Crack Paths 2006

Crack Propagation Criterion

Consider a crack whose tip is located at (x1, y1) as shown in Fig. 1(b). The tangential

VT near the crack tip was calculated from the stress intensity factor for

stress range

modeI, KI , and for modeII, KII, of the crack by

§ ·

sin

¨ ¸

(1)

I S

2 GT § · ¨ ¸ © ¹

II S

2 GT § · ¨ ¸ © ¹ © ¹ 2 GT

cos

cos

3

2 K

r

2 K

r

3

2

V

T

where GT is the change of the angle of crack extension from the current crack direction

and r is the distance from the current crack tip. The direction of the maximumtangential

stress direction is given by

§ ·

2

I I 1 1 t a n 8 2 4 K 4 K K GT § · ¨ ¸ ¨¸©¹ © ¹ I I

(2)

VT in one cycle is calculated from loading conditions. Three

The variation of

versions of the maximumtangential stress criterion are used for prediction of fatigue

crack propagation.

(1)

'VTmax

'VT max criterion assumes the direction of crack extension

criterion: This

coincident with the direction perpendicular to the maximumof the total range of the

tangential stress including the negative stress at the crack tip. The crack closure is

neglected. (2)

'V Tmax

criterion: For fatigue crack propagation, only the tensile part of the cyclic

stress can be effective The 'V Tmax

criterion assumes the direction of crack

propagation coincident with the direction perpendicular to the maximumof the positive

range of tangential stress at the crack tip.

(3)

'V *Tmax criterion: Under reverse loading, crack surfaces may come into contact

with each other. By taking into account of crack-face contact and neglecting the

frictional force, the minimumvalue of SIF was calculated by B F Mand is denoted by

K*min. For closed cracks, the modeII component K*IImin is not zero, while K*Imin= 0. The

range of the tangential stress and the crack direction are calculated by substituting the

ranges of stress intensity factors, 'KI* and 'KII*, for KI and KII in Eqs (1) and (2).

Simulation of Crack Propagation

The simulation of fatigue crack propagation was conducted through step-by-step

process. Figure 1(b) illustrates a crack propagated from a precrack by one step. The

crack tip is now located at point (x1, y1) and the angle of the crack with respect to the

T1. The SIF values of KI and KII were first calculated by BFM. The

precrack is

GT is determined from the three criteria described above.

direction of crack propagation

The deviation of the crack propagation direction is caused by the mode II stress

intensity factor, and the crack propagates straight under pure mode I loading. The

amount of crack extension for one step is determined by

( ) d c d N

(3)

'

c

u

N

where N = 1000 cycles. The value of dc/dN (m/cycle) is the power function of the

maximumstress intensity factor kImax (MPa) for a medium-carbon steel as