PSI - Issue 17

Jürgen Bär et al. / Procedia Structural Integrity 17 (2019) 308–315 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

309

2

Keywords: Aluminium Alloy, Copper, Thermography, Dissipated Energy, TSA, Fatigue

1. Introduction

During fatigue loading of metallic materials energy is dissipated leading to a heating of the specimen. This temperature increase can be used to determine the fatigue limit of the material (Luong (1995), La Rosa et al (2002), Meneghetti (2007), De Finis et al (2015)). Another method which is used to determine dissipated energies is the thermoelastic stimulated Lock-In-thermography. In this method, the measured temperature signal is dissected into sine waves coupled with the loading frequency using an incomplete Discrete Fourier Transformation (DFT). In a cyclic loaded material, a periodic change of the temperature is caused according to the thermoelastic effect (Thomson (1853)). For a specimen loaded with a stress amplitude  a at a loading frequency f L the resulting temperature at a mean temperature T m is given by Eq. (1): ( ) = − ∙ 0 ∙ ∙ ⁡(2 ∙ ) (1) The parameter K 0 represents the thermoelastic constant and can be calculated from the coefficient of thermal expansion  , the density  and the specific heat capacity c p of the material. The specimens have to be painted in order to enhance the thermal emissivity of the materials surface. For unknown thermal emissivity of the surface or unknown material parameters the thermoelastic constant K 0 in equation (1) can be replaced by a constant K c by calibrating the system with defined stress amplitudes (Urbanek and Bär (2017)). In a specimen loaded sinusoidal with a force the temperature change due to the thermoelastic effect results in a sine wave coupled with the loading frequency (E-Mode). According to Sakagami et al (2005) and Brémond (2007) dissipated energies are assigned to a sine wave with twice the loading frequency (D-Mode). The corresponding evaluation is based on an incomplete DFT. Urbanek and Bär (2017 and 2017a) extended the approach to higher harmonic frequencies, resulting in additional D1 and D2 modes: ( ) = + ∙ 2 ( ∙ + ) ⏟ ℎ − + ∙ 2 (2 ∙ + ) ⏟ ⁡2 − + ∑ ∙ 2 (( +2) ∙ + ) =1 ⏟ ℎ ℎ ⁡ℎ + ⏟( ) ሺʹሻ This DFT delivers beside the mean temperature T m an amplitude and a phase image for each part (E, D, D1, D2,...). With this dissection of the temperature signal the noise  (t) of the temperature signal can be eliminated, leading to a temperature resolution of a few mK in the resulting amplitude images. Previous investigations by Bär and Urbanek (2019) have shown that temperature changes caused by dissipated energies cannot be described with a sine function with the double loading frequency and therefore a quantitative determination based on a Lock-In evaluation is not possible. Therefore, the appearance of D-Mode amplitudes can just be used as a qualitative criterion for non-linear effects caused by dissipative energies. In this work a detailed examination of the temperature changes due to dissipative effects were undertaken and compared with the results from a DFT evaluation of the measured temperature signal.

2. Experimental Details

2.1. Material and Test Procedure

The experiments were performed on flat specimens of oxide free copper (OF-Cu) and the aluminium alloy AA7475 T761. The geometry of the specimens is shown in figure 1. The AA7475-specimens exhibit a reduced thickness in the testing section due to the limited force of the testing machine. All specimens were painted in the testing section with black paint to enhance the emissivity for infrared radiation.