Issue 14

C.M. Sh b is the crack g angle.

aranaprabhu et depth of th

alii, Frattura ed e specimen,

Integrità Strutt w is the width

urale, 14 (2010) of the spec

27-35; DOI: 10 imen, t is the

.3221/IGF-ESIS.

14.03

ere p is the a cimen and 

wh spe

pplied force, is the loadin

thickness of

the

M I I

NIMUM PLA

STIC ZONE

RADIUS CR

ITERION

t is assume radius evalu

d in this stud ated from th

y that the di e von Mises

rection of cr yield criterio

ack initiation n. The crack

coincides w initiation can

ith the direct be determin

ion of minim ed by minimi

um plastic z zing r [4]:

one

2



 

r         

2 r

 

0



0



(8)

 



  adius of plas o 

 tic zone. Th

o  e von Mises  

ere r is the r owing form. ( xx   ere  y is the y gular stress f ressed in the  , I r K

be written in

yield criteria

for the three

dimensiona

l object can

the

Wh foll

2 ) (  ield stress in ield of equa following fo  1 , 4 II K    52 sin 2 16 II     ion angle is g yy yy   ral-purpose f n [10] under to as the C the dimensi 2]. The loadi –I) to study long the six y applying u ilar manner ENT ANALY

2 ) (

2 )    ion. As an ap in the abov zz xx 

2  proximate d e yield criter 2 6( xy yz  

2 ) 2 zx    etermination ion and solv

 2 y of the plasti e for the pla

  

(9) an substitute dius r . It can

zz

wh sin exp

uniaxial tens tions 1 to 3 rm.  2 2 3 1 4 I y K       6 sin 3 16   iven by Eq. inite elemen mixed mode ompact Mixe ons of the s ng of the sp the plastic d holes as show niaxial point to that demo SIS

the be

c zone, one c stic zone ra

15 2 4

9 2 4  

   

cos 2    

2 II K    

 cos 2 

2 2cos

2

sin





2

2sin     

I K K 

(10)

Th

e crack initiat

8, the relative

minimum m

ust have pos

itive circumf

erential stres

s.

F IN

ITE ELEM

T

he gene specime referred

t (FE) code loading has d Mode (CM pecimen con ecimen is app eformation ah n in Fig. 3. I loads F 1 to nstrated by R

ABAQUS is been conside M) specime sidered in th lied at variou ead of the c n the presen F 6 as shown ichard [11].

used in thi red in the pr n [4]. The s e analysis ar s angles (  ), rack-tip. The t FE analysis in the Fig.

s study. A C esent study. pecimen geo e similar to 0° (pure Mo load is appli the specimen 4 and estima

ompact Ten This kind of metry used i the one used de-II), 18°, 3 ed at various loading at v ted by Eqns

sile Shear (C specimen is n the analys in the work 6°, 54°, 72° angles  usin arious angles . 11-13 as gi

TS) also is is of and g a (  ) ven

sho Bo 90° loa is a bel

wn in Fig.2, rrego et al. [1 (pure Mode ding jig [10] a scertained b ow, in the sim

b c

    cos 2 1

  

F F F

sin









(11)

1

6

F F   F F 5 F  F

sin



(12)

2

b c

    cos 2 1

  

sin







(13)

4

3

n made on th al two-dimen ed in this ana ional elastic F

A s geo Th et a

eries of elast metry due to e loading and l . [12] and ar

ic finite elem the lack of l displacemen e clearly sho

ent calculatio oading symm t boundary c wn in Fig.4.

ns have bee etry. A typic onditions us Two-dimens

e CTS speci sional FE m lysis are simi E calculatio

men (Fig. 2) esh used in t lar to the one ns were perf

he full specim shown in Fi work of Borr eight noded

en g. 4. ego iso-

considering t he analysis is used in the ormed using

29