13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- element framework where zones of cracking are Known a-priori and cohesive zone elements are placed along these element boundaries. Gao [14,15] proposed that materials undergoing brittle fracture have large non-linear elastic deformations and that a hyper elastic description of the crack tip behavior provides a better explanation of dynamic Crack tip in stabilities. Gao and Klein[16] developed a method, called the virtual internal bond(VIB)model ,In which a cohesive type law is directly incorporated in to the constitutive model. This is done by treating the Body as a collection of randomly distributed material points inter connected by a network of cohesive bonds. The Cauchy–Bornrule of crystal elasticity is used to derive the overall constitutive relations. This is done by equating the strain energy of the bonds to the potential energy stored in the continuum due to applied loads and deformations. As this is implemented in a hyper elastic frame work deformation continuum mechanics, the Green–Lagrange strain tensor can be evaluated from deformation gradient, and the second Piola–Kirchoff stress tensor can be computed from the potential energy expression. The main advantage of this method is that, as in the cohesive boundary element approach [9], no separate fracture criterion is needed. Furthermore, the cohesive law is now embedded directly into the constitutive equations, thus no special boundary elements between regular elements are needed. This study implements a finite element model to study the thermal fracture behavior of functionally graded materials. Stress intensity factors (SIF) are evaluated using a thermo mechanics and fracture mechanics approach. The results show that the components gradation of the FGM composites has significant influence on the specimens' thermal behavior. 2. Thermo-mechanical finite element modeling of FGM A problem which is encountered in three-dimensional finite element analyses is the large number of elements and as a result, a remarkable and time consuming computation. Also, because of very rapid changes in the geometrical parameters around the crack front region, mesh generation of this region must be done with a great care. This may lead to increase the run time which makes it difficult to reach valid results and conclusion [17]. The main objective of this study is to model and analyze a three dimensional inclined semi-elliptic surface crack in a plate made of Functionally Graded Material (FGM). FGM is 100% zirconia-yttria (ZrO2-8wt%-Y2O3 ) at x=0 and 100% nickel-chromium–aluminum– zirconium (NiCrAlY) at x= t. The thermo mechanical properties of the FGM structure are assigned according to variation function by using the centroid of each finite element. This procedure is developed by utilizing ANSYS codes. A unique material property is assigned to each element with the help of this method. In this study three different ratio regarding to modulus of elasticity (E) are considered as E2/E1= 20, E2/E1= 0.05 and homogeneous material case.E1and E2 are the values of the elastic module at x= 0 and x=t, respectively. Except elastic module a total of five material parameters are required to be known in order to carry out the transient thermal fracture analysis. These parameters are Poisson’s ratio υ, thermal expansion coefficient αt, thermal conductivity k and density multiplied by specific heat ( ܿߩ ௧). (ܿߩ ௧) can be evaluated using the relationship ܦ ൌ݇ ܿߩ ௧ ൗ where D is the thermal diffusivity.
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