Issue 40

Z. Zhang et alii, Frattura ed Integrità Strutturale, 40 (2017) 149-161; DOI: 10.3221/IGF-ESIS.40.13 151 Which could illustrate that there is a dynamic balance between the mechanical energy and thermal energy under adiabatic condition. The negative sign in this equation shows that the temperature would decrease when the material is under tension while the temperature would increase when the material is under compression. Thermo-elastic effect could not influence the average temperature rise on the sample surface during the fatigue process, it could only affect the temperature around the average temperature periodically, which is in accordance with the period of principle stress with a difference of the phase about 180 0 . Infrared thermography has been widely used in nondestructive testing in many materials and structures in recent years, with the advantage of large detecting area, high speed and non-contact when compared with other nondestructive testing method such as acoustic emission, magnetic-leakage nondestructive examination, X-ray and Eddy Current Testing. The theory of infrared nondestructive testing was firstly built by Carlomagno[21]. For an infinitely large plate ignoring the lateral heat flux diffusion, the heat conduction equation under the periodic heat flux of q = I 0 e j w t with only considering the heat transfer along the direction of thickness is shown below:       2 2 T T t x (4)      0 at  0 : jwt T x k I e x (5) In which, T is a function of temperature distribution in space and time, α = k /( ρc ) is the thermal diffusion coefficient, k is the thermal conductivity coefficient, w is angular frequency. Solving this PDE with the separation of variables, the temperature T could be expressed as a function of x and t :        0 , x jwt I T x t e e K (6) In which            2 / 1 1 / w jw a j j a , and   2 a w is the diffusion length, which is also known as the damping coefficient. This equation describes the heat conduction along x under Modulation frequency control. At least four thermographs in one period must be collected to obtain the phase φ and amplitude A, also Fourier analysis of the thermal image is necessary:           3 1 4 2 S S arctan S S (7)         2 2 3 1 4 2 A S S S S (8) Since the thermal properties are different with/without damage under the periodic heat load. Non-uniform heat flux would appear and could result in different temperature amplitudes and phases according to heat conduction theory. Thus the damage could be determined based on this difference. Infrared thermography experiment method could also monitor the temperature change in real time for structures under cyclic loading so as to find the high stress region and key region of local cumulative fatigue damage. Infrared thermography could provide efficient improvement or maintenance solutions to ensure the safety and reliability. Thus, it is significant to evaluate the safety of structure via Infrared thermography to monitor the local thermal evolution in real time, which not only could ensure the good functioning of structure but also could avoid or reduce the loss due to fatigue damage. Energy balance during the hysteresis loading proces Since the elasto-plastic deformation during the fatigue process is irreversible because of cumulative plastic strain energy in aspect of cumulative energy. The thermal energy dissipation evolution is similar with the evolution of temperature field with