Fracture Analysis on Multiferroic Composite Plates Under Concentrated Forces
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摘要: 针对多铁性板状复合材料在外表面任一点处存在集中力的界面裂纹问题,建立断裂力学模型.利用Fourier(傅里叶)积分变换和Green(格林)函数推导出该裂纹模型的Cauchy(柯西)奇异积分方程组;通过Chebyshev(切比雪夫)配点法将该方程组离散为对应的代数方程组,进而数值求解裂纹尖端应力强度因子.通过对数值结果的分析可以得到:在外表面集中力作用下,压电层厚度、裂纹长度以及集中力作用位置是影响裂纹尖端应力强度因子的3个主要因素.分析讨论了在该模型下各项参数对应力强度因子的影响规律,可以在工程应用中为此类复合材料的防断裂优化设计提供一定的理论参考.Abstract: The fracture mechanics model was established for the interfacial fracture problem of a multiferroic composite plate under concentrated force on the outer face. The Fourier integral transform and Green’s functions were employed to obtain the Cauchy-type singular integral equations, which were further discretized into algebraic equations through the Labatto-Chebyshev collocation. The algebraic equations were numerically solved to determine the stress intensity factor (SIF). Analysis of the numerical results indicates that, the thickness of the piezoelectric layer, the crack length and the concentrated force location are 3 major factors to influence the stress intensity factor at the crack tip. The effects of physical and geometric parameters on the stress intensity factor in this model provide theoretical references for the anti-fracture optimal design of related composite materials in engineering.
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Key words:
- concentrated force /
- multiferroic /
- plate /
- interfacial fracture /
- stress intensity factor
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