6. Conclusions

pressure. While the values of v obviously increase, the contact pressure is observed. The results also show that the larger applied normal load is needed to create the same contact region and the same maximum indentation depth δ<sup>0</sup> for larger values

Contact traction distributions for selected values of the shear modulus ratio μ0=μ ∗ with P=μ ∗ h0

Finally, the axisymmetric contact problem of a functionally graded coated halfspace is indented by a rigid spherical punch in the case of the partial slip. The linear

<sup>2</sup> <sup>¼</sup> <sup>4</sup> � <sup>10</sup>�<sup>4</sup> and <sup>f</sup> <sup>¼</sup> <sup>0</sup>:16 are

<sup>2</sup> <sup>¼</sup> <sup>4</sup> � <sup>10</sup>�<sup>4</sup> and f <sup>¼</sup> <sup>0</sup>:16: (a) p rð Þ and

<sup>2</sup> <sup>¼</sup> <sup>4</sup> � <sup>10</sup>�<sup>4</sup>

The normal contact traction and radial tangential traction for some selected

shown in Figure 12 [14]. The solid lines correspond to the uncoupled solution, and the scatter symbols correspond to the coupled solution. We can observe that consideration of the coupling between the normal and tangential tractions may result in the increase of the peak contact tractions but slight decrease of the contact tractions near the edges of the contact region for a given shear modulus ratio μ0=μ ∗ . With the increase of μ0=μ ∗ , the peak normal and tangential contact tractions increase. Figure 12b also shows that the stick region and the contact radius decrease with the increase of μ0=μ ∗ . This behavior provides a way for us to change the

distribution of the contact pressure by adjusting the stiffness of the coating surface. Figure 13 presents the effects of n on the contact traction distributions with

traction (Figure 13a) increases, and the peak tangential traction (Figure 13b) decreases. This behavior provides a way for us to change the distribution of the

<sup>2</sup> <sup>¼</sup> <sup>4</sup> � <sup>10</sup>�<sup>4</sup> and <sup>f</sup> <sup>¼</sup> <sup>0</sup>:16 [14]. With the increase of <sup>n</sup>, the peak normal

multi-layered model is used to solve the problem.

Mechanics of Functionally Graded Materials and Structures

Contact traction distributions for selected values of n with P=μ ∗ h0

values of the shear modulus ratio μ0=μ ∗ with P=μ ∗ h<sup>0</sup>

of v.

Figure 12.

and f ¼ 0:16: (a) p rð Þ and (b) q rð Þ.

P=μ ∗ h<sup>0</sup>

Figure 13.

(b) q rð Þ.

110

In this chapter, we introduced the axisymmetric indentation response for FGM coating under frictionless and partial slip condition by using the three types of computational models. The exponential function model can solve the axisymmetric contact problem for FGM coating whose elastic modulus continuously varies, but it cannot simulate FGM with arbitrarily varying properties. The linear multi-layered model allows arbitrarily the variation of the material properties of FGM, but it requires Poisson's ratio which is 1/3. The Piece wise exponential multi-layered model can simulate functionally graded coating with arbitrarily varying material modulus with no limit to Poisson's ratio, but numbers of sub-layers are larger. In practice, the computational model is chosen according to properties of the problem. Hankel integral transformation technology and transfer matrix method are used to solve the axisymmetric contact problem of FGM coating based on the cylindrical coordinate system. The results show that the contact behavior can be improved by adjusting the gradient of FGM coating. The present investigation will be expected to provide a guidance for design considerations and applications of FGM coating.
