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Computational Methods for Debonding in Composites

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1 <strong>Computational</strong> <strong>Methods</strong> <strong>for</strong> <strong>Debond<strong>in</strong>g</strong> <strong>in</strong> <strong>Composites</strong> 13<br />

The displacement field φφφ is considered as a function of two k<strong>in</strong>ds of variables; the<br />

ord<strong>in</strong>ary displacement field u, which will be split <strong>in</strong> a displacement of the top and<br />

bottom surfaces ut and ub, respectively, and the <strong>in</strong>ternal stretch parameter w:<br />

φφφ = φφφ(ut,ub,w) (1.24)<br />

The derivation of the stra<strong>in</strong>s and the f<strong>in</strong>ite element <strong>for</strong>mulation can be found <strong>in</strong> [15],<br />

or <strong>in</strong> [17].<br />

Us<strong>in</strong>g the solid-like shell element, the behaviour of a Glare panel with a circular<br />

<strong>in</strong>itial delam<strong>in</strong>ation and a s<strong>in</strong>usoidally shaped out-of-plane imperfection (with<br />

an amplitude of 0.003 mm) subject to a compressive load has been exam<strong>in</strong>ed. The<br />

failure mechanism is slightly complicated, s<strong>in</strong>ce the delam<strong>in</strong>ated zone grows <strong>in</strong> a<br />

direction perpendicular to the ma<strong>in</strong> load<strong>in</strong>g direction. As a result, the delam<strong>in</strong>ated<br />

area trans<strong>for</strong>ms from a circular area <strong>in</strong>to an ellipsoidal one. Consequently, the buckl<strong>in</strong>g<br />

mode will change as well, and some parts of the top layer will tend to move<br />

<strong>in</strong>wards. For this reason, the possibility of self-contact has been <strong>in</strong>cluded and a<br />

contact algorithm has been activated.<br />

The specimen of Fig. 1.14 consists of an alum<strong>in</strong>ium layer with thickness h1 = 0.2<br />

mm and a Glare3 0/90 ◦ prepreg layer with a thickness h2 = 0.25 mm. An <strong>in</strong>itially<br />

circular delam<strong>in</strong>ation area with radius 8 mm is assumed. The layers are attached to<br />

y<br />

σy<br />

x<br />

σx 40 mm<br />

R<br />

σy<br />

40 mm<br />

delam<strong>in</strong>aton<br />

=8mm<br />

z<br />

x<br />

σx<br />

Al 2024-T3, 0.2mm<br />

Glare3 prepreg, 0.25 mm<br />

Al 7075 back<strong>in</strong>g plate<br />

Fig. 1.14 Geometry of a Glare panel with a circular <strong>in</strong>itial delam<strong>in</strong>ation

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