Issue 3

M. Zakeri et e curved sha ickness. Th D finite elem in a circula crack tip a technique o

al., Frattura pe of the c is latter effe ent model. r arc form; re generated n quadratic

ed Integrità S

trutturale, 3 k length fo ation is obta hromatic fri

(2008) 2 - 10 r central c ined. Solvin nges in pres

whic front also i crack singu apply node 2 M IS Base of an press

h could be r through the nvestigated front is ass lar element ing the qua elements. ATHEMA OCHROM d on the cla isochroma ed as [11]:

elated to th specimen th by using a 3 umed to be s around the rter point

rack ct is The and by 20-

racks, a qu g this equa ence of T-str

adratic alge tion, the loc ess is determ

braic us of ined

crac equ isoc as:

2 b b + ± S

34)(1 ( ) sin 2 θ

− −

(6)

r ′

=

S B

) 1(2

−

2 3 cos θ

2 sin θ

⎜ ⎝ ⎛= sin b

⎟ ⎠ ⎞

+ 2

θ

whe

re:

TICAL RE ATIC FRIN ssical conce tic fringe a

LATIONS GES pts of photo round the c

OF

s equation p tinuous alon le, in the ca ic fringes is ed loops, sy , similar to , 14]. A typi

redicts asym g the crack se of zero T obtained as mmetric ab the earlier a cal scheme o

metric fring edges (see -stress, the Eq.(7) that out direction nalytical re f these loop

es which ar Fig. 2-a). M locus of iso suggests a s θ = 0° an sults present s is shown in

e not ean- chro- set of d θ = ed in Fig.

Thi con whi mat clos 90° [11 2.b.

elasticity, lo rack tip is

cus ex-

Nf = h

(

3)

2τ

m

e τ m is max ringe order is the thic stress τ m is with this eq

imum in-pla and materia kness of spe related to uation [11]:

ne shear str l fringe valu cimen. Also the Cartesia

ess. N and f e, respectiv , the maxim n stress com

are ely, um po-

wher the f and h shear nents

2

II hK 1

2π Nf ⎡ ⎢ ⎣

⎤ ⎥ ⎦

( ) 2 4 - 3sin θ

r =

(7)

(

4)

2 xx ) = (σ - σ

2 ) + 4σ

2

(2τ

yy

xy

m

Subs math aroun prese param S = ⎛

tituting stres ematical eq d a mode I nted in ref. eters: 2 Nf hT ⎞ ⎟ ⎠ , B =

s terms from uation for I crack tip [13] and d

Eqs. (2,3) a fringe l is written in efining thre

in Eq. (4), oop develop a simple f e dimension

the ing orm less

II T πa K

, r ′

= r/2a

(

5)

⎜ ⎝

Figu tip:

re 2. Typical a) T≠0, b) T=

isochromatic 0.

fringes arou

nd a mode II

crack

In wh

ich a is the

crack lengt

h for edge c

racks and se

mi-

Figure 3

. Created sem

i-natural cra

cks: a) front v

iew, b) throu

gh the sheet th

ickness.

4