13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- Figure 7. Circumferential stress distribution along radial axis From equation (1) and (8) it is possible to expressed the associated stress intensity factor Ktemp. We obtain after integration: at r r r at -r at r k Eq K R R R R R temp 4 Ei 1 4 20 exp 40 2 80 2 3/2 2 at r F at at r F at R R 4 , 4 7 , 2 1 , 4 3 , 4 1 4 7 10 4 , 4 3 , 2 1 , 4 1 , 4 1 3 4 7 10 2 2 2 1/4 2 2 2 1/4 at r F at r at r F at r R R R R 4 , 4 9 , 2 3 , 4 5 , 4 3 4 1 8 4 , 2 3 , 4 5 , 4 3 , 4 1 5 4 1 8 2 2 2 1/4 2 2 2 1/4 , (9) With the hypergeometric function ! , , ; , , ; 1 1 1 1 1 i z b b a a F a a b b z i i q i i p i i q p p q , where 1) ( 1)( 2) ( ( ) ) ( a i a a a a a i a i is the Pochhammer symbol and 0 1e d ( ) u u x x x the Euler Gamma function. The value of Ktemp, the thermal correction on the stress intensity factor, is estimated for a line heat source of 153Wm-1 and the typical material characteristics detailed in table 1. Eq. (9) gives a thermal correction on the stress intensity factor of -0.521MPa m. 2.2. A finite plate with a central through crack For being representative of a real crack propagating problem let us now consider a finite plate with a central through crack. In such case thermal losses due to convection on the specimen faces, the effect of the temperature gradient near the crack front and thus the thermal correction of the stress
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