One-Dimensional Non-Fourier Heat Conduction And Thermal Stress

Classical Fourier heat conduction law can describe most of the unsteady heat conduction problems in common condition. However, it can not be competent for all the cases. For the ultra-short pulse laser heating effect which cycle time is very short, super high frequency and exceptional heat conduction problem, the non-Fourier heat conduction law applied enhanced markedly. For example, it involves strong transient heat conduction problems, such as metal rapid solidification, a rocket launch heating, cryotherapy and laser surface heat treatment. Now the non-classic heat conduction research has gradually become hot. And, in practical projects many parts working under such moments, severe temperature cycle changes, probably cause thermal fatigue damage and destruction. Therefore, under the conditions of non-classic heat conduction, it is particularly urgent and important to solve stress intensity problem. This paper mainly studies the stress and temperature field of one-dimensional semi-infinite long flat in non-Fourier thermal circumstance, and the stress intensity problems of the flat with crack.In general, the material medium will lead to deformation and fracture because of the thermal fatigue crack. With the material technology improved and non-Fourier effect more widely applied, it is very necessary to research the thermal stress intensity. Few people combined non-Fourier effect with fracture mechanics to analyze the stress intensity questions of the corresponding temperature field.The main contents include:1) First we deduce the non-Fourier heat conduction equation, and establish the mathematical model in the one-dimensional semi-infinite of flat. Using the algorithm of separation of variables on temperature field distribution to solve the equation. Apply the matlab software to make temperature field distribution, and compare the temperature distribution of non-classic heat conduction with the classic conditions.2) Based on linear thermal elastic theory, we first establish the mathematical model of stress field in one dimensional semi-infinite of flat. Then we obtain the stress field in the basis of temperature field and constraint. Finally, we analyze the results.3) According to weight function method, we get the stress intensity factor of one dimensional semi-infinite of flat that has the surface cracks. We define the Non-Fourier stress intensity factor.