Research On Parallel Vertical Cracks And Common Arc Cracks In Functionally Graded Materials

With the development and application of various new materials,the study of new material fracture problems has become a research hotspot in the field of fracture mechanics.Many scholars have tried to study cracks in different forms and cracks in different states,trying to realistically simulate various fracture phenomena that may exist in reality,thus further enriching the theoretical study of new material fracture problems.Functionally graded materials(FGM),as a new type of composites,are widely used in many popular fields.Therefore,the analysis and research of various crack models existing in functionally graded materials,and the continuous improvement and optimization of the research methods are crucial.In this context,the problem of two parallel vertical cracks in functionally graded materials and two arc cracks with a common circle are studied in this paper.By understanding the characteristics of functionally graded materials and the related knowledge and research methods of fracture mechanics,and according to the existing cracks in wood flooring in the actual investigation,the corresponding mathematical model is established,and the effective boundary conditions are given.For the parallel vertical crack model,Fourier transform method and complex method are used to solve the problem,and the displacement of the crack tip and its surrounding area reflected by the displacement function image of the crack is obtained by MATLAB numerical simulation,and the external factors affecting the further change of the crack are analyzed.For the study of the problem with common arc cracks,it can be found through many attempts and calculations that the Fourier transform method is no longer applicable at this time.Therefore,this paper will use the complex variable function method to further demonstrate the better applicability of the complex variable method.