Crack Paths 2012

based on the repeated tensile plasticity range, and the effective stress intensity range,

respectively. W eshall present a brief account of these methods below.

Crack growth model based on KRP

The main procedure of the simulation is summarized as follows;

1. calculate the stress intensity range at points A and B of the elliptical crack subjected

to repeated tensile loading,

2. near-tip plastic deformation including crack opening, closure, and repeated tensile

plasticity are analyzed by the strip-yielding model subjected to the k-field as the

far-field boundary condition at the crack front points A and B6),

3. the repeated tensile plasticity range of stress intensity, 'KRP, is used as the measure

of the size of repeated plasticity region at each crack tip in order to calculate the

crack growth rate7,

8)

4. crack tips A and B are moved to the extended crack tip so as to form a next

embedded elliptical crack, and go back to step1 to continue the simulation.

Toyosada et al.

7, 8) defined a load, at which the tensile yielding begins to develop

ahead of a crack tip under a reloading process. The stress intensity factor corresponding

to this load level is defined as kRP, and the effective stress intensity range, KRP, is

defined by

(1)

, R P R P k k K '

max

where kmax corresponds to the stress intensity factor at the maximumload. The crack

growth law based on KRP is expressed by

. ) ( / R P m K C d N d a '

(2)

With regard to the mechanism of fatigue crack growth during each load cycle, there still

exist several unknown phenomena. The possible difference of residual plastic wake of a

fatigue crack surface is illustrated in Fig.5, in which if a fatigue crack extends during

the unloading process, the crack tip may fully be stretched with its crack opening

displacement denoted by x )(v(left-hand side of the figure), while if it occurs during

min

the loading process, it maybe minimized as denoted by

) ~c ;( 'c (rixght-hand vside

min

of the figure). Possible plastic deformation during the crack growth may be assumed

somewhere between these two extremes and expressed by;

;(

'

'

(3)

,1 N N N c c x v x v c c x v 0 ) , ~ ;( ) ( ) 1 ( ) min min min

J J D

N, is approximated by

where the parameter,

°¯°® 1 1 ) / ( f o r ) / ( n p i e n p i e J J D

N

! , 1 ) / ( f o r n p i e J J D

(4)

The quantity,

e is the previously formed maximumplastic zone size, while pi is the

plastic zone size generated by the current maximumload, and and n are the material

186