Fatigue Crack Paths 2003

wherefor simplicity it is assumedthat R0 = RGO/RG.

The damage growth for stress states lying within the domain boundedby the failure

surface Rfa= 1 and the damage initiation surface Rfo-o = 1 is specified by the damage

evolution rule

dcon = A,, [R‘’ _R° J dR"

(20)

1_Ro 1_R0’

where A and n are material parameters. The effective failure function increment dRG is

specified by the following relation

.

dR; for dR; > 0 and R7 > R0

(1R, =

*

(21)

0 f o r d R U § 0 o r R 6 § R O

and

M 2 = aide,+ °R6 d1,

(22)

80,,

81,,

A n alternative specification of increment dRG can be expressed in the following form

+ 4 d +ri d f

23

n a r m nl a T n 2 n2

( )

where effective stress increments (for RcS > R0) are specified by the relations

d6" = don for don 2 0 and G" 2 0

(24)

d6” =0 for d6n<0anGdn < 0

dim. = drn, for t'm-dt'm~ 2 0

and

(25)

dt2 = 0 for t'mdt'm- < 0

Thedamageparameteris assumedto affect both 6c, Tc, so that

6 c( C 0 ) : G : ( l _ a ) n )p7

T c ( C 0 ) : T : ( l)_p a ) n

where G: and t‘: are failure stresses in tension and shear for the undamaged material, p

is material parameter.

The present model is conceptually similar to the cohesive crack model, as the

existence of damage zone preceding the crack front is assumed. However, the analysis

is fully based on linear elastic stress distribution and no decohesive displacement is