Issue 14

M. N. James e re there is a l tical values o by the equat K 2 /(1 – ν 2 )E stress intens associated d Plasticity is pparent crack (perhaps < 0 rate on the en sub-critic – K min . With diction und ) questions ation of phe ould seem li ack tip durin boundary c enclave surr ility-induced ratio ν = 0.5 CJP model rding stress nsity K S . An full-field pho stergaard or nting the CJ ion for 2-term 3 2 Bz z C    1 2     D, while the 3 2 Bz z    D and D+E contact stre ) and a comp his provides erpendicular   ' z  o Eq. 4 to gi 3 2 z z  A (A+B = 0

t alii, Frattura e imited extent f stress inten ion G = K 2 / . ity approach ecoupling of primarily con length), stre .6) of the yie basis that if al crack grow the developm er cyclic load remain as to nomena tha kely to assist g fatigue crac onditions tha ounding the stresses at , whilst in el [12, 14] for intensity K R alysis of its toelastic dat Williams [15] P model is gi s, K and T 0 z

d Integrità Strut of crack tip sity factor an E where E have proven local crack t sidered throu ss state and ld strength o critical crac th under cyc ent of fractu ing has beco why, and ho t explicitly a in resolving k growth [10 t would be crack. Thes the elastic-pl astic deform crack tip str which captu capability in a, indicate a l equations. ven below al stress is:

turale, 14 (2010 plasticity (wh d strain ener is the elastic very useful i ip microstru gh its influe through the s f the alloy. k growth un lic loading m re mechanic me the prim w, an elastic rise from pl a number o , 11]. The ex imposed on e arise from astic interfac ation ν ≈ 0.3 esses leads t res wake con characterisin ower fitting ong with 2-t

) 5-16; DOI: 10 ich arises fro gy release ra modulus of n characteris cture and pla nces on speci tipulation th Paris [8] ext der monoto ay be gover s into a matu e applicatio approach to astic deform f controversi planation ad the applied crack wake c e. Plastic d and plastici o a modified tact influenc g near-tip fri error than eit erm and 4-te

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cra stre as pla Lin in c eve (via lev the gov of are inte Ex abl Sat wit wo pla pla con stre driv cra dif T -s Th the

cked body is ss concentra recognised in ne strain this ear elastic fr racked and s nts from the the Irwin pl els should be K concept erned by the the applied st a of fatigue nsity approa tremely inter e to provide isfactory ans h plasticity-in rk on this is stic ‘inclusion sticity-induce stant volum sses must ex ing crack gr ck tip, and a ference in pri tress) or four e stress varia Williams sol Nf h  ere the two u ne. The 4-te Nf h  ere the four u Nf h  ere the four u ck growth K nsity acting stic interface parable with nsidering dis ction is given  2 u   placement fi

linear and ela tion at the cr the case of relationship acture mecha tressed struc bulk applied astic zone co a relatively to fatigue c stress inten ress intensity crack growth ches. esting (and la an adequat wers to these duced shield sue [12-14] c ’ representin d closure) a e process wi ist at the in owth forwar shear-induce ncipal stresse -term solutio nt of the equ ution. The W

stic, i.e. whe ack tip). Cri plane stress becomes G = nics and the tures with an elastic field. rrection to a low fraction rack growth sity factor, th , ΔK = K max and life pre rgely ignored e characteris questions w ing of the cr onsiders the g the plastic nd compatib th Poisson’s terface. The ds K F , a reta d stress inte s [14], using ns to the We ation represe illiams solut fficients are s:     A, B, C and e A, B, C and crack flank k growth K R K S term). T data. elds, both p xy A z  1 2 xy Az      ' z z   ubstituted int   1 2 xy Az    

m the high l te are equival the material. ing critical st sticity contro men complia at nominal st ended the us nic loading ned by the ra re discipline, n area for st crack growt ation proces es [9] associ vanced in re elastic field b ontact (so-ca eformation ty-induced sh stress inten es ahead of nge patterns her two- ( K rm equations

ocal ent, In ates lled nce ress e of was nge the ress h is ses. ated cent y a lled is a ear sity the for plus for

i

2

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  

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y

x

wh pla

nknown coe rm solution i

) and C and

z is the coo

tressed poin

t in the com

rdinate of a s

plex

1 2

1 2

( B z z  

0 ) z Cz D   (

i

) z z 

2



  

(2)

y

x

wh

nknowns are 2 y x     nknowns ar F , T -stress, a to retard crac (leading to a photoelastic placement fi by:   iv z   elds can be s i

CJP model i 1 0 2 Cz Dz l   = 0. This m ss with a 1/ atibility-indu fringe pattern and parallel

s given as: 3 2 nz Ez zln   odel allows √r distributio ced shear str s for differe to the crack

z for calculatio n behind th ess as a boun nce in princi face, the M

(3) intensity driv leading to st on at the ela hich are dire i complex st

wh cra inte pla com Co fun

n of a stress e crack tip ( dary conditi pal stresses w uskhelishvil

ing ress stic ctly ress

(4)

Dis

ve:

7