各向异性材料中螺型位错与含非完整界面圆形夹杂干涉效应
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摘要
复合材料中位错与夹杂之间的干涉效应问题,是当前固体力学与材料科学研究领域的前沿热点课题。本文针对各向异性复合材料中位错与非完整界面的弹性、粘弹性和电弹性干涉进行理论分析。研究了圆柱型各向异性材料中螺型位错与含非理想界面圆形夹杂以及螺型位错与含粘弹性界面圆形夹杂的干涉问题;横观各向同性压电材料中多个螺型位错与含非理想界面涂层夹杂之间的干涉问题。
运用复变函数解析延拓原理,将上述问题转化为Riemann-Hilbert边值问题,结合复应力函数奇性主部分析方法、广义Liouville定理和Cauchy型积分别获得了上述问题复势函数的精确解答。根据Peach-Koehler公式,分别导出了相应位错力的解析表达式。研究了位错力随材料相关参数和非完整界面参数的变化规律。
研究结果发现,非完整界面对螺型位错与夹杂的干涉作用具有强烈的扰动效应。在圆柱形各向异性材料中,当界面为非理想时,随着界面非理想程度的增大,材料各向异性夹杂对位错的影响逐渐增强。当基体各向异性系数小于夹杂各向异性系数时,非理想系数存在一个临界值改变位错力的方向。对于粘弹性界面,刚开始夹杂的各向异性性质对于位错力的影响较大,随着时间的推移,位错力先是快速减小然后变幅趋于平缓,而夹杂的各向异性性质对于位错力的影响也显著减弱。在压电材料中,当界面为非理想界面圆环涂层时,非完整界面吸引位错,吸引力随着涂层内外边界非理想系数减小而增大。硬夹杂和硬界面层排斥位错,排斥力随着涂层相对厚度的增大而增大。
本文结果不仅可为相关复合材料的结构设计提供科学依据,而且可为进一步研究相关结构材料的强韧化机理提供基本解。本文的解答可以作为Green函数,获得相关问题的系列解答,且作为本文特例包含了以往文献中的若干结果。
The interaction of dislocation, inhomogeneity and interfacial defects is a greatly significant subject in the fields of solid mechanics and materials science. The elastic, viscoelastic and electroelastic interaction effects between imperfect interface and screw dislocations in anisotropic materials are investigated in this paper. The solutions for a screw dislocation interacting with imperfect interface,viscoelastic interaction between a screw dislocation and a circular inhomogeneity with Kelvin-type viscoelastic interface in cylindrically anisotropic composites; electroelastic interaction between multiple piezoelectric screw dislocations and an annular interphase layer with imperfect interfaces in transversely isotropic piezoelectric materials are presented.
Using Riemann-Schwarz’s symmetry principle of complex functions, the above problems are transformed into Riemann-Hilbert boundary problems. By combining the analysis of singularity of complex functions, generalized Liouville’s theorem and Cauchy model integral, the explicit solutions to the complex variable functions of above problems are provided. With the aid of the Peach-Koehler formula, the image forces on dislocation are obtained respectively. The dependence of image force on materials’properties and imperfect interface parameters are calculated, plotted and discussed.
As a result, analysis and discussion show that the influence of imperfect interface on the interaction between screw dislocation and inhomogeneity is significant. When the interface is imperfect, in anisotropic composites, the influence acting on the dislocation of the anisotropic properties of cylindrically composites increases with the increase of the interface imperfection degree. When the anisotropic properties parameter of matrix is less than the one of inhomogeneity, there will be a critical value of imperfect interface parameter which changes the attraction-repulsion direction of the image force of dislocation. Due to the viscoelasticity of the interface, with the process of time, the image force decreases dramatically first and then evolves toward a steady-going value, meanwhile, the influence of anisotropic properties of inhomogeneity attenuate obviously. For the annular interphase layer with imperfect interfaces in piezoelectric composites, the imperfect interface attracts dislocation which increases with the decrease of the imperfect interface parameter while the hard inclusion and the hard interphase layer repel the dislocation and the repellence increases with the increase of the relative thickness coated interphase layer.
