Issue 14

C.M

. Sharanaprabh

u et alii, Frattu

ra ed Integrità S

trutturale, 14 (2

010) 27-35; DO

I: 10.3221/IGF-E

SIS.14.03

ngles,  =0 o t ind that for s note that th . The nature wn in Fig. 7 arameters can r p , (ii) maxim om the crack are schemat

To the loa var var enc step (iii) zon

illustrate the contours are ding angles (  ious  remai ious loading laves shown s and loadin angle at wh e radius (MP

developmen superimpos ), the plastic ns almost sim angles is in in Fig. 7, Fig g angle (β), ich the maxi ZR) and (v)

t of the crack ed and show zone under ilar, with so good agreem . 8 and Fig. such as: (i) p mum extent angle at whic

-tip plastic z n in Fig. 9. F -goes a rotati me change in ent with the 9, several pla lastic zone si of plastic zo h MPZR occ

ones for vari rom this figu on. It is also the size and theoretical r stic-zone cha ze along the ne occurs,  , urs,  o . Thes

ous loading a re one can f interesting to orientation esults as sho racterizing p crack plane, measured fr e parameters

o 90 o and ap imilar applie e shape of th of growth of . From the r be estimate um plastic z plane, (iv) ically illustrat

plied load 10 d load at var e plastic zon plastic zone esults for pla d at various l one size, (r p minimum pla ed in Fig. 10.

kN, ious e at for stic oad ) max , stic

Figure 9 : Ty

pical shapes o  =0 o - 90 o un the plastic z nd Fig.13 re p estimated b be noted th is slightly l oth the an Fig. 11 illust for a particul for  =0 o (m es that of M of K eff , mode f the analytic so noted tha is slightly la e is less than e magnitude and (r p ) max ) agnitude of in Mode-I is one area ah dered to be m of θ with the the loading a s (  ) changes

f crack-tip pla der 10kN load one characte spectively. F y analytical at for variou arger than th alytical and rates that the ar magnitude ode-II). The ode-I. Thes -I loading ca al and the fin t for various rger than tha 2% of error of (r p ) max for indicate clea K eff . This an much lower ead of the c ore dangero loading angl ngle, β is ob from 0 o to 9

stic zones for .

Figure 10 : Sc

hematic repre characterizing

sentation of p parameters.

lastic zone

and  vs .  f K eff for var rticular value size along t nd that there be due to ip increases w the value of 0 o and 90 o f lastic zone r any mixed m r various loa astic zone si r effective st nd finite ele =90 o (mode de-I is much ude of K eff th n conclude f early fractur theoretical v repancy in th le at which t or the analyt

vs . K eff

Th Fig ma fac elem esti

e variation of .11, Fig.12 a gnitudes of r tors. It must ent analysis mation of b roximation. figure that, it is highest ich is 3.33 tim ticular value e variation o . 12. It is al ent analysis nd that ther icates that th de-II). ese results (r p the similar m the material aller plastic z ding is consi FEA values ues of θ with e size occur

rizing param ig. 11 show Eq. 10 and F s loading an at of the th FEA results plastic zone of K eff (for e difference in e results infe n lead to ma ite element loading ang t of the analy in estimatio a particular rly that the a alysis infers t than under rack-tip, the us than mod e, β is depict served. This 0 o as  is va

eters r p and ( s the variati EA are com gles (β), the eoretical valu . This discr size ahead o xample, 500 magnitudes r that, due to terial fracture values of (r p ) les (β), the tical values f n of both th value of K ef rea of plastic hat for the si Mode-II load mode-I load e-II. The var ed in Fig. 13. plot indicates ried from 0 o

r p

) max

or CTS speci ious loading s of effectiv he crack pla is less than the finite ith K eff . It i r p is least for or K eff = 500 adius ahead o ode or mode ding angles ( ze (r p ) max est ress intensity ment results. -I) and it is smaller than e energy abs rom this ana e, hence in alues of θ ar e analytical a he maximum ical and the F

men is show angles (  ). e stress inten ne for the fi 2% of erro element ana s also clear f  =90 o (mod is about 5 m f crack-tip f -II loading.  ) is depicte imated by fi factor. It is This figure highest for  that of mod orption capa lysis that, du fracture, Mo e compared w nd finite elem extent of pla EA results.

n in The sity nite r in lysis rom e-I) m, or a d in nite also also =0 o e-II city e to de-I ith ent stic It is

on of r p vs . pared for pa plastic zone es. It is fou epancy may f the crack-t MPa mm 1/2 ) of r p for  = minimum p earlier than max vs . K eff fo maximum pl or a particula e analytical a f is least for  zone in mo milar magnit ing. One ca ing leads to iation of the A small disc that the ang to 90 o both f

app this and wh par

Th Fig elem fou ind (mo

Th for of sm loa the val zon

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