Weight Functions For Two Collinear Cracks And Its Application In The Analysis Of Multiple Site Damage

The fatigue crack growth life and residual strength of structure with multiple site damage are significantly reduced,and therefore threating the aircraft safety.Many catastrophic accidents were caused by the presence of MSD in aircraft structures.Efficient and accurate methods for obtaining the stress intensity factors(SIF)and crack opening displacements(COD)of the multiple site cracks are the key to predict the fatigue crack growth and residual strength.The configuration of two collinear cracks in a sheet is one of the most common MSD configurations.In this paper,the weight functions of the two collinear cracks were derived and be used to obtain the SIFs efficiently and accurately.Moreover,the SIFs of stiffened panel with two collinear cracks are analyzed as well,which provides a useful tool in the analysis of MSD.The main works of this paper are summarized as follows:(1)An exact weight function(WF)solution for two unequal-length cracks is derived and provided in this paper.When the crack lengths are equal,this weight function can be reduced into the weight function of two equal-length cracks.When the crack lengths are unequal,the weight function obtained from the finite element analysis is almost identical to that given in this paper.The relative different between the present weight function and that from FEA is less than 0.3%.(2)The SIFs and CODs of two collinear cracks under different loading conditions are calculated by using the present weight functions.All the results are verified by the existing solution for two equal-length cracks and FEM results.It is observed that the weight function given in this paper is accurate and reliable.(3)An approximate method for analyzing the SIFs of stiffened infinite panel with two equal-length cracks is proposed by using the weight functions for the two unequal-length cracks.The method is widely verified by FEA.It is observed that,for most conditions,the relative difference between the SIFs obtained from this approximate method and those from FEA is less than 6%.However,this approximate method is much more efficient than FEM,and therefore providing a useful tool for analyzing MSD.