Crack Paths 2012

The temperature evolution was recorded by the infrared camera FLIRSC5000 at the

frequencies ranging from 350 to 950 Hz and a minimumspatial resolution of 2·10-4m.

Calibration of the camera was made based on the standard calibration table.

During the experiment the grips and the specimen were shielded from the external

heat sources by a special screen. The surface of the specimens was polished in several

stages by the abrasive paper (at the final stage of polishing the grit size does not exceed

3 μm). Before starting the experiment, the polished surface was covered by a thin layer

of amorphous carbon.

T E M P E R A T UE RV OEL U T I O N S M O O TSHP E C I M ESNU R F A CUEN D E R

E L A S T I C Y C L ILCO A D I N G

Figure 2a presents the Fourier expansion of the temperature signal from the smooth

specimen surface. The second harmonic amplitude of order of 10-3 can be readily

separated from this data.

The nonlinear thermoelastic equation [7] is used to describe the second harmonic of

temperature evolution. Assuming that the elastic material constants are the function of

temperature we can write

ρ λ + ν − β

ρ μ + λ μ μ + λ μ + λ σ μ + ρ σ μ + λ

tcos + ω σ ω Δ ⎟ ⎟ ⎠ ⎞

⎜ ⎜ ⎝ ⎛

− =

c ) 2) 3 ( 2 5 . 1 ( c ) 2 3 ( 2 TLog 2 ρ μ + λ μ μ + λ μ + λ μ + ρλ μ + λ +

2 ω ω σ Δ T 0

t

T

0 2

2 c ) 2 3 (

c ) 2 ) 3 ( 2 5 . 1 (

2c 1

(1)

⎜ ⎜ ⎝ ⎛

⎟ ⎟ ⎠ ⎞

(

)

T 2

T

2

2

2

2

2

2

2

t2sin

where T λ , T μ is the first derivative of the Lameconstants with respect to temperature.

a)

b)

Figure 2. a) Spectra of the experimental and theoretical temperature signals (1 -solution

of the equation (1), 2 - experimental data).

b) second harmonic of the temperature spectrum versus the square of the stress

amplitude (for frequency of 1 Hz: 1 - solution of equation (1), 2 - experimental data; for

frequency of 5 Hz, 3 - solution of equation (1), 4 - experimental data).

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