Issue 53

P. Ferro et alii, Frattura ed Integrità Strutturale, 53 (2020) 252-284; DOI: 10.3221/IGF-ESIS.53.21

The effective thermal conductivity may be defined as [75]:

  

  

 N 2

1 1  L

k e  k g

0.5ln(1  L )  ln(1  L ) 

 1

(22)

where N is the coordination number and L is the ratio of a constant and power particle diameter. The constant value depends on the shielding gas type; for argon, it is equal to 5.4 x 10-4 m-1 while k g is given by the following formula [76]:

 0.1125 T

 1.33  10  3 T  1.453  10  7 T 1.5

k Ar 

(23)

In [77-79] the effective thermal powder conductivity (k e ) is defined as:

      

      

      

      

  

    1  

  

    1

 1  1     1 

 k r k g

k e k g

k s k g

 k r k g

2

1

(24)

ln

k g k s

k g k s

1 

1 

where  is the porosity (say, 0.4) and k r is the thermal conductivity which is changed by radiation:

3 D

k r  4F  B T

(25)

r

In Eqn. (25) F is the apparent coefficient, usually 1/3, D r is particle diameter and  B is the Stefan-Boltzmann constant. In order to simulate the transformation from powder to consolidated alloy, the thermal conductivity is changed when the powder reaches its melting temperature (T m ). In [80] the following relations were used:

   

0.01  k s , T  T m k s , T  T m

k e 

(26)

Ning et al. [81] used a simplified definition for the powder density and thermal conductivity:

 

 e  (1   )

(27)

 

k e  (1   )

(28)

where γ and β are coefficients that can be taken as 1 [82]. The latent heat can be taken into account by the equivalent capacity method [80,83]:



C s , T  T s C s  2L g (T  T s )/(T l  T s ) C s  2L v (T  T l )/(T v  T l )

 

2 , T 2 , T

C e 

s  T  T l l  T  T v

(29)

  

where T l , T s and T v are the liquidus, solidus and vaporization temperatures, respectively, and L g and L v are the latent heat (J/K) of fusion and vaporization. In their work, Xiang et al. [84] distinguished also the emissivity of the powder layer from that of the dense material as follows:

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