6.3. Plate with a major edge crack, minor cracks, holes and inclusions under linear elastic condition

In this case, a major crack of length a = 20 mm. is taken at the left and the right edge of the plate (100 200 mm) as shown in Figures 12 and 13 respectively. In addition to the major edge crack, 36 minor cracks, 15 holes and 15 inclusions are randomly distributed in the plate. The length of the minor cracks varies from 3.5 to 4.5 mm, and orientation varies from 0 to 60 randomly. The holes and inclusions have variations in their radii from 3 to 4.5 mm randomly. A cyclic mode-I mechanical load is applied at the top edge of the plate. The plots for crack extension with number of cycles are shown in Figure 14.

It is also observed that the crack deflects in all the materials. Moreover, it is seen that the number of cycles to failure in case of aluminum alloy is about 18,111 cycles whereas in case of FGM with crack on the alloy and ceramic rich sides is 14,622 cycles and 3111 cycles respectively. The fatigue life of the composite plate is found to 6956 cycles. Thus, it can be stated that

Figure 12. Plate with an edge crack on the alloy rich side under mode-I loading.

Figure 11. A plot of crack extension with number of cycles.

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Fatigue Fracture of Functionally Graded Materials Under Elastic-Plastic Loading Conditions Using Extended… http://dx.doi.org/10.5772/intechopen.72778 185

Figure 11. A plot of crack extension with number of cycles.

pure aluminum alloy undergoes 19,145 cycles before failure. It is also observed that when a major crack initiates from the ceramic (alumina) rich side then it fails much earlier (4872 cycles)

These plots show that when a crack is present on the ceramic rich side, the life diminishes by a considerable extent as compared to when a crack is present on the alloy rich side. The equivalent composite shows the minimum life except in case when a crack is present on the ceramic side. It is also observed that the crack follows nearly a straight path in all the materials.

6.3. Plate with a major edge crack, minor cracks, holes and inclusions under linear elastic

In this case, a major crack of length a = 20 mm. is taken at the left and the right edge of the plate (100 200 mm) as shown in Figures 12 and 13 respectively. In addition to the major edge crack, 36 minor cracks, 15 holes and 15 inclusions are randomly distributed in the plate. The length of the minor cracks varies from 3.5 to 4.5 mm, and orientation varies from 0 to 60 randomly. The holes and inclusions have variations in their radii from 3 to 4.5 mm randomly. A cyclic mode-I mechanical load is applied at the top edge of the plate. The plots for crack

It is also observed that the crack deflects in all the materials. Moreover, it is seen that the number of cycles to failure in case of aluminum alloy is about 18,111 cycles whereas in case of FGM with crack on the alloy and ceramic rich sides is 14,622 cycles and 3111 cycles respectively. The fatigue life of the composite plate is found to 6956 cycles. Thus, it can be stated that

as compared to when the crack initiates from the aluminum alloy side.

Figure 10. Plate with an edge crack on the ceramic rich side under mode-I loading.

extension with number of cycles are shown in Figure 14.

condition

184 Contact and Fracture Mechanics

Figure 12. Plate with an edge crack on the alloy rich side under mode-I loading.

due to the presence of minor cracks, holes and inclusions, the life of the aluminum alloy is reduced by about 5.42%, whereas the fatigue life of the FGM with crack on the alloy and ceramic rich sides goes down by 6.03 and 36.15% respectively. The fatigue life of the equivalent

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A rectangular FGM plate of length (Lt) 100 mm. and height (Ht) 200 mm. with 100% copper nickel alloy on left side and 100% ceramic (alumina) on right side is considered. Property variation is taken in x-direction, where x varies from x = 0 to x = 100 mm. A uniform traction of 100 MPa is applied on the top edge of the rectangular domain along y direction. Cyclic loading is applied at top edge of the plate with a maximum value of σmax ¼ 100 MPa and minimum value of σmin ¼ 0 MPa. A uniform mesh of size 117 � 235 nodes is used for the analysis in each case. The values of SIFs are computed at the tip of the major crack. The variation of SIF with crack length is plotted in each case. The material properties are taken

In this case, a major crack of length a ¼ 20 mm is taken at the edge of the domain (100 � 200 mm) as shown in Figure 15. Cyclic loading is applied at the top edge of the FGM plate, and a crack propagates due to this loading. The plots of SIF with crack length for an crack configuration is shown in Figure 16. The failure crack length obtained for edge crack is

Material properties Values Elastic modulus of copper nickel alloy Ealloyð Þ GPa 160 Elastic modulus of alumina (ceramic) Eceramic ð Þ GPa 386 Elastic modulus of soft inclusion Einclusionð Þ GPa 100 Elastic modulus of Hard inclusion Einclusionð Þ GPa 400 Poisson's ratio of copper nickel alloy νalloy 0.35 Poisson's ratio of alumina (ceramic) νceramic 0.21 Poisson's ratio of inclusion νinclusion 0.3 Poisson's ratio of inclusion νFGM 0.23

<sup>m</sup><sup>p</sup> ð Þ <sup>79</sup>

<sup>m</sup><sup>p</sup> ð Þ <sup>5</sup>

<sup>m</sup><sup>p</sup> ð Þ�<sup>m</sup> <sup>3</sup> � <sup>10</sup>�<sup>11</sup>

IC MPa ffiffiffiffi

IC MPa ffiffiffiffi

Paris exponent m 3

6.5. A major crack in FGM plate under elastic: Plastic loading condition

composite is reduced by 11.78%.

6.4. Example 2

from Table 2 [43].

0.0402 m.

Fracture toughness of copper nickel alloy Kalloy

Fracture toughness of alumina (ceramic) Kceramic

Paris constant C in m=cycle MPa ffiffiffiffi

Table 2. Material property table.

Figure 13. Plate with an edge crack on the ceramic rich side under mode-I loading.

Figure 14. A plot of crack extension with number of cycles.

due to the presence of minor cracks, holes and inclusions, the life of the aluminum alloy is reduced by about 5.42%, whereas the fatigue life of the FGM with crack on the alloy and ceramic rich sides goes down by 6.03 and 36.15% respectively. The fatigue life of the equivalent composite is reduced by 11.78%.
