Issue 3

ed Integrità S

M. Zakeri et

al., Frattura

trutturale, 3

(2008) 2 - 10 θ ⎛ ⎞ ⎛ ⎜ ⎟ ⎜ ⎝ ⎠ ⎝ θ θ 1 - sin ⎡⎞ ⎛ 2 2

II K= sin 2πr

θ cos

3θ cos + 2

⎞ ⎛ ⎞ ⎟ ⎜ ⎟ ⎠ ⎝ ⎠ 3θ sin 2 ⎤ ⎞ ⎛ ⎞ ⎟ ⎜ ⎟⎥ ⎠ ⎝ ⎠ ⎦

( ) 1/2 O r

(2)

σ

e r and θ a tip (Fig. 1) he singular II stress in often called f the distanc expansion, r which are nated zone.

wher crack are t mode term, ent o this terms domi

re the polar . The two fi stresses, dep tensity fact the T-stres e r from the epresented usually n

coordinate rst terms in ending on ors K I and s, is constan crack tip. T by O(r 1/2 ), a eglected in

s centred at each expan the mode I K II . The sec t and indepe he next term re higher o the singula

the sion and ond nd- s of rder rity

yy

K

⎛ ⎜ ⎝

( ) 1/2 + O r

=

cos

σ

II

⎟ ⎠

⎜ ⎝

⎢ ⎣

xy

2

2

2πr

crack param rmined usin mental meth hod of phot ulating the cimens [e.g. n suggested photoelast ng the stress tal optic equ eral, a non- e unknown have been ch, the over a more ac d method th or more ges. The re erically, an ton-Raphso ares. Anoth se and Pat lysis which i ough the fu degree of lems, some e mode II. O gest that the e II condit e been obse ]. As describ sistency bet to neglectin cimens. main obje ence of T i isochromati g the exper owing, a bri resented. Th mental prog a mechanica sheets (thic kling in the d to make B tral cracks, l observed f erical predi validated by M). Althou ement with

eters K II

an

d T in these analytical, n the experim as been fre ameters in over, severa to determi terns. nsion (Eq. n isochroma tion is obta I , K II , and T o solve this stic techniqu sis [11]. Be he coordina ints on giv -linear equa g process i and the m technique based on licated. hods genera mode I and sults are no hand, the t rns are alw owever, as of the prev ous research eory and ex of T-stress s paper is t specimen, terns around hod of phot the analyti t steps of th cribed: crack sufficiently mm) to av ading phas specimens de II conditi s are finall , calculated s from finite rimental re re were so

equations c umerical, an ental techni quently use various cra l procedures ne K I , K II a 1) and the f tic fringe [1 ined in term . Different m equation a e is able to cause it is a tes r and θ en isochro tions are s nvolves bot ethod of is propose complex Fo te solutions mixed mod t satisfactor heoretical r ays symmet ymmetric fr ious experim es [2,13], th periments c in some mo o investigat and its effec the crack t oelasticity. I cal relations e performe s are create thick polyca oid problem e. This proc containing ons. y compared crack param element an sults had a me minor e

an be d ex- ques, d for cked have nd T unda- 1], in s of eth- mong pro- full- from matic olved h the least d by urier with e I/II y for esults ric in inges ents is in- an be de II e the ts on ip by n the [13] d ex- d, us- rbon- s of ess is sharp with eters alysis good rrors

The dete peri met calc spe bee from Usi men gen thre ods whi vide fiel four frin num New squ Nur ana Alth high prob pur sug mod hav [13 con due spe The pres the usin foll is p peri ing ate buc use cen The num are (FE agre

g different ods. Among oelasticity h crack par 9,10]. More and utilized ic fringe pat series expa ations for a linear equa parameters K suggested t - determini curate analy at can use t arbitrary po sultant non d the fittin n method er full-field terson [12], s more comp ll-field met accuracy for times the re n the other fringe patte ions [11]. H rved in some ed by previ ween the th g the effect ctive of thi n a mode II c fringe pat imental met ef review on en, differen ram are des l shock, in kness of 10 following lo razilian disk oaded in mo ringe pattern ctions. Also using result gh the expe FEM, the

F

igure 1. Crac

k tip coordina

tes and stress

components.

d on the cl s [1], the T- of mode I ition. Howe tical and nu lso exist in t can introdu II brittle fra onstant stre rack tip. The portant effe rials, whethe elastic-plas stress influe path. Presen the crack to sitive, the c effect is not nd Abbasi considerably re path in m ts the mode is the mos tip constrai ecimens exh d the crack fects the siz es inside th ntly by a re ode II can ing of mode idering this rack tip in m ate system a

assical defin stress exists and II, and ver, some p merical rese mode II prob ce significa cture. ss term T ac amounts of ct on the br r in predom tic cases. It nces the sta ce of the n grow along rack deviate restricted to [6] have sho the angle ode II as w II fracture to t important nt in constra ibiting smal tip, Ayatolla e and shap e plastic zo mote T-stres introduce c II brittle fra point, the el ode II can b s: θ 2 + cos 2 ⎡⎞ ⎛ ⎟ ⎜ ⎢ ⎠ ⎝ ⎣

ition of cra only in mod it vanishes ublished re arches indica lems [2-4], nt inaccurac ts over a larg this stress a ittle fracture inantly linea has been sho bility and d egative T-s its plane, w s from its i mode I con wn that the between the ell. Presence ughness. It parameter fo ined yieldin l to moderat hi et al. [8] e of the pl ne are also s. Thus, ign onsiderable cture. astic stress c e expressed

ck deforma e I or comb in pure mod sults of sev te that this t and ignorin ies in predic e distance f nd its sign h of enginee r elastic ma wn that the irection of f tress in mo hile when th nitial plane ditions. Aya T-stress can crack line of T-stress has been sh r describing g [7]. For m e scale yield have shown astic zone. influenced oring the T-t inaccuracie omponents in Cartesian

tion ina- e II eral erm g its ting rom ave ring teri- sign rac- de I e T [5]. tol- af- and also own the ode ing that The sig- erm s in near co-

Base mode tions cond analy can a effec mode The c the c an im mate als or of T- ture leads is po This lahi a fect fractu affec that T crack II sp aroun T af stress nifica in m study Cons the c ordin

II K -θ sin

⎤ ⎞ ⎛ ⎞ ⎟ ⎜ ⎟⎥ ⎠ ⎝ ⎠⎦

3θ cos + 2

⎛ ⎜ ⎝

( ) 1/2 T + O r

xx = σ

2

2πr

3