Investigation On Fracture Mechanics Of Non-homogeneous Materials Based On Conservational Integrals And Phase-field Fracture Model

Advanced non-homogeneous materials,represented by composite materials such as functionally graded materials and particulate-reinforced composites,have excellent designability and material properties compared with traditional materials.They have been widely used in national high-end equipment manufacturing such as aerospace and energy industries.Under complicated and volatile service environments and load conditions during applications,these materials are under threat from fracture failure,one of their most common failure modes.As a process of initial damage evolution,crack nucleation and crack propagation,their fracture failure behaviors still challenge existing fracture mechanics theories.Therefore,focusing on the mechanical challenges raised from the non-homogeneous characteristics of advanced materials in national high-end equipment manufacturing and developing new fracture mechanics models of these materials is of either scientific significance or engineering applied importance.Such fracture mechanics models should consider both the evolution of crack growth and the evaluation of crack-tip characteristics,and consequently,provide theoretical foundations and supports for the structural design and strength evaluation in national high-end equipment manufacturing.The main contents of this thesis include:Firstly,a domain-independent interaction integral method for three-dimensional cracks in non-homogeneous thermoelastic materials is studied.A domain-independent interaction integral method is established for curved cracks in general three-dimensional conditions to solve the crack-tip mixed-mode stress intensity factors under complex thermal-mechanical loads.A new auxiliary field is developed to deal with the complex thermal-mechanical interface in the material.The integral expression of this method does not include any derivatives of the thermoelastic material properties.The interfacial integral along the complex thermal-mechanical interface is also eliminated.This method provides important theoretical support to analyze three-dimensional non-homogeneous materials with discontinuous thermoelastic material properties.Several typical threedimensional numerical examples are investigated to verify the method and demonstrate the practical application capability of this method with the engineering background.Secondly,determinations of key input parameters for the phase-field fracture model is investigated.An experimentally validated calibration method is proposed to determine the phase-field input parameters.The two key parameters,fracture energy density gf and the length scale parameter lc,in the phase-field fracture model can be determined simultaneously based on benchmark experiments.Two epoxy resins,which are commonly utilized as matrices of fiber-reinforced composites,are used as examples to reproduce and predict the experimental results,verifying the effectiveness of this calibration method.Then,a generalized J-integral method of the phase-field fracture model for nonhomogeneous materials is developed to deal with the low accuracy of local characteristics on a diffused crack-tip.This method maintains the integral domain independence for both homogeneous and non-homogeneous materials.It can take advantage of the J-integral method in solving the characteristic parameters of a diffused crack-tip.This method is verified by a benchmark calculation example of mode I crack.Finally,the generalized J-integral method developed in previous contents is extended as a generalized Jk integral of the phase-field fracture model.A domain-independent generalized Jk integral method is proposed to separate mixed-mode stress intensity factors at the diffused crack-tip in the phase-field fracture model.Taking the functionally graded resin fracture test as an example,the phase-field fracture model is used to reproduce the crack propagation phenomenon in the test.The mixed-mode critical stress intensity factors at the diffused crack-tip are calculated.The effectiveness of this method is verified by comparison with the results given in the reference.