The Higher Order Crack Tip Fields for Arbitrary FGM Composite Functions

Abstract

As the material properties function at the crack tip greatly affects the structure of crack tip field, especially in the study of comparatively thin FGM composites whose properties functions are equipped with the feature of high gradient variation, it is not enough to adopt the simple linear function to depict the property testpoints of the material. A new method, which is more precise to deal with the experimental data and to depict FGM composite properties functions (e.g. elastic modulus E), is proposed in this paper. Beside the linear function, quadratic term, cubic terms and so on are added. Then, the solution is first given for the general power function, and the more precise analytical solution of higher order crack tip fields will be obtained by means of superposition method. Actually, any other complicated or arbitrary material functions can be treated similarly by using Taylor series expansion at the crack tip. Finally, the obtained higher order crack tip fields or the eigen-functions which can depict the arbitrary material function would provide the theoretical basis for the fracture experiments and numerical simulation, and this method is of great universal significance.