Analysis Of Multi - Crack Tip Field By Complex Variable Function Method

With the rapid development of science and technology, composite material has become an indispensable material, it plays an important role in all walks of life. In the condition of high stresses, it is very easy to appear cracks for composite material, and three cracks is an important mechanical model between the multiple cracks’ interaction. To research the problems of three cracks can help us have a thorough understanding of the fracture mechanism, it has a practical significance in engineering. Although the problem of multiple cracks has been made a lot of theoretical research, and it has obtained some achievement, the research of three cracks is not systematic for orthotropic composite material plate in the far field under uniform loading using the complex variable function method.In this paper, fracture problem of three cracks in the composite material plate is studied using the complex variable function method. Using complex function theory, crack tip stress field problem in orthotropic plate comes down to a partial differential equation boundary value problem. By constructing an appropriate mapping, the complex three cracks is transformed into the simple parallel cracks, it simplifies the boundary conditions of a partial differential equation. In complex domain, parallel problem of three cracks can be converted to a single crack problem using the Westergaard stress function and the cyclicity of functions, we can solve the partial differential equation boundary value problem and get the analytical solution in mathematical plane. The stress intensity factor of three uniform distribution cracks tip is defined, and the analytical expressions of stress field and displacement field in orthotropic composite material plate with open type(or typeⅠ), sliding mode(or type Ⅱ) and mixed type(or + Ⅰ Ⅱ) is obtained near the crack tip stress intensity factor. The stress intensity factor of three cracks for type Ⅰ and type Ⅱ was got through the Mat Lab procedure, and the stress field and displacement field along with the change of polar angle curve is obtained as well.