Investigations Of Analytical Fracture Mechanics Models Of Functionally Graded Materials With Definite/Stochastic Properties

Functionally graded materials (FGMs) are typical nonhomogeneous materialswhich can be applied significantly in the aeronautic field, astronautic fied and someother engineering fields. Fracture is one of typical failure manners of FGMs.Therefore, fracture mechanics investigations can provide key supports for the safeapplication of FGMs. Considering the limitation of the analytical methods for thefracture mechanics problems of FGMs in the past thirty years, this thesis focuses onthe investigations of analytical models in fracture mechanics of FGMs.In Chapter1, the background and significance of the subject are introduced.Then, the research status of the studies related to the fracture mechanics of FGMs isreviewed. The shortages of the present analytical models in fracture mechanics ofFGMs are discussed. Based on the review and discussion, the main contents of thisthesis are determined.In Chapter2, the fracture mechanics model for an arbitrarily oriented crackcrossing the interface in a functionally graded layered structure is established.Applying the superposition principle and Fourier integral transform, the stress anddisplacement fields are derived. By introducing a group of auxiliary functions, themixed-mode crack problem can be turned into solving a group of singular integralequations from which the mixed-mode stress intensity factors (SIFs) can be solved.Using this model, the influences of the material and geometry parameters on theSIFs are studied. With the above model, not only is the arbitrarily orientedcrossing-interface crack problem solved, but also the basic problem is solved forestablishing the fracture mechanics model of FGMs with general mechanicalproperties.In Chapter3, the fracture mechanics model is proposed for FGMs with generalmechanical properties and an arbitrarily oriented crack. Prefiously, in order to solvethe crack problems of FGMs analytically, some ideal assumptions are usuallyadopted. They are:1) the mechanical properties of FGMs are usually assumed to bevery particular functions;2) the crack is usually assumed to be vertical to (orparallel to) the gradient of FGMs. In this chapter, a general piecewise-exponentialmodel (GPE model) is proposed. The studied FGMs are divided into somesub-layers with each layer’s properties varying exponentially so that the generalmechanical properties can be approximated by a series of exponential functions.Due to the assumption of exponential properties, hundreds of analytical modelspublished in the past30years once were doubted. However, the present GPE model indicates that these analytical models become more significant because they canform a strong base for establishing a general model for FGMs with generalmechanical properties.In Chapter4, an analytical fracture mechanics model is established for FGMswith stochastic mechanical properties. A “bridge” is built between the macrofracture mechanics model and stochastic micromechanics model so that thestochastic fracture mechanics model can be established for predicting theprobabilistic characteristic of SIFs in FGMs with stochastic mechanical properties.Considering the stochastic description of the phase volume fractions, a stochasticmicromechanics model is proposed to study probabilistic characteristics of theeffective properties of FGMs. Then, a thought for choosing the samples efficiently isproposed so that the stable probabilistic characteristic of SIFs can be obtained. Thisis the first analytical model of stochastic fracture mechanics of FGMs in the pastthirty years.In Chapter5, a fracture mechanics model is established for FGMs with generalviscoelastic mechanical properties. The relaxation functions are assumed to take theform separable in space and time. Then, using the correspondence principle andLaplace transform method, the crack problem of the viscoelastic FGMs is turnedinto a corresponding elastic crack problem of FGMs with general mechanicalproperties in Laplace domain. Using the aforementioned GPE model and the inverseLaplace transform method, the SIFs of viscoelastic FGMs can be obtained. Finally,the influences of the material and geometry parameters on the SIFs are studied.