Issue 46

V. Rizov, Frattura ed Integrità Strutturale, 46 (2018) 158-177; DOI: 10.3221/IGF-ESIS.46.16

Figure 6 : Cross-section of the internal crack arm loaded in bending and torsion.

Figure 7 : Two three-layered functionally graded circular shafts loaded in centric tension and torsion with cylindrical delamination crack located between (a) layers 2 and 3 and (b) layers 1 and 2. In (55), there are two unknowns, d M and L  . One more equation with unknowns d M and L  is derived by considering the equilibrium of the cross-section of the external crack arm. Obviously, (55) can be used as equation for equilibrium of the cross-section of the external crack arm. For this purpose, 1 n has to be replaced with 2 n ( 2 n is the number of layers in the external crack arm). Besides, d M has to be replaced with d M M  (this follows from the fact that the sum of the bending moments in the two crack arms is equal to M ). Thus, the equation for equilibrium of the cross-section of the external crack arm is written as     2 4 4 5 5 1 1 1 1 1 4 5 i n d L i i i L i i i i M M r r r r                      (59)

Eqns. (55) and (59) should be solved with respect to L  and d

M by using the MatLab computer program.

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