Fatigue Crack Paths 2003

a complex variable approach (Muskehelishvili [5]) has demonstrated that the stress field

at the crack tip can be expressed by:

a, +o'y I4Re{¢'(z)} o'y —ox + 2irxy I2-{z¢l|(z)+l//l(z)}

(2)

u + i v I 2 i { 7 ¢ ( z ) + z ( W ) — l / T ) }

a

then generalised stress and displacement can be written as:

(81(2): 5'12)“, TI1(Z):C1A'ZA_1 > W1(Z):c127L

(3)

(752(2): 6'22)“, 772(2): % A Z J H1 W2(Z):C22A

where a1, a2, c1, c2, are complexcoefficients that can be evaluated through the

satisfaction of boundary conditions. A represents a minimumvalue solution of the

following eigenfunction:

h2(— 40:2 + 4afi)+ 2062 — ZOtfi + 2a— 6 — I + (— 20:2 + 2043 — 204 + 2B)c0s7t1r I 0 (4)

Finally, the Cartesian stress can be expressed by:

e. : Z,,R@l/1.r’"‘1b.l(2f1.

— gR)c<>s(7ln

—1)l’—(2f1 — gJSmUl. — 00+

— 0. — 00.. m0. — 019- f1 m0. — 0101}

6y I ZnReHnrAFIb[(nZfR + gR)cos(7ln — 1)0— (2f, + gl)sen(jtn _ 1)§+

+ (1. — I)(fR c080,. — 3)19— f1 86710.. — 3W1}

(5)

Txy : 2,,R@l7LnrA"_1bn [gR Sena._ U19 + g, COSULn — I)19 +

+ (An _1)(fR sfinvln — 3)19+ f, cos(7tn —

}

Until nowthere was found no formulation of the stress field for the case of a crack

lying entirely in one material, therefore it is important to investigate this case to

understand the critical condition of a bimaterial joint.

E X P E R I M E NSTEATLU P

Aluminium6061 T6 as high Youngmodulus material and PSM-l polycarbonate as

other material have been chosen to manufacture test specimens. These materials have

been chosen because their joint presents the same Dundurs bimaterial constants of that

in classical epoxy/glass-fiber composite materials and because they can be joined with

epoxy Araldide® D glue that has the same elastic characteristic of PSM-l, thus