Fatigue Crack Paths 2003

6e

(1+7t1)cos(1—7t1)0

cos(1+7t1)0

6 =7t1r7“_’a1

(3—7t1)cos(1—7t1)0 ‘I'Xbl(1—7\,1)

—COS(1+A1)9 +

1,

(1-P.,)sin(1-P.,)0

sin(1+71.1)0

(3)

1,-7.1

(I‘I'II1)COS(I_II1)9

0050-14109

+ 4 ( q

Xa, (3_II1)COS(I_I'L1)9 ‘I'Xc, — c O S G ‘ H M ) 9

q ’"

(1—Il1)Sin(1—Il1)9

sin<1+1100

Analogous expression were derived for mode11 stress components [21].

In Eqs 3 coefficient 7» is the well knownWilliams’ eigenvalue valid for sharp V

notches [29], while u is an additional exponent, essential to describe the stress field in

the vicinity of the blunt notch tip. Finally Xb, Xd and X6 are linearly dependent terms,

whose expressions were derived by applying the local boundary conditions on the notch

free edge [21]. W h e nthe tip radius is null, Eqs 3 are exact and coincide with the well

knownsolution for sharp V-shaped notches due to Williams [29].

v = const.

X

Figure 1: Auxiliary system of curvilinear

Figure 2: Coordinate system and symbols

coordinates (u, v).

used for the stress field components.

Table 1: Parameters in Eqs 3 for modeI stress distributions.

2 0 (degrees)

(1

A1

[[1

X111

X01

Xdi

(1)1

0

2.00

0.500 -0.500

1.00

4.00

0.00

2,00

45

1.750

0.505

-0.432

1.166

3.752

0.083

1,738

90

1.500

0.544 -.0345

1.841

2.506

0.105

1.080

135

1.25

0.674

-0.22

4.153

0.993

0.067

0,345

150

1.167

0.752

-0.162

6.362

0.614

0.041

0,165