Issue 35

G. Meneghetti et alii, Frattura ed Integrità Strutturale, 35 (2016) 172-181; DOI: 10.3221/IGF-ESIS.35.20

0°

(a)

(b)

0°

10 4 4·10 4 h [W/m 2 ]

10 4 5·10 4 h [W/m 2 ]

45°

-45°

45°

-45°

 K=26.3 MPa·m 0.5  K=28.4 MPa·m 0.5  K=35.6 MPa·m 0.5  K=49.6 MPa·m 0.5  K=64.1 MPa·m 0.5 V_3 specimen

 K=31.5 MPa·m 0.5  K=36.7 MPa·m 0.5  K=78.7 MPa·m 0.5  K=98.0 MPa·m 0.5 V_4 specimen

10 3

10 3

-90°

90°

10 2

-90°

90°

10 2

-135°

135°

Crack

-135°

135°

Crack

180°

180°

0°

(c)

0°

(d)

10 3 2·10 3 q [J/(m 2 ·cycle)]

h [W/m 2 ]

6·10 4

-45°

45°

45°

-45°

10 4

10 2

 K=30.3 MPa·m 0.5  K=36.9 MPa·m 0.5  K=45.7 MPa·m 0.5  K=53.2 MPa·m 0.5  K=66.9 MPa·m 0.5 V_5 specimen

 K=30.3 MPa·m 0.5  K=36.9 MPa·m 0.5  K=45.7 MPa·m 0.5  K=53.2 MPa·m 0.5  K=66.9 MPa·m 0.5 V_5 specimen

90°

10

-90°

10 3

90°

-90°

-135°

Crack

135°

135°

-135°

Crack

180°

180°

Figure 5 : Distribution of the thermal flux h along the boundary of the control volume for different  angles for (a) V_3, (b) V_4 (c) V_5 specimen and (d) and corresponding energy flux per cycle q of V_5 specimen.

C OMPARISON BETWEEN EXPERIMENTAL AND THEORETICAL TEMPERATURES CLOSE TO THE CRACK TIP

A

n analytical solution is available in order to evaluate the time-dependent temperature field in the case of a homogeneous and isotropic infinite plate with a time-independent heat generation h L distributed along a line in the thickness direction [18]. At the time t=0 when the heat generation starts, the temperature is supposed homogeneous and equal to T 0. Between time t=0 and t, the temperature variation  T(r,t)=T(r,t)-T 0 can be expressed by Eq. (11) [18]:

     

    

2

h

r

( , )    L T r t

(11)

Ei





4





t

4

 



c

x  

  

 



where Ei is the integral exponential function given by . Since the major source of heat power is the cyclic plastic zone, the linear heat generation h L according to [3]. Fig. 6a shows the cyclic plastic zone idealised as a circle having radius r p u e u du   Ei  and x= 2 4 r t c   

 

was applied in its centre, . According to Irwin [20], the

cyclic plastic zone radius in the plane stress condition is equal to:

2



 

K

1 2 2  

  

r

(12)



'      ,02 p

p

178