Crack Paths 2006

N U M E R I CEAVLA L U A T I OFNT H ESTRESSINTENSITFY A C T O R

Stress-Intensity Factor values for bending loading MX are calculated by applying the

finite element method and linear elastic fracture mechanics (LEFM). Because of

symmetry, only a quarter of the round bar has been modelled, using 20-node

isoparametric finite elements and one ring of quarter-point wedge finite elements in the

vicinity of the flaw front (Fig. 2). The SIF is computed at points A, L, J, N, C (Fig. 1b)

using the one-quarter point displacement method, and assuming the plane strain

condition along the whole crack front. Each point on the crack front is identified by its

dimensionless coordinate h / * ] ] (Fig. 1b).

Cracked zone

Figure 2. Three-dimensional finite element mesh.

The dimensionless SIF under ModeI is computed as follows:

K

X M , I

K

*M,IX

X M

V

(1a)

S

a

where

MD

V

S

; a crack depth at pointA (1b)

X M

X

32

SIF for bending;

X M , I K

3

As far as the numerical simulation of the crack growth is concerned, the most

significant zones along the crack front are the central zone (point A) and the external

zone (point C). Therefore, the SIFs for such two points are plotted in Fig. 3 against the

relative crack depth [, for D equal to -1.2, -1.0, -0.8, -0.6, -0.4, -0.2, 0.0.