6.6. A major edge crack in FGM plate with holes, inclusions and minor cracks under elastic-Plastic loading condition

In this case, a major crack of length a ¼ 20 mm is taken at the edge of the domain (100 � 200 mm) is taken as shown in Figure 17. Minor cracks, holes and inclusions are randomly distributed in the plate. All 36 minor cracks have varying length randomly from 3.5 to 4.5 mm, with varying orientation from 0 to 60�. In addition to these 15 inclusions are also distributed in the domain randomly. The holes and inclusions have variation in their radii from 3 to 4.5 mm. A cyclic mode-I loading is applied due to which the major crack propagates. The plots for SIF variation with crack length of edge crack is shown in Figures 18 and 19 for soft and hard inclusions respectively. The failure crack length for edge crack is obtained 0.0384 and 0.0392 m. for soft and hard inclusions respectively.

Fatigue Fracture of Functionally Graded Materials Under Elastic-Plastic Loading Conditions Using Extended… http://dx.doi.org/10.5772/intechopen.72778 189

Figure 16. Plot for variation of SIF with crack length.

6.6. A major edge crack in FGM plate with holes, inclusions and minor cracks under

In this case, a major crack of length a ¼ 20 mm is taken at the edge of the domain (100 � 200 mm) is taken as shown in Figure 17. Minor cracks, holes and inclusions are randomly distributed in the plate. All 36 minor cracks have varying length randomly from 3.5 to 4.5 mm, with varying orientation from 0 to 60�. In addition to these 15 inclusions are also distributed in the domain randomly. The holes and inclusions have variation in their radii from 3 to 4.5 mm. A cyclic mode-I loading is applied due to which the major crack propagates. The plots for SIF variation with crack length of edge crack is shown in Figures 18 and 19 for soft and hard inclusions respectively. The failure crack length for edge crack is obtained 0.0384 and

elastic-Plastic loading condition

Figure 15. FGM plate with an edge crack.

188 Contact and Fracture Mechanics

0.0392 m. for soft and hard inclusions respectively.

Figure 17. FGM plate with an edge crack, 15 inclusions, 15 holes and 36 minor cracks.

7. Conclusions

Nomenclatures

W~ : Strain energy

u: Deformation

Author details

Somnath Bhattacharya1

2 BARC, Mumbai, India

1986;25:311-323

References

C: Compliance matrix E: Modulus of elasticity

γ: Coefficient of thermal expansion

KIC: Critical stress intensity factor (Fracture toughness)

\*Address all correspondence to: somnathb.iitr@gmail.com

1 Department of Mechanical Engineering, NIT, Raipur, India

\*, Kamal Sharma<sup>2</sup> and Vaibhav Sonkar<sup>1</sup>

[1] Agarwal BD, Kumar P, Khanna SK. Determination of the fracture toughness of fabric reinforced composites by the J-integral approach. Composites Science and Technology.

σ: Stress ε: Strain

In this chapter we have discussed the simulation of cracks in a FGM plate has been carried out in the presence of multiple inhomogeneities by XFEM using both linear elastic as well as elasticplastic formulations. SIF has been calculated at the tip of the major crack using interaction integral approach. The variation in the SIF at the tip of the major crack has been studied when multiple inhomogeneities are present in the domain. From this study it is observed that minor cracks have least effect in the FGM plate's failure crack length, whereas soft inclusions have moderate effect and holes have the most severe effect. It is found that the FGM plate's life increases in each case when soft inclusions are replaced by hard inclusions. Hence the presence of the hard inclusions in

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191

the plate increases the failure crack length of the plate i.e. plate survives more.

Figure 18. Plot for variation of SIF with crack length for soft inclusions.

Figure 19. Plot for variation of SIF with crack length for hard inclusions.
