Numerical Methods For Heat Flux Intensity Factor And Thermo-mechanical Coupling Problems

With the wide application of high temperature structural materials in aero-engine,gas turbine and super high speed aircraft thermal protection structures,their structural reliability and service life have been widely concerned.In the service or preparation process of high temperature structural materials,due to the mismatch of material parameters,cracks and other defects will appear in the structure.Near the crack tip,the heat flux and stress fields behave singularity,which are the main cause of failure and fracture of high temperature structural materials.Therefore,it is of great theoretical significance and application prospect to study the heat flux and stress singularity near the crack tip of high temperature structural materials.Firstly,this paper defines the J_T integral near the crack tip and proves the path independence of the J_T integral.On the one hand,based on the path independence of the J_T integral,the relationship between the J_T integral and the heat flux intensity factor(HFIF)near the crack tip is obtained.On the other hand,the J_T integral in the form of line integral is transformed into the equivalent domain integral by the Gauss divergence theorem.In order to simulate the heat flux singularity near the crack tip,the extended finite element method(XEFM)is presented to solve the heat conduction problem of cracked structures.In addition,based on eight-node quadrilateral element,a singular iso-parametric element for simulating heat flux singularity is presented.A numerical example is utilized to compare the XFEM with the singular iso-parametric element method.Based on the numerical simulation results,the path independence of J_T integral is verified.Furthermore,the HFIF calculated by the interaction integral is compared with the theoretical value in the literature,and the effectiveness of the interaction integral method for extracting HFIF is verified.At the same time,the interference between two cracks in homogeneous materials is simulated and studied by means of the method proposed in this paper.Secondly,considering the discontinuity of temperature across the crack surfaces,the singularity of heat flux near the crack tip and the discontinuity of material properties at the interface,the XFEM is proposed to solve the heat conduction problem of multilayer structures with interface cracks.The method of discretizing the temperature field and displacement field simultaneously by the XFEM to study the thermo-mechanical coupling problem with interfacial cracks is described.In the thermo-mechanical coupling analysis,the XFEM is used to analyze the heat conduction,and then the temperature field obtained by XFEM is utilized as the predefined field to solve the displacement field for thermo-mechanical coupling analysis.The correctness of the XFEM is verified by comparing the numerical simulation results of the XFEM with those from finite element method(FEM).Based on the XFEM,the effect of material parameter mismatch on the thermal stress intensity factor(TSIF)of multilayer structures with interfacial cracks is studied.For multilayer structures with interfacial cracks,J_T integral is defined near the interfacial crack tip.The path independence of J_T integral is proved theoretically.The relationship between J_T integral and HFIF near the interfacial crack tip is obtained.The interaction integral for calculating HFIF near the interfacial crack tip is established.The proposed XFEM is utilized to simulate the heat conduction problem with interfacial cracks.The numerical results verify the path independence of J_T integral near the interfacial crack tip and the effectiveness of the interaction integral for calculating the HFIF.The effect of geometric and material parameters on the HFIF of interfacial cracks in the two-layer and multi-layer structure models are simulated by the XFEM.Finally,in fact,considering that the high temperature structural materials are often subjected to transient heat flux loads,the transient HFIF is defined for the transient singular heat flux near the crack tip.The transient J_T integral is given and the path independence of the transient J_T integral is proved.By introducing the known auxiliary temperature field,the interaction integral for extracting the transient HFIF is established,and the computation scheme for calculating the transient HFIF is also given.The path independence of the transient J_T integral and the effectiveness of the interaction integral for computing the transient HFIF are verified by numerical examples.The variation of transient HFIF near the crack tip of a multi-cracked structure under transient heat flux load is simulated and studied.The problems of multilayer structure with interfacial cracks and homogeneous materials with cracks are also considered.The research results of this paper provide a theoretical foundation for the study of thermo-mechanical coupling and interfacial crack propagation in high temperature structural materials.