Crack Paths 2012

— oil? a — a — — _ ( W ) _ W — | : { r — c ] S 1 + \ / g S 2 + S 3 : | ’

(4)

§1(T)=1+—V(anF§1 +a12FK1FK2 M22112); S2(T)=1+—V(bnFK1+b22FK2);

— —

_

— 2 —

ThePisarenko-Lebedecvriterion (PL)

This criterion represents a superposition of elastic and plastic limiting state

theories [4]

X9i(6e)+(1_X)9;(6ee)=9*~

(5)

The linear-elastic material behavior is described by the m a x i m u mtensile stress

criterion (Eq. 3), While the plastic limiting state is related to the von Mises theory in the

form of effective stress 66

a :: ( a / z r c

+ _ jl,xxjl,yy+ ) +F 1 5 2(f22,xx + f22,yy + f l x x f z d+’ y

) +

+ FK, F19 (_ 2jl,xxf2,xx + 2fl,yyf2,yy _ fhxxflyy + fZ’XXfLW + 6f1’xyf2’xy) +

(6)

+ T V a / Z [FFCK1(_2jl,xx _ fl,yy)+FK;(zflxx_ f l y)y]+ T 2

The angle of the crack propagation 6* has to be determined according to the

following conditions:

8 2

8 6 a 59

59

0;?

69

592

The stress intensity factor functions containing to equations (3-5) can be Written as

FK1 =0.5[(l+r|)—(1—r])cos2ot]-Y1(ot,a/W,T,r|);

(7)

FK2 =0.5(l—n)sin 2ot-Y2(ot,a/W,T,n) .

D E T E R M I N TI-NSGT R E SAS N DS T R E S IS N T E N S I TFYA C T O R S

In order to use all generalized criteria to facilitate prediction of crack path it is necessary

to determine at each successive position of the crack front, the stress intensity factors

(SIF), K1 and K2, and T-stress. However, for the actual bent crack geometry, the

expressions for the SIF cannot be easily determined. To overcome this difficulty an

745