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Theoretical Investigation and Numerical Value Simulation Analysis of Stress Field Near Crack Tip in Functionally Graded Materials

Author: SuiZhongHe
Tutor: LiJunLin
School: Taiyuan University of Science and Technology
Course: Applied Mathematics
Keywords: Functionally graded materials Orthotropic Anti - plane fracture I, II, III -type crack Integral transform Complex variable method Stress intensity factor
CLC: O346.1
Type: Master's thesis
Year: 2008
Downloads: 187
Quote: 1
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Abstract


The functional gradient material, due to its special structure of the material, so that the material parameters can be continuously changed in the space, thereby effectively eliminating the traditional composite material parameters in the interface does not match, and thus can effectively reduce or eliminate thermal stress and residual stress greatly ease the stress concentration, potential applications in aerospace and other cutting-edge areas and ultimately lead to the damage of the material due to the material generated in the course of various cracks, cracks extended functionally graded materials study is especially important. functionally graded materials are generally the material parameters of the exponential function, and rarely seen other functional form, and rarely seen dynamic crack problems reported this paper put forward its development of functionally graded materials application described, then the use of the integral transform - dual integral equation method, it is assumed that the material parameters according to the arbitrary power of two-parameter power function model of infinite orthotropic gradient material III crack anti-plane loaded under static and dynamic problems and moving crack problem has been studied; solved numerically and image simulation with Matlab software, and reached a series of important results. use of complex variable method infinite strip the opposite sex, anisotropic functionally graded materials I, type II crack plane loading case were studied. research process and results are as follows: 1. functionally graded materials in an infinite plate III crack anti-plane The static fracture Results orthotropic functionally graded materials, the crack tip stress field has the same r1 inverse square root singularity, and θ1 angular distribution function identical orthotropic homogeneous material; With the increase of material non-uniformity coefficient, the value of the stress intensity factor increases. therefore, can be suppressed by increasing the shear modulus perpendicular to the direction of the crack surface crack driving force .2. study the infinite plate functionally graded materials III crack anti-plane dynamic fracture results show orthotropic functionally graded materials, the crack tip stress field has the same r1 inverse square root singularity, θ1 angular distribution function and orthogonal to the heterosexual uniform material situation is exactly the same; With the gradient parameters and material non-uniformity coefficient decreases, the value of the dynamic stress intensity factor decreases .3. Yoffe-type moving crack in the infinite plate with functionally graded materials results dynamic stress intensity factor decreases with increasing crack speed of movement, with finite width infinite strip of functionally graded materials moving crack dynamics problem is just the opposite conclusion; dynamic stress intensity factor with increasing gradient parameter decreases increase with the increase of material non-uniformity coefficient; crack driving force and can be suppressed by increasing the shear modulus perpendicular to the direction of the crack surface .4. infinite orthotropic and anisotropic features The graded material I, type II and I II mixed mode crack problem. was first introduced orthotropic and anisotropic material parameters along the gradient direction of the arbitrary function form continuous changes of functionally graded material plates I, II and type I II mixed type of crack tip stress field, displacement field and gradient stress intensity factor theoretical calculation results show that the crack-tip stress field the same r inverse square root singularity. based on the basis of this theory, we can use widely used in homogeneous material orthotropic anisotropic functionally graded materials problems fracture mechanics method to study the results of the above study for the preparation and performance of functionally graded materials optimization provides an important theoretical guidance, will also have to further develop and promote the application of functionally graded materials important role.

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CLC: > Mathematical sciences and chemical > Mechanics > Solid Mechanics > Strength theory > Fracture theory
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