Enriched Finite Element Method For Interface Fracture Analysis

Interface fracture problems and its structural integrity analysis,such as Solid Rocket Motor interface debonded cracks,interface stress concentrating,coating cracks and cut slots widely exist in solid rocket.The so called enriched finite elements are established by incorporating the base functions in which the basic unknown quantities are the generalized stress intensity factor(SIF)into finite element displacement interpolation model.The theories including formulation of enriched elements and the evaluation of fractural parameters for elastic and viscoelastic interface fracture problems,are studied.The main research contents of this paper are as following:In order to obtain the asymptotic displacements used to construct the displacement models of enriched element of interface fracture problems,eigenvalues and characteristic matrix of several typical interface fracture problems including the crack normal to and terminating at interface,bimaterial V-notch are formulated based on the Williams' series expansion.The asymptotic displacement fields are uniformly expressed as the matrix-vector product by using the linear transforms of characteristic matrix and definitions of stress intensity factor.The formulations and procedure possesses favorable simplicity and convenience for constructing enriched elmenets of interface fracture problems.The enriched finite method for 2D elastic and viscoelastic interface crack problems are established.According to the basic displacements fields of elastic interface crack tip,the crack tip asymptotic displacement fields of viscoelastic interface crack are derived through the correspondence principle and an approximate Laplace inverse transform method.By incorporating the asymptotic displacement field into conventional 2D element,the enriched elastic and viscoelastic interface crack elements are constructed.Based on the integral constitutive relation of viscoelastic material,the incremental equilibrium equations of enriched viscoelsatic interface crack element are deduced.The SIF and strain energy release rate(SERR)are calculated for typical plane problems of elastic and viscoelastic interface crack.The enriched finite element method is developed for 2D crack normal to and terminating at interface.The crack tip asymptotic displacement fields in the method is derived through an approach based on the Williams' series expansion and linear transforms.By incorporating the displacement expressions to the displacement model of common element,the enriched and transition element displacement models are deduced,and the enriched finite element equations are derived consequently.The enriched finite element models of typical plane problem containing a crack normal to bi-material interface are established and the stress intensity factors are obtained directly by solving the enriched finite element equations.The enriched finite methods for 2D and 3D bimaterial V-notch problems are established.The enriched element displacement model is obtained by incorporating the asymptotic displacement expressions of V-notch tip to the common isoparametric element,then the enriched finite element equation is formulated consequently.The 2D enriched finite element models for bi-material V-notch problem with real and complex eigenvalue and 3D enriched finite element models are constructed respectively,and the factor affecting the accuracy of SIF is analyzed as well.The enriched finite methods for 3D elastic and viscoelastic interface crack problem are established.Based on the fundamental solutions of asymptotic displacement field for plane and antiplane problem of interface crack,the local asymptotic displacement fields of 3D elastic and viscoelastic interface crack are obtained.The transformation relation between local prism coordinate system and global coordinate system is developed.The 3D enriched elastic and viscoelastic interface crack element are established by enriching the transformed asymptotic displacement field into the conventional 8noded hexahedron element.The related formulas of enriched finite element method for 3D elastic and viscoelastic interface crack are deduced and the SERR for 3D viscoelastic interface crack is presented.Finally,the engineering applications of enriched finite element method for interface fracture are investigated.Three enriched finite element models,including solid rocket mortor grain with interface crack,a TBC structure with crack normal to and terminating at bi-material interface and a flat lap interface end,are constructed.By analyzing the results of the examples,some useful conclusions are obtained.In conclusion,some progress has been obtained in theory and applications of enriched finite element method for elastic and viscoelastic interface fracture problems.The methods and conclusion in this thesis would be available for the structural integrity analysis of solid rocket.