PSI - Issue 18

Vedernikova A. et al. / Procedia Structural Integrity 18 (2019) 639–644 Author name / Structural Integrity Procedia 00 (2019) 000–000

641

3

3. Heat source estimate from infrared thermography measures The computation of heat sources induced by irreversibility of deformation mechanisms a heat conduction equation (1) is applied to infrared thermography data:

2

2

2

  

  

( T x, y, z,t

)

( T x, y, z,t

)

( T x, y, z,t

)

( T x, y, z,t

)









(1)

( Q x, y, z,t k  )

c









2

2

2

t

x

y

z









where ( ) T x, y, z,t – temperature field,  – mass density, c – specific heat, k – heat conductivity, ( sources field, x, y, z – coordinates, t – time. Infrared camera allows registering a two-dimensional representation of the object surface temperature distribution without control through the specimen thickness. Enough thin specimens were used in experimental investigations that makes possible to assume that the temperature distribution through the specimen thickness is homogeneous. Equation (1) averaged on volume is used for estimation of integral power of the heat source. A standard averaging procedure was conducted. The difference '( ) t  between the average temperature and the initial temperature of specimen in the thermal equilibrium with the environment 0 T is defined as: ) Q x, y, z,t – heat

/ 2 / 2 / 2    / 2 / 2 / 2 a b h a b h   

'( ) 1 t 

( ( T x, y, z,t T dxdydz  ) )

(t)   

T



(2)

0

0

V

where a , b , h are length, width and thickness of the specimen, respectively, V is volume. Here, the boundary conditions are expressed as follows:

( , , z, )

( , , z, )

T x y t

T x y t





 

x

x





2 a

2 a

x

x





(3)

/ 2

a

g

( , , z, )

T x y t





( ( , , z, ) T x y t T dxdydz  ) ,

k





x

0

x

a



x a 

/ 2

a



2

where x g means the heat exchange coefficient between the specimen and the environment on the corresponding edge of the specimen. Therefore, considering expressions (2) and boundary conditions (3), integration of equation (1) allows obtaining relation (4) for estimate of heat source field caused by irreversible deformation:

(t) t      

( )

( ( ) V t T 

),

S t

mc



(4)

0

where  is the average temperature of the examined surface, m is the mass of the area where the average temperature is taken from, ( ) S t is the heat sources field (W),  is the material parameter that determines heat losses, associated with the heat exchange between the sample surfaces and the surroundings. Fig. 2a shows the typical infrared imaging and mean temperature variations of the specimen surface during of test on the example of titanium alloy Grade 2. At the beginning test, experience an initial decrease in surface temperature due to the thermoelastic effect. When the thermoplastic effect prevails, the temperature of the specimen to increase up until the destruction. Dependence of the heat source field on test time for specimens from titanium alloys Grade 2 and Ti-1Al-1Mn was estimated according equation (4) based on temperature versus time data recorded during the mechanical test. The