Application Of Complex Function Method On The Research Of Cracked-hole Problem

The hole edge crack is a kind of common crack configuration in aircraft structures,and it is also one of the most improtant resaons that affect the aircraft structural integrity.Stress intensity factor calculation is the the key for solving problems,which include fracture mechanics analysis,fatigue crack growth life prediction and residual strength analysis for the structures with hole edge cracks,and is also the basis for damage tolerance design.For the fatigue crack growth life prediction model based on crack closure theory,the crack opening stress is the most important parameter,which can be obtained through the crack surface opening displacement.There are many methods used to research problems of stress intensity factor and crack surface opening displacement for hole edge cracks.In this paper,the complex function method is used to calculating stress intensity factors and crack surface opening displacements of two-symmetric(or asymmetric)cracks emanating from a circular hole?non-circular hole and multi-holes in an infinite plate.The results calculated from the complex function method ? the weight function method and the finite element method(FRANC3D software)can prove the correctness of complex function method.The research results of this paper can further enrich the application for solving hole crack problems by the complex variable function method.In this paper,the main research contents and innovation works:1.Researching the problems of stress intensity factors and crack surface opening displacement for two collinear cracks with arbitrary length emanating from a circular hole in an infinite plate under remote tension.First,the stress intensity factor values from the complex function method were compared with many scholars' results when two cracks from a circular hole are symmetric;Then,calculating mixed-mode stress intensity factors of hole edge cracks under the different angles and different crack lengths,analyzing the influence of the angle and the crack length for the stress intensity factor;Finally,calculating the crack face opening displacements when two collinear cracks with arbitrary length emanating from a circular hole are symmetric or asymmetric,analyzing the influence of crack length for the crack surface opening displacement.The results show that the method can be used to solve the stress intensity factors and crack surface opening displacements for two collinear cracks with arbitrary length emanating from a circular hole under remote tension.2.According to the stress intensity factors for cracks emanating from a hole with arbitrary shape in an infinite plate under remote tension,this paper proposed a universal complex variable function method.Such as elliptical hole edge cracks,caculating the stress intensity factors for two symmetric cracks emanating from elliptical hole who have different short semi-axis,the correctness of the proposed method is demonstrated by comparing the calculated values with other scholars,and analyzing the influence of elliptical hole short semi-axis for stress intensity factors.Finally,caculating the mixed-mode stress intensity factors of elliptical hole edge cracks under the different angles,semi-axis ratios and crack lengths;analyzing the influences of the angles,elliptical semi-axis ratios and the crack lengths for the stress intensity factors.The results show that the complex variable function method can be used to calculate the stress intensity factors for two cracks emanating from a elliptical hole under remote tension,the stress intensity factors caculation of the cracks can be extended to the solution of arbitrary shape hole edge cracks problem.3.According to the stress intensity factors for the multi-hole edge cracks in an infinite plate under remote tension,this paper proposed a modified approximate superposition method,solved the stress intensity factors for cracks with arbitrary length emanating from double holes and three holes,and the calculated values are compared with other methods,analyzing the influence of adjacent hole distance and crack length for stress intensity factors.The results show that this modified approximate superposition method can be used to calculate the stress intensity factors for multi hole edge cracks under remote tension,the calculated results can meet the needs of engineering application.4.Researching the problems of stress intensity factors and crack surface opening displacements for two collinear cracks with arbitrary length emanating from a circular hole in an infinite plate under uniform stress applied to a segment of the crack surface.First,the calculated values are compared with weight function method when two cracks emanating from a circular hole are symmetric,proved the correctness of this method.Then,when two collinear cracks emanating from a circular hole are asymmetric,the left crack is a fixed value,caculating the stress intensity factors and the crack surface opening displacements for the right crack,analyzing the influence of crack length.The results show that the complex variable function method can be used to calculate stress intensity factors and crack sueface opening displacements for two collinear cracks with arbitrary length emanating from a circular hole in an infinite plate under uniform stress applied to a segment of thecrack surface.