Theoretical Investigation in a Functionally Gradient Material with Finite Width under Antiplane Fracture Analysis 

Author  ZhangJiePing 
Tutor  LiJunLin 
School  Taiyuan University of Science and Technology 
Course  Applied Mathematics 
Keywords  Finite Width Functionally graded materials Anti  plane fracture Hyperbolic functions Dual integral equation Stress intensity factor 
CLC  O346.1 
Type  Master's thesis 
Year  2008 
Downloads  95 
Quotes  0 
In recent years, the concept of functionally graded material is introduced into the project structure. Because this material has a lot of advantages, therefore, people functionally graded materials more and more attention. Their application fields of aerospace, aviation , nuclear energy, electronics, optical, chemical and biomedical fields, the prospects are bright. functionally graded materials from the point of view of the application of mechanics, nonuniform body, its nonuniformity has a great influence on the mechanical properties of materials. In order to provide technical support to the materials scientists and materials design and preparation of personnel, many scholars have been considerable effort invested in the theoretical and experimental study of the mechanical properties of functionally graded materials, however, research on fracture mechanics of functionally graded materials still not enough, and is infinite strip of functionally graded materials are generally the material parameters using the exponential function in the form rarely seen other functional form infinite strip of functionally graded materials fracture mechanical issues further. Firstly, this paper put forward its development of functionally graded materials applications, and then assume that the material parameters of the hyperbolic function model changes, the use of integral transform  dual integral equations, finite width isotropic graded materials slats III crack antiplane loaded under static problem; finite width orthotropic functionally graded materials slats III crack antiplane loading were studied under static problem and moving crack problem with the last solved numerically in Matlab software and image simulation and obtained a series of results, the main course of the study, and the results are as follows: 1. study the infinitely long finite width isotropic functionally graded materials III crack antiplane static fracture results show , in plate width given case, the crack closer to the middle of the smaller the rate of change of the stress intensity factor as the crack position; crack closer to the board edge, the stress intensity factor is more obvious with the change of the crack location, crack position also affect one of the factors of the stress intensity factor .2. infinitely long finite width orthotropic functionally graded materials III crack antiplane static fracture results orthotropic functionally graded materials With the increase of material nonuniformity coefficient, the value of the stress intensity factor but reduced and therefore, can be suppressed by increasing the shear modulus parallel to the direction of the crack surface crack driving force .3. study the crack position parallel mobile infinitely long finite width orthotropic functionally graded material III crack antiplane static fracture problem results of crack location on the stress intensity factor, corresponding to the crack location and III crack in functionally graded material roughly the same as the impact of the stress intensity factor; stress intensity factor increases with increasing crack length, and decreases with increasing material gradient parameter, and with increasing crack length, material gradient parameters on the stress intensity factor is increased large .4. study Yoffetype moving crack in an infinite strip of functionally graded materials slats The results show that the dynamic stress intensity factor increases with increasing crack movement speed; coefficient increases with the material is uneven and less small.