Complex Variable Method Analysis Cycle Parallel Crack Tip Field Problems

Composite materials are a very promising class of structural materials, whichare widely used in many filed such as transportation, space technology andnational defense. In a state of high stress levels, composite materials are easierto appear many micro-cracks; however, periodic crack is the importantmechanical model to study the interaction of multiple cracks. Consequently, theresearch on periodic cracks problem contributes to making an intensiveunderstanding of failure mechanism of materials, and this is very important toengineering practice effectively.Complex function method is one of the most effective methods ofmathematical methods. With the application of complex function theory andundetermined coefficients method, the mechanical problem is turned into theboundary value problem of partial differential equation, and then studying thestress fields and displacement fields’ problem of periodic cracks. By usingcomplex function method, we have obtained some systematic theoretical resultsin the studies of collinear periodic cracks problems, but the study of periodicparallel cracks problems in an orthotropic composite plate subjected to thedistributed load within the cracks surface is seldom seen, need to further study.In this paper, the periodic parallel cracks fracture problems in an orthotropiccomposite plate are studied by using complex function method. With theapplication of complex function theory and undetermined coefficients method,the mechanical problem is turned into the boundary value problem of partialdifferential equation. In the complex domain, the periodicity of parallel crackscan be removed by using the periodicity of the hyperbolic function andconstructing proper Westergaard stress function. The boundary value problem ofpartial differential equation can be solved with the help of boundary conditions.Stress intensity factor on the periodic parallel crack tip is defined in the firstplace, the analytic expressions for stress intensity factor, stress field anddisplacement field near the periodical parallel crack tip for Mode I, Mode II andMode I+II in an orthotropic composite plate are obtained. The stress intensity factor around the crack tip of periodic parallel cracks in an orthotropiccomposite plate depends on the shape factor, and when the vertical distance ofcracks tends to infinity, the stress intensity factor degenerates into a singlecentral crack situation. The result analysis of interaction between the periodicparallel cracks contributes to studying the interaction between multiple cracksand designing the strength of the material.