Crack Paths 2006

T T ) ( ) ( T T t t c VV V V N

) ( 3

T T ) ( ) ( t c t c V V V ˜ (8)

J

T

1

2

c

,

T

T T

) ( 3

) ) ( ) ( (

) ) ( ) ( (

equal to the compressive and the tensile yield temperature-dependent

)T,( )T ( t c V V

with

stress of the material, respectively.

If the tensile strength and the compressive strength are equal to each other and

characterised by the same temperature dependence ( ) ( ) ( ) ( T T T y t c V V V , typical of

metal-like materials at ordinary or high temperatures), the yield condition becomes:

) (

) ( ) ( ) ( T T T y V

V V ˜

(9)

2 , 0 ) ( with 0 ) ( ) , ( 2 2 1 T T T T T J J I F t c t c V V N J N ) ) ( ) ( ( 3

3

that is, we obtain the classical VonMises criterion.

On the other hand, a brittle behaviour can be observed at very low temperatures: in

such a case, the tensile strength can be assumed to be much more lower than the

) ( T

), and the yield condition reduces to:

V

c V V

compressive one (i.e.

) ( ) ( T T y

t

(10)

with 0 ) ( 3 3 ) , ( 2 1 2 1 # ˜ T T J I J I F J N

3 1 ) (

which is a hydrostatic stress-dependent law (i.e. a particular case of the Drucker criterion).

For intermediate values of the temperature, a transition behaviour can be assumed

between the situations described by eqns (9) and eqns (10) (Fig.2).

temperature decreasing

principal stress, V

Figure 2. Generalised Drucker criterion.

E X P E R I M E N T EASLTS

Thin edge-cracked aluminium alloy plates have been subjected to mixed-mode loading at

different temperatures (below and above 0 ºC), by employing a universal test machine

under uniaxial displacement control conditions (Fig. 3). The material is characterised by

Q

the following mechanical and physical parameters:

E

,76GPa

,34.0

,330MPa

y V

O

5 º 1031.3 ˜

C

(Young modulus, Poisson coefficient, yield stress, thermal expansion

1