonal form grains, themechanical properties of multi-grain thin film have been studied. There are someconclusions obtained. It is illustrated that slip system affects the hardening of thin film.The fact that dislocations escape from free surface more easily, makes the thin filmsoftening. The dislocations, which pile up at grain boundary, lead to the thin filmhardening. With increasing the grain boundary density, the hardening influence of thinfilm becomes stronger. The simulation results reasonably show that the grain boundarydensity is linear to the yield strength and hardening rate, respectively.
基于原子势的连续化方法，研究了晶体片的位错非均匀形核问题。采用Cauchy-Born准则描述其变形，推导了本构关系，得到了基于稳定性的位错非均匀形核准则。研究了六边形晶格结构的晶体片拉伸作用下的位错非均匀形核问题。通过应力-应变曲线和应变-准则曲线，预测了二维晶体片的位错形核应力和形核位置，结果表明晶体片的手性对位错形核应力具有周期性影响。
采用分子动力学方法研究了剪切作用下Cu（100）扭转晶界的强化机制问题，得到了剪切强度的临界角度，当扭转角度大于临界角度时，剪切强度随着扭转角度的增加而减小，屈服形式表现为晶界的滑动；当扭转角度小于临界角度时，剪切强度随着扭转角度的增加而增加，屈服形式表现为晶界处的位错形核与扩展。进一步研究了Cu（111）扭转晶界的强化机制，得到了扭转晶界存在拉伸和压缩强度的不对称性，拉伸屈服形式为偏位错的形核与扩展，偏位错相遇会形成新的偏位错形核；压缩屈服表现为位错环的发射，位错环相遇形成位错的交截；剪切屈服表现为位错切过晶界导致扭转晶界的增殖。
阐述了孪晶界的层间距与屈服强度之间的关系，模拟结果表明对于剪切强度和压缩强度存在临界间距d大约为1nm，当d大于1nm时，压缩和剪切强度随着d的增加而减小，当d小于1nm时，压缩和剪切强度随着d的增加而增加。拉伸和压缩作用下，晶界的屈服表现为晶界与自由表面位错形核与位错扩展，剪切作用下，屈服表现为晶界沿垂直剪切方向的运动。
最后将基于缺陷能的梯度塑性理论进行了有限元实现，针对四边形晶粒和六边形晶粒，系统研究了单向拉伸载荷作用下多晶薄膜的塑性硬化问题。在模拟中，晶界被处理为不可穿透晶界，揭示了滑移系对薄膜硬化特性影响的机制，给出了位错从自由表面逃逸导致薄膜软化，位错在晶界处的塞积作用导致了薄膜硬化，同时得到了晶界密度与薄膜屈服应力、硬化率的近似满足线性关系。
High strength and hard toughness of crystalline solid are intensively investigated atsub-micron and nano scales. The yield strength of perfect crystal depends on thedislocation nucleation. The interactions between dislocations and grain boundary affectthe plastic properties of crystal material. The research work is mainly focused on thedislocation nucleation and the interactions between dislocations and grain boundary.
Based on the atom potential method, the stability theory is developed, and thenonhomogeneous dislocation nucleation of crystal sheet is studied. The Cauchy-Bornrule is introduced to describe the deformation of2D hexagonal crystal sheet. Thenonhomegeneous dislocation nucleation criterion is deduced. The onset of dislocationnucleation and the criterion distribution map are illustrated. Furthermore, the loadingamplitude corresponding to the dislocation nucleation can be determined by comparisonbetween the stress-strain curve and criterion-strain curve easily. The results show thatthe dislocation nucleation stress is related to the crystal sheet orientation angles.
By using molecular dynamics method, yield strength of copper with (100) twistgrain boundary effect are investigated under shear loading. The critical twist angle isobtained, which mediates the hardening mechanism of twist grain boundary. When twistangle is lower than critical value, the yield strength increases with the increase of thetwist angle, and the yield form of twist grain boundary is the dislocations nucleation attwist grain boundary and dislocations piling-up in the grain interior. When twist angle isgreater than critical value, the yield strength decreases with increasing the twist angle,and the yield form of twist grain boundary is the grain boundary sliding instead ofdislocation nucleation. Furthermore, the hardening mechanism of copper with (111)twist grain boundary is illustrated also. The yield form of twist grain boundary fortensile stress is the partial dislocation nucleation and propagation. The yield form oftwist grain boundary for compression is emission and propagation of dislocation loops.When two dislocation loops meet, the intersection of dislocation loops occur. The yieldform of twist grain boundary for shear load is proliferation of the twist grain boundary.
The relationship between the twin boundary spacing and yield strength is obtained.The critical twin boundary spacing is founded for shear strength and compression strength. When the twin boundary spacing is lower than the critical value about1nm,the compression strength and shear strength increase with increase of the twin boundaryspacing. When the twin boundary spacing is greater than the critical value1nm, thecompression strength and shear strength decreases with increasing the twin boundaryspacing. The tensile and compression yielding forms are the dislocation nucleation andpropagation from the section of free surface and twin boundary. The shear yielding formis the twin boundary motion perpendicular to the direction of shear load.
Based on the gradient plastic theory of defect energy, the implementation finiteelement is illustrated. Considering rectangular and hexagonal form grains, themechanical properties of multi-grain thin film have been studied. There are someconclusions obtained. It is illustrated that slip system affects the hardening of thin film.The fact that dislocations escape from free surface more easily, makes the thin filmsoftening. The dislocations, which pile up at grain boundary, lead to the thin filmhardening. With increasing the grain boundary density, the hardening influence of thinfilm becomes stronger. The simulation results reasonably show that the grain boundarydensity is linear to the yield strength and hardening rate, respectively.
引文
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