Crack Paths 2012

Taking the loading frequency (20 kHz) and the maximumframe rate of the IR camera

(100 Hz) into account, the periodic thermoelastic sources are in this situation out of

reach. It is also assumed that the widthwise heat losses are negligible compared with the

lengthwise ones so that:

2

( )

θθ2

θ θ

1 ( x 2 k ) 2 1 1d 2 k d

(3)

ρC

(

t

τ

)

The last stage is to compute d1 estimating the different partial derivative operators,

using discrete, noisy thermosignals. Local spatiotemporal fitting was used to

approximate the temperature field by this function:

1 P x y tP ,x y ) (,2 2 ( , ) ( , )

(4)

a p p θ

Where Pi(x,y) are second-order polynomials in x and y. These polynomials are finally

identified using a least-squares method and then used to compute the intrinsic

dissipation.

R E S U L TASN DDISCUSSION

Thermal results

Fig. 2 shows the temperature recordings (for the different applied stresses) versus the

number of cycles. As previously published [9], the temperature has a sharp increase at

the beginning of the test and tends progressively towards an asymptotic if there is no

crack. Higher is the stress, higher is the temperature level.

90

120 M P a

80

110 M P a

70

( ° C )

60

100 M P a

50

90 M P a

40

80 M P a

30

-15 -10 -5

0 5 10 15

position (mm)

Figure. 2 Temperature evolution versus the number of cycles for differe t stres vels

Figure. 3 temperature evolution along

the length of specimen

688