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Extra info for Achromatic and Superchromatic Fringes with a Calcite Rhomb
For n = 15 Eq. 11) leads to an accuracy of better than 10−9 . One can readily show that the ﬁrst term in Eq. 11) is exact and the second term results in neither resultant force nor moment. This approach avoids any computational error that leads to a non-zero resultant force and/or moment, which increasingly inﬂuences the computed result as crack size increases. 2 for calculating the summation of Legendre polynomials directly. The stress distribution σy (x) in Eq. 12) i=0 where σi is an amplitude factor to be determined for the ith order polynomial Pi (x).
16 shows the compliance functions for R/t = 10 and 20 as a function of a/t for an axisymmetric bending stress on the crack faces. 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.
0 0 2 4 6 8 10 Depth to width ratio (d/2w) Fig. 7. Ratio of the strain response for a slot to that for a crack subjected to diﬀerent stresses. We now turn to the hole-drilling method which has widely been used for near surface residual stress measurement and has been extended to measuring stresses varying with depth . Since there is no analytical solution available for a blind hole, the relationship between measured strains and released stresses has to be either calibrated experimentally [6, 107] or calculated numerically by the ﬁnite element method [114, 7, 120, 4, 55, 115].