PSI - Issue 2_B

Reza H. Talemi et al. / Procedia Structural Integrity 2 (2016) 3135–3142

3139

Reza H. Talemi et al. / Structural Integrity Procedia 00 (2016) 000–000

5

experimental temperature by applying the standard lock-in correlation. Krapez (1998) has introduced an approach which relies on the multiplication of signal s ( t ) by the in-phase and quadrature reference signal p f ( t ) = sin (2 π f t + ϕ r ) and q f ( t ) = cos (2 π f t + ϕ r ) and then on separate summation of these in SP f and SQ f :

N i = 1

N i = 1

SP f =

T exp ( t i ) p f ( t i ); SQ f =

T exp ( t i ) q f ( t i )

(3)

2 N

2 f

SP 2

T 1 =

f + SQ

(4)

where, N is number of images per lock-in period (lock-in period is taken as one fatigue cycle), t i is sampling interval which is 0.05 sec , since the acquisition frame rate is 20Hz, p f and q f are in-phase, sin( ω t ), and in-quadrature, cos( ω t ), lock-in correlation functions, respectively. In order to monitor the evaluation of temperature at bending root, two tests were performed under force and displacement controlled conditions. During the force controlled test ( F = 40kN) the evolution of temperature was monitored continuously. Fig. 3(a) shows the variation of temperature range versus numbers of cycles to failure in a logarithmic scale for the force controlled test. The data were extracted at nine points in the middle of bending area as depicted in Fig. 3(b). From Fig. 3(a) it can be noticed that the temperature ranges drop around 12 × 10 3 cycles. These temperature drops can be related to multiple micro cracks initiation onset. These interesting results reveal that the fatigue crack initiation lifetime is about 55% of total lifetime. Three distinguishable behaviours can be detected from logarithmic scale figure. It can be understood that, the temperature range of the surface rises non-linearly in the

0.4 ∆ [-]

0.5 ∆ [-]

phase 3

phase 1

phase 2

R1 R2 R3 R4 R5 R6 R7 R8 R9

R1 R2 R3 R4 R5 R6 R7 R8 R9

0.4

0.3

0.3

0.2

0.2

N i

R9 R8 R7 R6 R5 R4 R3 R2 R1

R9

R1

0.1

0.1

0

[cycles] ( a )

0

[cycles] ( b )

10 0

10 1

10 2

10 3

10 4

10 5

10 0

10 1

10 2

10 3

10 4

10 5

0.5 ∆

[-]

phase 1

Force controlled

0.4

0.3

Displacement controlled

0.2

phase 2

0.1

0

[cycles] ( c )

10 0

10 1

10 2

10 3

10 4

10 5

Fig. 3. variation of temperature range versus fatigue cycles to failure for (a) force and (b) displacement controlled experiments; (c) comparison of temperature range variation versus fatigue number of cycles between force and displacement control tests.