By Olav Tirkkonen (Author), Risto Wichman (Author)

ISBN-10: 0470024801

ISBN-13: 9780470024805

ISBN-10: 0470845422

ISBN-13: 9780470845424

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5 A Ring With a Radial Crack To obtain the compliance functions for a cylinder of mean radius R and wall thickness t, we may introduce a radial crack from either inside or outside wall. Here, we focus our attention on a cut made from the outside the wall. This leads to a conﬁguration shown in Fig. 17. Again, instead of resorting to a numerical computation we separate conceptually a small element containing the crack from the cylinder as shown in Fig. 17. The stress distribution on the crack faces corresponds to the original residual hoop stress in the uncracked body with an opposite sign.

This is possible because the compliance functions can be determined directly at an arbitrary location on the free surface. Additionally, the compliance functions for the measurement of shear stresses can also be obtained using the same approach presented here. In this case another strain gages will be installed on the other side of the cut shown in Fig. 3 to allow strain variations measured on both sides of the cut. If the stress is nonuniform along the length of the cut, strain variations in both depth and length can be measured using an array of gages installed along the cut, as shown in Fig.

4 for diﬀerent crack sizes. 0 Normalized distance on back face Fig. 3. Normalized horizontal displacements on front and back faces. A postulate made by the authors in [12] states that the displacement at a region more than one thickness away from the crack becomes a rigid body movement. 9) where um = (uu + ul )/2 is the mean vertical displacement at distance s. To verify this relation, the quantities on the left and right hand sides of Eq. 9) are plotted against s in Fig. 8. It is seen that the two curves indeed merge into one for s less than unity.

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