Fatigue Crack Paths 2003

propagation rate was examined from the view points of the J-integral and the striation

spacing.

J - I N T E G REA SL T I M A T IFOONRM I X E D - M OCDREA C K

EnergyMethod

Considera circumferentially cracked cylindrical bar under an axial load, P, and torque,

T, as shown in Fig. 1(a). The J-integral value can be determined by the change of the

strain energy with crack extension under constant-displacement, u, or constant-twist

angle, 0 (Fig. 1(b)). The J-integral values of modeI under axial loading, J1, and of mode

111 under torsion, J11], were given by

J I : _” °L_P d u : _aUIL

(1)

27th 0 8a ,

2n'b 8a u

1 M 5 9;al d e b ;

(2)

27th 0 8a 9

27th 8a 9

where U1 and U111 are energy for modeI and III loadings, respectively.

In mixed-mode(I+III) loading, the J-integral value is determined by the change of

the total strain energy with crack extension. Since the total strain energy is the sum of

the mode I and III strain energies under constant-displacement and twist angle, the J

integral value of mixedmode, J1+1]1, was given by

1

8 U

J + I _

1+111

3

1 11

27th [ 8 a l fl

( )

Although J-integral values estimated from the energy method are exact, it is very

difficult to apply the energy methodto fatigue tests.

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Cracklength, a

(:1) Load vs. displacement or

(b) Strain energy vs. crack length

Torque vs. twist angle

Figure 1. J-integral estimation from the energy method.