PSI - Issue 5

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

788

4

a new approach assuming that the mean stress is the sum of residual stress and applied stress. In the fully reverse loading condition the mean stress is only influenced by residual stress hence plasticity. Despite the results of Patterson were not as clearly as expected, this approach is taken to investigate the influence of plasticity in front of a crack in combination with 2f-methode for identifying the plastic zone mentioned by Sakagami (Sakagami 2005).

2.4. Lock-In- filtering and evaluation types of stress pattern

The Lock-In method bases on the assumption that all effects measured on a specimen stressed with a fixed loading frequency f L are connect to this frequency or higher harmonics. Therefore, a discrete Fourier transformation (dft) of the temperature signal of each pixel within a recorded sequence is performed with self-written program described by Urbanek and Bär (Urbanek 2017). The analysis leads to spectrum of frequencies. Only the frequencies referring to the loading frequency are accounted; all other frequencies are contributed to noise. Equation 3 shows the sorted result of the dft of the temperature signal of a single pixel:

N

 k 1  max

 

  t













i2 f t

i2 2f t

i2 (k 2)f t

  

  

   

T t

T

T e

D T e

D T e

(3)



 

 



 

L

E

L

D

L

k

m

E

k

average Temperatur

 thermo elastic

 dissipativ 2f part

Noise

L

higher harmonics

The dft transformation leads to amplitude images (T m , T E , T D, T D1 etc.) for each frequency showing the temperature amplitude and corresponding phase images (φ E , φ D, φ D1 etc.) showing the phase shift between the loading signal and the temperature signal. From the amplitude images of the thermo-elastic part stress images can be calculated according to equation 4:

1 T K T

(4)

  

E

A

0 m

Figure 2 shows E-stress images of an unnotched and a notched specimen with a crack. The unnotched specimen shows a homogenous color indicating the same stress within the specimen, in the cracked specimen the stress field in front of the crack tip is visible. Furthermore, two tools for a quantification of the results are displayed. Type 1 is a square box which allows to determine the mean, minimum and maximum values within an area, the line in figure 2b allows to determine profiles of the measured values.

a)

b)

Fig. 2. a) unnotched specimen with evaluation square b) specimen with crack and evaluation line in the ligament.