PSI - Issue 5

Ralf Urbanek et al. / Procedia Structural Integrity 5 (2017) 785–792 Author name / Structural Integrity Procedia 00 (2017) 000 – 000

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compression. These grips guarantee an accurate definition of the loading of the notched and unnotched specimen. All experiments were performed under fully reversed loading conditions (R=-1) with different loading frequencies. In the notched specimens with the pins cracks with a defined length were introduced. The crack length measurement was performed with a DC potential drop method. Detailed descriptions of the testing equipment are given by Bär and Volpp (Bär 2001).

2.2. Thermographic Measurements

The thermographic measurements accompanying the experiments are performed with a CEDIP Titanium HD 560 camera. The properties of the camera are shown in table 2.

Table 2. Camera properties Camera

Cedip Titanium HD 560

Detector material Number of pixel Spectral response

InSb

640 x 512 (full frame)

3.6 -5.6 µm

Focal length

50 mm with 12mm distance ring <25mK @ 25°C, (20mK typical)

NETD

Each single measurement consists of 990 frames. The frames with a size of 640 x 512 pixel are recorded with a frame rate of 99 Hz. The images have a spatial resolution of 34 µm/pixel and the noise level of each measurement according to the NETD is lower than 1.59 mK (Urbanek 2017). For lock-in analysis, the force signal is digitalized (14bit) and stored with each recorded frame by the thermographic camera.

2.3. Basic equations of thermo-elastic stress analysis

The simplest approach of measuring thermo-elastic stress bases on a simple linear equation proposed by Lord Thompson (Thompson 1853). Equation 1 shows the adopted version for uniaxial sinusoidal loading:   0 sin m A T t T K t     with 0 p K c     (1) The temperature change (temperature amplitude) is only dependent on the average temperature T m , the stress amplitude and the thermo-elastic constant K 0 . This analysis depends on three constraints given by Dulieu-Barton (Dulieu-Barton 1998):  the material behavior is linear elastic (I)  the temperature changes in the material occur adiabatically (II)  the relevant material properties are independent of the temperature (III) Wong et al (Wong 1988) discovered in their experiment a mean stress dependence of the temperature change in their experiments and formulated an extended version:

T

E

E

1

1

  





  

  

  

2   cos 2 t

T t

sin     t

( )



 







0

(2)

m

2 E T 

2 E T 

c

4



0 

p

In this extended version constrain (I) and (II) are still to be adhered. Equation (2) considers additionally the mean stress and the change of the Young’s modulus E with the temperature. All experiments in this paper were carried out under fully reversed condition therefore the mean stress σ m is always zero. Patterson et al. (Patterson 2008) proposed