Crack Paths 2006

contact ellipse, is placed (Fig. 6.a). As discussed also in a previous study [20], referring to the

crack centre, the crack positions reported in Table 2 are analysed; that is, the crack has been

moved along the x-axis and the y-axis laying on a plane parallel to the free surface to a depth

equal to 0.25 m m(corresponding to the position where the shear stress is maximum). In Figure

6.a, the crack in the four extreme positions (corresponding to an eccentricity on x-axis equal to

±1.0 m mand on y-axis equal to ± 10 m m )is reported. Figure 6.a also shows that all the crack positions have been analyzed considering the meshing step from the 19th through 31st; in fact, it

has been verified that, for such crack positions, all the remaining loading steps have no

significant influence on the SIF value. It is finally convenient to define four points on the crack

front (Fig 6.b): points A and B are aligned with the x-axis; points C and D are aligned with the

y-axis. These points are the ones considered for the stress intensity factor calculation. Making a

conservative assumption, contact between crack faces is simulated as frictionless.

a – Crack position on the tooth surface.

b – Calculation points along the front.

Figure 6. Schematization used in the analysis and definition of the main parameters.

Table 2. Positions of the crack considered in the analysis.

CrackCenter Coordinate

CrackCenter Coordinate

x [mm] y [mm] z [mm]

x [mm] y [mm] z [mm]

y-10

x-1.0

-1.00

0.00

0.25

0.00 -10.00 0.25

y-8

x-0.8

-0.80

0.00

0.25

0.00 -8.00

0.25

y-6

x-0.6

-0.60

0.00

0.25

0.00 -6.00

0.25

y-4

x-0.4

-0.40

0.00

0.25

0.00 -4.00

0.25

y-2

x-0.2

-0.20

0.00

0.25

0.00 -2.00

0.25

x 0.0

0.00

0.00

0.25

y 0

0.00

0.00

0.25

y+2

x+0.2

0.20

0.00

0.25

0.00

2.00

0.25

y+4

x+0.4

0.40

0.00

0.25

0.00

4.00

0.25

y+6

x+0.6

0.60

0.00

0.25

0.00

6.00

0.25

y+8

x+0.8

0.80

0.00

0.25

0.00

8.00

0.25

x+1.0

1.00

0.00

0.25

y+10

0.00 10.00 0.25

3.1 Stress intensity factors

In this paper, being the aim to investigate the crack growth mechanisms, just a brief overview

about that SIF results is provided; a more detailed description about this issue is kept in [20].

Due to the fact that the contact between the mating surfaces is simulated as frictionless, no

surface traction loads are present and consequently the SIF for modeI is always null.

Onthe other hand, KII values shown significant fluctuation when the load position is varying:

Figure 7.a reports, referring to point A, the trend of KII for the crack in position (x = 0; y = 0)

and Figure 7.b summarizes the trend of KII versus the crack positions along the x-axis in the

same point. It is simple to figure out that the value of KII remains quite stable around 7

MPa¥m.The trends of KII in point B has been verified to be very similar to the ones reported for

point A. Value of K for modeIII in points A and B has been found to be always lower than 0.2