Orthotropic Viscoelastic Material, The Crack Tip Field

In the actual project, coming forth much new type material of the viscoelastic properties, with the extensive application of various materials and the rapid development of experimental technology, the study of viscoelastic problem becomes increasingly important. More factors are considered in the solution of viscoelastic problem, i.e., space, time, temperature, etc. Therefore, solving the viscoelastic problem is very complicated. Then, when orthotropic viscoelastic problems are studied, the basic functions about time which are considered are more than solving isotropic viscoelastic problem. So, the orthotropic viscoelastic problems are more complex, and it is a litter research from now on. Correspondence principle is an important mathematical tool, when studying viscoelastic problem, i.e. , the solutions in the Laplace field from the correspondent of elastic solutions, final the reversed solutions into time field by inverse transformation. Based on these,using correspondence principle, this article researches on crack tip fields of orthotropic viscoelastic materials.The stress field and displacement field at the crack tip are studied about the orthotropic viscoelastic material in the symmetric loading and the skew symmetric loading. Firstly, the problem of the orthotropic viscoelastic is solved through the transformation from the orthotropic viscoelastic to the orthotropic elastic of the Laplace space by Laplace integral transform method. Secondly, on the base of the solution about the crack tip of the orthotropic elastic material plate, the solution, about the crack tip of the orthotropic viscoelastic material in the Laplace domain, is obtained, using quasi-static viscoelasticity-static elastic correspondence principle. Finally, using the F. Durbin numerical inversion methods, the orthotropic viscoelastic material solutions of the crack tip are obtained. Through the comparison with the solutions of the Crump numerical inversion method under the same condition, the more accurate solutions could be obtained through the F. Durbin numerical inversion method. The influence of material parameters on the stress and displacement is discussed. For the foundation of the future research about the problems of the anisotropic viscoelasticity and viscoelastic on the interface crack.