Crack Paths 2009

I

I

II h h W F h ! "

(1)

=%

II

h

# '

$ & (

!

"

In the present case, the crack is composed by two straight lines, thereofore the SIFs

components can be obtained by splitting the integration of the W F and stress

components into two parts:

KI = hI!a,",a0,#,!$() %!M",!$()+hI&a,",a0,#,!$()%&M",!$() '(

)*d!$

,

+

+1

+ hI!a,",a0,#,!$()%!K",#,a,!$()+hI&a,",a0,#,!$()%&K",#,a,!$()'()*d!$ ,

(2a)

+2

KI = hII!a,",a0,#,!$()%!M ",!$()+hII&a,",a0,#,!$()%&M",!$() '(

)*d!$

,

+

+

,

(2b)

1

+ hII! a,",a0,#,!$()%!K",#,a,!$()+ hII&a,",a0,#,!$()%&K",#,a,!$() '(

)*d!$

+2

! is the curvilinear coordinate along the crack path, hMµ and hMµ (with M = I

where d !

or II and µ = σ or τ) represent the W Fcomponents, while !M, !M and !K , !K are the

normal and shear nominal stress distributions acting on the main and on the kinked

crack, respectively. The nominal stress is usually defined as the stress acting along the

segment of the crack location in the equivalent uncracked body, subjected to the same

constraint and loading conditions of the cracked body.

Figure 1. Schematic representation of the problem.

The diagonal W F components hIσand hIIτ represent the direct effect, i.e. the

contribution on KI produced by ! and the contribution on KII produced by ! respectively, while the off-diagonal components hIIσand hIτ represent the coupling

effect, i.e. the contribution on KII produced by ! and on KI by ! respectively. When

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