چكيده به لاتين
Anisotropic materials are necessary to be characterized since they have wide applications in researches and industrial fields, including studying and using composites, minerals exploitation, hydraulic fracturing and many other usages. A missing research area in this field is the fracture mechanics of anisotropic materials, which despite its broad applications mentioned above, is only investigated limitedly.
In the present study, crack problem in anisotropic bodies is analyzed implementing both analytical and numerical methods. First, elasticity of anisotropic materials is reviewed and important equations are provided. Second, entering the fracture mechanics topic and using a stress-based definition for pure modes of loading, analytical stress field for cracked anisotropic plates is discovered and expressed in infinite series form. The second stress term, known as 𝑇-stress is also found analytically for planar anisotropic problems. Next, strains and displacements are evaluated and their analytical fields are defined utilizing infinite series expressions. Moreover, the second displacements term containing rigid body rotation is also obtained. Afterwards, relative displacements on the crack flanks are calculated which are then used along with a popular method called displacement correlation to find the stress intensity factors (SIFs).
In order to calculate the higher order terms of stress field, a method namely finite element over deterministic (FEOD) method is employed to solve a system of algebraic equations. To proceed with this method, finite element (FE) results (i.e. numerical values of stress/displacement in selected nodes) are provided as inputs to a computer program to find and solve an over deterministic system of equations that finally outputs the crack parameters. This process is done by using once the stress field and once the displacement field, both of which analyze two types of problems, an infinite and a finite cracked plate. Results convergence and independence of number of terms, number of points and the ring number (from which nodes are selected) are also investigated by plotting the results. In addition, excellent agreement is observed between stress/displacement analytical fields and FE results which approves the accuracy of mathematical relations and numerical calculations, as well. This point is found that displacement field is able to provide more precise results thus imposing less error on the solution. Also, the influence of dimensions of the cracked plate on the constancy of SIFs is evaluated.
The last part of this research deals with brittle fracture in cracked anisotropic plates and uses the maximum tangential stress (MTS) criterion to find the fracture angles of various cases with different anisotropy angles. Polar variation of fracture toughness in anisotropic materials which is proposed earlier is now modified to be capable of calculating the fracture toughness even if the crack is not situated at the material orientation angle.
