PSI - Issue 2_A

Daiki Shiozawa et al. / Procedia Structural Integrity 2 (2016) 2091–2096 Author name / Structural Integrity Procedia 00 (2016) 000–000

2092

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increasing attention in various industrial fields (Luong, 1992). The analysis of fatigue with infrared thermography has been performed considering different approaches, such as (1) the measurement of the superficial temperature (Luong,1992), (2) the evaluation of the thermal heat sources (dissipative source envaluation) (Krapez, 2000) and (3) the evaluation of the thermoelastic source and phase thermoelastic signal (Palumbo and Galietti, (2014)). Only few works have proposed an automatic and iterative estimation procedure based on the measurement results with infrared thermography by Luong (1995, 1998) and Cura (2005). In this study, the new fatigue limit estimation scheme is proposed. Fatigue limit of steels is affected by plastic forming process. The new fatigue limit estimation scheme is applied to the pre-strained specimen for discussing the effectiveness of this scheme.

Nomenclature  a

Stress amplitude Fatigue limit

 w  ’ w  ” w  T E  T D

Fatigue limit estimation by conventional method Fatigue limit estimation by the new estimation method

Thermoelastic temperature change

Temperature change due to the energy dissipation

Dissipated energy

q

 Phase difference between the temperature change due to the energy dissipation and the wave with the double frequency of thermoelastic temperature change

2. Dissipated energy and fatigue limit estimation Temperature rise is observed under compressive stress, and temperature fall is observed under tensile stress, as shown in Fig. 1. This phenomenon is called as thermoelastic effect. Thermoelastic temperature change Δ T E is formulated by thrmoelastic coefficient k , absolute temperature T , and sum of principal stresses Δσ, as shown in the following equation. Δ T E = − k T Δσ (1) The thermo-elastic temperature change Δ T E is a reversible phenomenon. In the actual case, temperature rise due to irreversible energy dissipation Δ T D occurs at the maximum tensile stress and at the maximum compressive stress. Thus, the measured temperature change T ( t ) on the surface includes Δ T E and Δ T D . Therefore, temperature change due to dissipated energy Δ T D can be obtained as the component having double frequency of the load signal using basically Fourier analysis. Dissipated energy q is calculated from Δ T D , density  and specific heat c of material.

Fig. 1 Schematic illustration of temperature change due to the thermoelasticity and energy dissipation

Fig. 2 Change of dissipated energy and the fatigue limit estimation based on dissipated energy.