金属裂纹板复合材料修补结构的超奇异积分方程方法

根据应力强度因子在线弹性范围内具有可叠加性,将金属裂纹板复合材料修补结构进行简化,在表面裂纹线弹簧模型的基础上,建立了基于超奇异积分方程的Line-Spring模型。利用第二类Chebyshev多项式展开的方法,将超奇异积分方程转化为线性方程组,推导出以裂纹面位移表示的应力强度因子表达式,得到了裂纹尖端应力强度因子的数值解,并利用虚拟裂纹闭合法加以验证。参数分析确定了影响对称修补裂纹板应力强度因子的两个主要参数:胶层界面刚度和补片与金属板刚度比,为胶接修补结构的承载能力分析以及改进设计提供理论依据。

METHOD OF HYPERSINGULAR INTEGRAL EQUATIONS APPLIED TO A CRACKED METALLIC STRUCTURE REPAIRED WITH ADHESIVE BONDING COMPOSITE PATCH

A cracked metallic structure repaired with adhesive bonding composite patches is simplified using the superposition principle of the stress intensity factor (SIF), commonly used in linear elastic fracture mechanics. A Line-Spring model, based on a hypersingular integral equation, is developed according to the linear spring model for surface cracking. The hypersingular integral equation is then transformed to a system of linear equations by the second Chebyshev polynomial expansion method. Then, the SIF is expressed in terms of the displacement discontinuities of the crack surface. The numerical result of SIF for the crack tip correlates very well with the finite element computations based on virtual crack closure technique (VCCT). The two relevant key parameters for stress intensity factor (SIF), adhesive interface stiffness,, and the ratio of the patch stiffness to the plate stiffness,, are identified and discussed. The present mathematical techniques and analysis approaches are critical to the successful design, analysis, and implementation of bonded repairs.