Study On Planar Isothermal And Thermal Fracture Problems By The Numerical Manifold Method

Fracture is one of the main types of material failure.The fracture of the material will directly degenerate its performances(e.g.,strength,stiffness and durability),and will eventually bring serious losses to the entire system in which it is located.Therefore,in-depth research on the relevant fracture behavior has important theoretical value and application prospects.In view of many merits such as wide applicability and low cost,the numerical methods have become the primary tools for solving various fracture problems.The numerical manifold method(NMM)is a powerful tool for fracture modeling due to its unique dual cover systems(namely,mathematical cover and physical cover),which can accurately characterize the local properties of cracks.In this thesis,the NMM is developed to study isothermal and thermal fracture of homogeneous and functionally graded materials(FGMs).The main fracture parameters such as the T-stresses and thermal stress intensity factors are obtained.The main results are as follows.(1)The NMM is developed to calculate the T-stresses of homogeneous materials with cracks.The NMM global equations are derived based on the governing equation,the associated boundary conditions,the NMM approximation function and the weighted residual method.The interaction integral for T-stresses computation is introduced.The main flow and momentous details of the program are also given.The domain-independence of the interaction integral,convergence and accuracy of the proposed approach are verified by typical numerical examples.After verification,the influences of crack configurations and boundary conditions on T-stresses are further discussed.(2)The NMM is developed to compute the T-stresses of cracked FGMs.The corresponding interaction integral formulae and its solving details are provided.The accuracy of the method and the influences of material gradients,crack configurations and boundary conditions on T-stresses are inspected through typical examples.(3)The NMM is developed to investigate steady and transient thermal fracture of FGMs.Based on the governing equations,the boundary conditions and the NMM approximation function,the NMM global equations for heat conduction and thermo-elastic fracture analysis are separately derived through the variational principle and weighted residual method.The interaction integral formulae and the numerical implementation details for extracting thermal stress intensity factors are presented.By means of several numerical cases,the accuracy of the method and the effects of material gradient,crack configurations and time step size on thermal stress intensity factors are revealed.