Crack Paths 2009

u I 0 i d K + — +—1n cos———cos(n—4)6

I

n

2

Model

":1

(1)

v1 2 ;;—IUQ,,{K—%—(_1)n]sin—(+n—3s4i06n}

and,

up _ _i;—2bn{K+£—(—1)n]s1nL—(£11c3o06s}

Mode II

":1 n y

(2)

v11 2 nié%bn{[l<—g+(1—)n]COS—+—co(sn

where, u and v are horizontal (x direction) and vertical (y direction) displacements in

modeI and 11. ,U is the shear modulus and K‘ : (3 — v)/ (1 + v) for plane stress and K : 3 — 4v

for plane strain conditions, where vis the Poisson’s ratio. a and b are constants and r and 0

are radial and phase distance from crack tip.

Mixedmodedisplacement fields (u and v) which are obtained from DIC, can be derived

by superimposing the modeI and II displacement fields. By defining fmm (n6), gmm (n6),

h m(m6) and lmm (n6) as follows (equation 3); the displacement field (equations 1 and 2)

can be written in a matrix form(equation 4).

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