The provided results can not only offer a scientific basis for the design of composite structures but also provide basic solutions to further investigation on the strength and toughness of structures. The present solutions can be used as Green functions to obtain a series of solutions of related problems, and also contain a number of previously known results which can be shown to be special cases.
运用复变函数解析延拓原理,将上述问题转化为Riemann-Hilbert边值问题,结合复应力函数奇性主部分析方法、广义Liouville定理和Cauchy型积分别获得了上述问题复势函数的精确解答。根据Peach-Koehler公式,分别导出了相应位错力的解析表达式。研究了位错力随材料相关参数和非完整界面参数的变化规律。
研究结果发现,非完整界面对螺型位错与夹杂的干涉作用具有强烈的扰动效应。在圆柱形各向异性材料中,当界面为非理想时,随着界面非理想程度的增大,材料各向异性夹杂对位错的影响逐渐增强。当基体各向异性系数小于夹杂各向异性系数时,非理想系数存在一个临界值改变位错力的方向。对于粘弹性界面,刚开始夹杂的各向异性性质对于位错力的影响较大,随着时间的推移,位错力先是快速减小然后变幅趋于平缓,而夹杂的各向异性性质对于位错力的影响也显著减弱。在压电材料中,当界面为非理想界面圆环涂层时,非完整界面吸引位错,吸引力随着涂层内外边界非理想系数减小而增大。硬夹杂和硬界面层排斥位错,排斥力随着涂层相对厚度的增大而增大。
本文结果不仅可为相关复合材料的结构设计提供科学依据,而且可为进一步研究相关结构材料的强韧化机理提供基本解。本文的解答可以作为Green函数,获得相关问题的系列解答,且作为本文特例包含了以往文献中的若干结果。
The interaction of dislocation, inhomogeneity and interfacial defects is a greatly significant subject in the fields of solid mechanics and materials science. The elastic, viscoelastic and electroelastic interaction effects between imperfect interface and screw dislocations in anisotropic materials are investigated in this paper. The solutions for a screw dislocation interacting with imperfect interface,viscoelastic interaction between a screw dislocation and a circular inhomogeneity with Kelvin-type viscoelastic interface in cylindrically anisotropic composites; electroelastic interaction between multiple piezoelectric screw dislocations and an annular interphase layer with imperfect interfaces in transversely isotropic piezoelectric materials are presented.
Using Riemann-Schwarz’s symmetry principle of complex functions, the above problems are transformed into Riemann-Hilbert boundary problems. By combining the analysis of singularity of complex functions, generalized Liouville’s theorem and Cauchy model integral, the explicit solutions to the complex variable functions of above problems are provided. With the aid of the Peach-Koehler formula, the image forces on dislocation are obtained respectively. The dependence of image force on materials’properties and imperfect interface parameters are calculated, plotted and discussed.
As a result, analysis and discussion show that the influence of imperfect interface on the interaction between screw dislocation and inhomogeneity is significant. When the interface is imperfect, in anisotropic composites, the influence acting on the dislocation of the anisotropic properties of cylindrically composites increases with the increase of the interface imperfection degree. When the anisotropic properties parameter of matrix is less than the one of inhomogeneity, there will be a critical value of imperfect interface parameter which changes the attraction-repulsion direction of the image force of dislocation. Due to the viscoelasticity of the interface, with the process of time, the image force decreases dramatically first and then evolves toward a steady-going value, meanwhile, the influence of anisotropic properties of inhomogeneity attenuate obviously. For the annular interphase layer with imperfect interfaces in piezoelectric composites, the imperfect interface attracts dislocation which increases with the decrease of the imperfect interface parameter while the hard inclusion and the hard interphase layer repel the dislocation and the repellence increases with the increase of the relative thickness coated interphase layer.
The provided results can not only offer a scientific basis for the design of composite structures but also provide basic solutions to further investigation on the strength and toughness of structures. The present solutions can be used as Green functions to obtain a series of solutions of related problems, and also contain a number of previously known results which can be shown to be special cases.
引文
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