Estimating the intrinsic dissipation using the second harmonic of the temperature signal in tension-compression fatigue. part I: theory

An analytical framework was developed to correlate the intrinsic dissipation to the second harmonic of the temperature signal evaluated by means of the Fourier Transform. The theoretical model assumes without loss of generality total conversion of the input mechanical energy into heat. Elastic-perfectly plastic or elastic-plastic materials obeying a Ramberg-Osgood law are considered. For the sake of simplicity, analytical solution of the thermoelastic and plastic temperature evolutions are obtained in the case of uniform stress and temperature fields. It was found that the intrinsic dissipation is correlated to the second harmonic of the temperature signal by means of a parameter (the  parameter) that, in the case of an elastic-plastic material, depends on the cyclic hardening exponent n'.