Crack Paths 2006

The NSIF approach was later applied to a large number of experimental data related

to fillet welded joints made of structural steels and aluminium alloy, see Figure 3 (from

Livieri and Lazzarin, 2005).

F R A C T U RM E C H A N IACPSP R O A (CfaiHlure from weld toe)

The stress intensity factor KI of a crack propagating in a zone affected by a stress

gradient can be evaluated taking advantage of Bueckner superposition principle and, in

particular, of Albrecht-Yamada’s simplified method (1977), which makes it possible to

determine the stress intensity factor as a function of the crack length a on the basis of a

unique linear elastic analysis of the uncracked component. As soon as the direction of

the propagating crack is knownor simply established a priori, the SIF of a through-the

thickness crack is (see Figure 1):

V S

a r

³

³ a0

«¬ª 2 a Y d r r a 2 a Y K S S S V T T a0 2 2 I

(5)

»¼º drdrdararcsin V˜¸¹·¨©§ T

The KI value depends on the crack dimension a and needs the distribution VT(r) to

be knownas well as its derivative with respect to radial distance r. Y is the shape factor,

initially equal to 1.122 (lateral crack in an infinite plate).

If the propagation of a fatigue crack is believed as to be due to VT, the crack will

grow along the direction T where such a component has its maximumvalue (according

to k1 and k2 mutual influence). In order to use Eq. (1), let us simplify the crack path as a

straight line. If such a direction coincides with the angle bisector (T = 0), the component

VT is independent of the sliding modeand turns out to be:

326.0

N

(6)

V

1 r

˜ K

T

1

2S

when the V-notch angle assumes its more typical value, i.e. 135 degrees. On the other

hand, if the direction T of propagation is perpendicular to the main plate surface (T =

22.5° when 2D=135°) the two contributions due to ModeI and ModeII should be taken

into account. Doing so, it is possible to write:

˜

(7)

V

r361.0 ˜

N2 K r 3 2 2 . 0 K ˜ ˜ 302.0 N1

T

326.0

By introducing, alternatively, Eq. (6) or Eq.(7) into Eq.(5), one obtains: