二维六边形压电准晶介质中的笔形裂缝问题的剪切模求解

IF 5 2区工程技术 Q1 ENGINEERING, MECHANICAL

Theoretical and Applied Fracture Mechanics Pub Date : 2024-11-16 DOI:10.1016/j.tafmec.2024.104762

Yuan Li , Shuhang Tang , Pengyun Li , Jingli Ren , Minghao Zhao

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引用次数: 0

摘要

本研究探讨了由具有压电效应的二维六方准晶介质组成的无限三维体中的剪切模式笔形裂缝问题。该裂缝在裂缝平面内受到一组剪切声子和声子载荷。该剪切模式裂缝问题被转化为上半空间的混合边界值问题。随后，利用 Fabrikant 的势理论方法对其进行了优雅的求解。推导出了二维六方压电准晶体中三维剪切模裂纹问题的边界积分微分方程，并将声子和声子位移不连续作为未知变量。提出了所有物理场量的闭式解，不仅局限于裂纹表面，而是全面扩展到整个空间。明确推导出了关键的断裂力学参数，如声子和法森位移不连续度、裂纹顶端的应力强度因子和能量释放率。提供的数值结果验证了所获得的分析解，并以图表形式说明了裂纹周围电-声子耦合场的分布。此外，这些数值结果还比较了所选压电准晶体与相应非压电准晶体的断裂力学参数，从而研究了压电效应对准晶体的影响。所获得的解决方案可作为压电准晶体剪切模裂纹实验和数值研究的基准。

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Shear mode solutions to penny-shaped crack problems in two-dimensional hexagonal piezoelectric quasicrystal media

This study investigates shear mode penny-shaped crack problems in an infinite three-dimensional body composed of a two-dimensional hexagonal quasicrystal medium with piezoelectric effect. The crack is subjected to a set of shear phonon and phason loadings within the crack plane. This shear mode crack problem is transformed into a mixed boundary value problem in the upper half space. Subsequently, it is elegantly solved utilizing Fabrikant’s potential theory method. The boundary integral–differential equations governing three-dimensional shear mode crack problems in two-dimensional hexagonal piezoelectric quasicrystals are derived with the phonon and phason displacement discontinuities serving as unknown variables. Closed-form solutions for all physical field quantities are presented, not merely limited to the crack surface, but rather extended comprehensively to the entire space. Key fracture mechanics parameters, such as phonon and phason displacement discontinuities, stress intensity factors at the crack tip, and energy release rate, are explicitly derived. Numerical results are provided to validate the obtained analytical solutions and illustrate the distribution of the electric-phason-phonon coupling field around the crack in graphical form. Additionally, these numerical results also compare the fracture mechanics parameters of the chosen piezoelectric quasicrystal with its corresponding non-piezoelectric quasicrystal, thereby investigating the influence of piezoelectric effect on quasicrystals. The obtained solution can be used as a benchmark for the experimental and numerical study of shear mode cracks in piezoelectric quasicrystals.

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来源期刊

Theoretical and Applied Fracture Mechanics 工程技术-工程：机械

CiteScore

8.40

自引率

18.90%

发文量

435

审稿时长

37 days

期刊介绍： Theoretical and Applied Fracture Mechanics'' aims & scopes have been re-designed to cover both the theoretical, applied, and numerical aspects associated with those cracking related phenomena taking place, at a micro-, meso-, and macroscopic level, in materials/components/structures of any kind. The journal aims to cover the cracking/mechanical behaviour of materials/components/structures in those situations involving both time-independent and time-dependent system of external forces/moments (such as, for instance, quasi-static, impulsive, impact, blasting, creep, contact, and fatigue loading). Since, under the above circumstances, the mechanical behaviour of cracked materials/components/structures is also affected by the environmental conditions, the journal would consider also those theoretical/experimental research works investigating the effect of external variables such as, for instance, the effect of corrosive environments as well as of high/low-temperature.