Study On Two Case Of Crack Boundary Value Problems Of Thermoelastic Partial Differential Equations

The main aim of fracture mechanics is to study the mechanical and phys-ical mechanism of.crack propagation.It can provide theoretical support for the reliability of materials,service life of materials and others.In this thesis,the problems of thermoelastic fields in transversely isotropic material with a circular crack under uniform thermal flux and mechanical loads are inversti-gated.The crack-tip thermoelastic fields for transversely isotropic solids with infinite domain and finite thickness are investigated.The main conclusions are covered as follows:(1)Under uniform thermal flux and mechanical loads,.the thermoelas-tic fields' problems for a penny-shaped crack embedded in a transversely isotropic material is investigated.A new thermal medium crack model is pro-posed.The thermoelastic partial differential equations are transformed into a set of ordinary differential equations by using the Hankel integral transfor-mation.Then the ordinary differential equations are further transformed into dual integral equations.By solving the derived dual integral equations,the analytical solutions of physical quantities of the thermoelastic fields are ob-tained.Based on numerical calculation and analysis,the variations of stress intensity factors and thermal flux at crack surface are investigated.The re-sults show that the thermal conductivity inside the crack plays an important role the partial insulation coefficient,the change of the crack temperature and the thermal stress intensity factor.The new thermal medium crack model has more widely applicability compared with the known thermal medium crack models.(2)Based on the new thermal medium crack model,the thermoelas-tic fields' problems for a penny-shaped embedded in a transversely isotropic material with finite thickness is investigated,under uniform thermal flux and mechanical loads.Using the Hankel integral transform method,the ther-moelastic partial differential equations are transformed into dual integral e-quations.Due to the finite thickness of the considered material,some new auxiliary functions are introduced.Then the dual integral equations are trans-formed into the Fredholm integral equations of the second kind.The method of approximate function and the Picard successive approximation method are used to solving the derived Fredholm integral equations of the second kind,and some approximate solutions are obtained.We also make some error anal-ysis for the approximate solution.The practicability of the method has been verified by using numerical examples.In conclusion,the obtained results develop the existing boundary condi-tions of the thermal elastic partial differential equations,and they are more appropriate to simulate the thermal medium crack.Furthermore,they enrich the theory and method of the thermoelastic fracture mechanics.