| This article analyses mostly plastic dissipated energy at circular crack tips under gigacyclic vibrating fatigue.By using ANSYS system, a non standard specimen which includes a small size circular crack (12μm to 1mm of diameter) is analyzed. The specimen vibrates at 20kHz and its fatigue life is in gigacycle range. The stress intensity factor (SIF) calculation model is respect to the test condition, i.e. under vibration. A generic formula for any metal has been obtained to determine K I vs. crack size, position, vibration amplitude under certain boundary conditios and size of singular elements at crack tip. Calculation of a crack of small size (12μm) has been realized successfully by using ANSYS while ANSYS limitation is 120μm. Under ideal plastic material supposition, the expression of plastic volume and theoretic strain on cycle loads are calculated. Plastic dissipated energy under fatigue, considered as heat observed during testing, is derived theoretically. The plastic dissipated energy keeps in the same order of experiment equipment power, which explains that calculation is reasonanble. This analysis will be useful to further researches on heat generated by the crack and further uses an infrared camera to study fatigue crack initiation mechanism.
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