**5. Summary and conclusions**

MHSed Ti under indentation further confirms that mechanical gradations provide resistance to interfacial failures. The smaller magnitude of the stresses and plastic deformation within the "stiffer" top layers and the greater plastic deformation in "softer" inner UFG core for the gradient system diffuse the total plastic deformation energy and offer a suppression to strain

Identifying the linkage between stress and strain concentration and the initiation of cracks experimentally observed is one of the most important issues in FEA analysis. There are three types of cracks in hard materials under indentation conditions: edge, radial and lateral shear cracks (also known as delamination) [26, 28]. Edge cracks begin at the contact edge of the indentation and extend into the material, and are associated with the local tensile and shear stresses [28]. Lateral shear cracks are the result of shear strain localization arising from the high shear stress during indentation testing [30]. Radial cracks generally initiate directly under the indentation and propagates in a direction parallel to the indentation at excessive radial stresses [28]. The cracks observed in the present study (**Figure 4d** and **f**) agree well with the stress concentrations predicted by FEA simulations (**Figure 7**). The location of the edge cracks observed experimentally in monolithic NG Ti are consistent with the tensile stress (S11) and shear stress (S12) locations where the maximum tensile stress and shear stress appear immediately below the indenter (**Figure 7**). However, within the MHSed Ti, the stress (S11 and S12) variation is more gradual, with the shear stress reduced by 38% (0.21–0.13 GPa) at the maximum stress location. Such stress distribution and stress magnitude reduction explains the experimental observation that edge cracks were absent from the MHSed Ti but clearly occurred in monolithic NG Ti. The shear stresses in monolithic NG Ti are distributed over the plastic deformation region and coincide with the sites where shear bands were experimentally observed. With regards to the MHSed Ti, the multilayering and grading reduce the magnitude of maximum shear stress (**Figure 7**), therefore, the shear localized deformation was absent in the MHSed Ti (**Figure 4g**). These analyses reveal that multilayering and grading can significantly modify the stress field and effectively reduced the maximum stress concentration within the materials, thereby reduce the probability of cracks and shear localization which was commonly experienced in monolithic materials under indentation condition.

Our previous study [31] using micropillar compression testing has shown the deformationinduced precipitation of nanocrystals in the outer A/NC layer. The interaction of microcracks and shear bands with these nanocrystals allowed high ductility in this layer. This plasticity was evident in the present study by the indentation-induced deformation in the A/NC layer (**Figure 4a** and **e**). Previous studies demonstrated that the inelastic deformation occurring in the graded ceramics can contribute toward the cone-crack suppression [11, 12]. The susceptibleness of the A/NC layer

to deform plastically reduces the propensity for cracking under indentation condition.

localization which occurred in the monolithic NG Ti (**Figure 4h**).

**4.4. Other aspects contribute to the contact load-bearing**

**4.3. Cracks and stress concentrations**

92 Contact and Fracture Mechanics

In summary, we report on both the contact load-bearing response and underlying deformation mechanism for MHSed Ti using indentation testing in combination with detailed computational simulations of local stresses and plastic deformation strain distributions. The results provide evidence for enhanced contact load-bearing resistance and energy dissipation by introducing multilayers and mechanical gradations into the surface region of the UFG material. This material design strategy is expected to applicable to a broad class of metallic materials. The following conclusions can be drawn from this study:

