Bimaterial Interface Crack Tip Singularity And The Stress Field

Bi-materials are made of two materials with different properties bondedtogether in some way, while the combining site is called interface. Due to thedifferent material character on both sides of interface, it is unavoidable that inthe interface would appear stress concentration phenomenon, and the singularpoint is caused by stress concentration (the singular point is regarded as thestress has singularity). Materials were often damaged begin with the interfacesingular point, and then become a problem of interface crack. The cracks furtherexpansion make materials bonding strength decline, and the whole structurewould be destroyed to the end. Therefore, it is necessary to in-depth study theproblems of stress singularities for interface crack, which could providenecessary theoretical foundation for improving the strength of materials.The attention focused on studying problems of stress singularities ofsemi-infinite interface crack for orthotropic bi-material. With the help of thecomposite fracture complex variable function method, we construct new stressfunctions with complex singularity exponents which based on the original stressfunctions with real singularity exponents, the problems of interface crack weretransformed into a class of generalized bi-harmonic equations boundary valueproblems. When the discriminants of the characteristic equations of thegoverning equations areΔ1>0andΔ2>0, the relationship between the singularexponents and engineering parameters of bi-material are discussedsystematically. There are four kinds of singularities near the interface crack tipof orthotropic bi-material are obtained. For a given load conditions, thecomputational formulas of stress intensity factors and the analytical solutions ofthe crack tip stress fields and displacement fields are acquired. The main resultsare as follows:1. For the material engineering parameters of the orthotropic bi-material And the existence of four kinds ofsingularity near the interface crack tip for orthotropic bi-material is tested by examples.2.When a given load conditions, the computational formulas of stress intensityfactors and the analytical solutions of the crack tip stress and displacementfields for four kinds of stress singularities are obtained.3. For the stress with real singularities, the stress fields of interface cracks tippossesses non-oscillatory and there is no overlapping of crack surfaces. Andfor the stress with complex singularities, the stress fields of interface crackstip possesses oscillatory behavior and there is overlapping of crack surfaces.We only give the discussion forΔ1>0, Δ2>0in the paper. Using thismethod the similar discussion for other case can also be conducted. The studynot only offer a beneficial method for solving the problem of bi-materialinterface crack tip field, it also provides the theoretical reference for solving thecorresponding problem encountered in practical engineering and buildingmaterials reliability evaluation.