压电压磁层合材料结构界面裂纹亚、跨、超音速传播平面问题研究

The layered magnetoelectric (ME) composites consist of piezoelectric layers alternating with piezomagnetic layers. Such composites are easily manufactured and possess superior ME coupling effect, which attract their potential applications in sensors, transducers and acoustic wave devices, etc. When subjected to dynamic mechanical and electromagnetic loads, the layered ME materials and structures easily fail. Thus, it is important to investigate the dynamic fracture behaviors of interface cracks in layered ME materials. By using theoretical, numerical and experimental methods and techniques, the crack tip properties of interface cracks in layered ME structures and moving in subsonic, transonic and/or supersonic speeds under plane deformations will studied in this project. The main contents are as follows: (a) to establish the plane problem models for piezoelectric/piezomagnetic layered composite structures with an interface crack moving in different speeds, derive the non-uniform Riemann-Hilbert equations and corresponding solutions for different crack surface electromagnetic conditions; (b) to explore the application of moving finite element method in moving interface crack problem of layered ME composites; (c) to carry out experiment study on piezoelectric/piezomagnetic laminates. The ultimate objective of this study is to reveal the effects of material properties, electromagnetic boundary conditions, geometric sizes, loading types and sizes on the crack tip fracture behaviors of moving interface crack in multilayered ME composite structures and with different propagation speeds. The completion of this project will give a better understanding of the dynamic fracture of interface cracks and provide a theoretical basis for the design and reliability analysis of layered ME materials and associated components.

由压电层和压磁层复合而成的层状磁电材料，具有磁电转换效率高和易于制作等优点，在传感、换能和声波领域具有广泛应用前景。这类材料磁电效应的转换和相关器件功能的实现与动态载荷密切相关，且其界面易于开裂和失效。因此，本项目拟采用理论分析、数值模拟和实验相结合的方法，研究平面变形下压电压磁层合结构界面裂纹亚音速、跨音速及超音速传播时不同的动态断裂特性。主要内容包括：建立压电压磁层状材料运动界面裂纹平面问题模型，导出不同裂纹面电磁边界条件下界面裂纹不同速度传播时各种裂纹模型对应的非均匀黎曼-希尔伯特问题的解；探究移动有限元法在磁电层合结构界面裂纹平面问题中的应用；进行压电压磁层合板的模型试验研究。项目的最终目的是获得不同传播速度下材料参数、电磁边界条件、几何尺寸、载荷类型及大小对裂尖断裂特性的影响，揭示多层磁电复合结构动态断裂失效机理，为层状磁电复合材料的设计和可靠性分析提供理论基础。

电磁材料是一种新型磁电转换材料，因其较高的积效应在智能驱动器和换能器中具有巨大应用前景。该类材料制造和使用过程中常含裂纹，因而关于这类材料裂纹问题研究具有重要价值。项目组通过四年的努力，对智能材料结构多场耦合断裂力学问题进行了系统研究，在压电压磁层合材料结构界面裂纹冲击、扩展及传播等领域取得了突破性研究成果。对含硬币型裂纹电磁弹性柱在力-电-磁荷载及热冲击荷载作用下的断裂问题研究取得了新的进展。对含不同裂纹超导柱在外加磁场和/或电流作用下的多场耦合断裂问题的研究取得了系列成果。同时丰富了微态热电磁材料弹性动力学基本理论。另外，在准晶圆柱壳体的屈曲和自由振动、功能梯度压电板的屈曲等方面也取得了新的进展。截止到2019年12月31，已发表SCI收录论文25篇（另外投出送审2篇），申请美国PCT国际专利一项，获河北省自然科学三等奖一项。尽管本项目取得大量成果，但限于时间和精力，课题组在实验研究方面还没有取得实质性突破，项目组成员在这方面将继续努力。相信本项目研究成果必将为智能驱动器和换能器等设备中的关键元器件的设计与制造奠定坚实的理论基础。

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