**4.2. Mechanical grading**

(discrete and gradient systems) showed a loading-dependency, which is not the case for the single homogeneous systems (**Figure 6c** and **d**). The effective modulus and hardness for discrete and gradient systems decreased nonlinearly between that of the A/NC layer at small loads and the values corresponding to UFG core at maximum load of 10 N. Good agreement in the magnitude and the load dependency was achieved between the effective hardness and the experimentally measured microhardness (**Figure 6d**). The effective energy dissipation of these two models was found to increase with increasing load and all fell in between the A/NC layer

The contact load-bearing behavior of the MHSed Ti was further assessed using FEA to simulate the stress and strain distributions within the materials. **Figure 7** shows the stresses and corresponding equivalent plastic strain contours after unloading (maximum load of 1000 N) for the simulated multilayered systems (discrete and gradient) as compared with that of the monolithic NG material. As presented by the color contours, both the stresses and the equivalent strains exhibit graded distributions within the gradient model, as opposed to the abrupt changes observed in the discrete model. The maximum magnitude of equivalent plastic strain in the monolithic NG material (0.17) is greater than those in both the discrete and gradient multilayers (0.14 and 0.13, respectively). However, the multilayered models (discrete and gradient) achieve deeper and a broader plastic deformation field than that of the monolithic NG material. These simulations further suggest that the structural multilayering and grading modified the stress and strain distribution and reduce the overall plastic strain level through-

The present experimental studies show the plastic deformed area for the MHSed material was markedly greater than that for monolithic NG (**Figure 4**) and this is consistent with the results obtained from FEA microindentation simulations, where the indenter increasingly induces the more compliant UFG core as the load increases (**Figure 6c** and **d**). Further FEA simulations showed that the degree of energy dissipation (occurring by the inelastic deformation) of multilayered cases (discrete and gradient) increased with increasing load (**Figure 6e**). These results indicate that the macroscopic indentation behavior was directly governed by the underlying micromechanics of the multilayered structure. The load–depth FEA simulations (**Figure 6**) revealed that there was negligible difference in the load–depth response for the discrete and gradient models, suggesting that it is the overall structural multilayering that provides the effective macroscopic mechanical loading resistance rather than the grading.

Recent experimental nanoindentation studies, supported by cross-sectional electron microscopy observations, revealed that the multilayered structures provide a higher resistance to deformation than monolithic counterparts [25–27]. FEA simulations indicated that the structural layering

and the UFG core (**Figure 6e**).

90 Contact and Fracture Mechanics

**3.5. Strain and stress simulation**

out the material under indentation conditions.

**4. Discussion**

**4.1. Structural multilayering**

The discrete and gradient models were shown to achieve similar macroscopic effective indentation modulus and microhardness (**Figure 6**). However, FEA simulations revealed differences in the stress and plastic equivalent strain distributions between gradient and discrete models after unloading (**Figure 7**). The magnitude of the equivalent plastic deformation in the top A/NC and NG layers in the gradient system is lower than that experienced in the discrete system. Further, the magnitude and area of plastic deformation in the UFG core are greater in the gradient system compared with the discrete system. This result reveals that the reduction in the stresses and plastic deformation in the top layers is a direct consequence of the increased deformation and energy dissipation accommodated by the softer inner UFG core. Moreover, the mechanical gradations in the successive layers and junctions are observed to give rise to more gradual stress redistribution between component layers, as opposed to the abrupt stress changes observed in the discrete model (**Figure 8**). Such graded stress distribution is believed to lessen the interface failure and increase the interfacial toughness, thus providing strong resistance to loading-damage [10, 29].

The different transition patterns between elastic and plastic deformation shown in **Figure 6** are consistent with the FEA simulation results. The smooth transitional region in the MHSed Ti is attributed to its graded stress distribution achieved by microstructural grading. The absence of any interfacial failure, such as delamination or fracture, observed between the layers in the

**Figure 8.** Distribution of Von Mises stress under the indentation regions in (a) discrete and (b) gradient models, while (c) shows the Von Mises stresses across the interfaces along the white dotted lines.

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

Residual stress may also be contributing to crack suppression in the deformed MHSed Ti structure. Residual surface compressive stress can be induced by various techniques to improve the contact damage resistance and strength of many brittle materials [32]. Further, multilayering and mechanical grading of a surface is known produce complex residual stresses [33, 34]. The residual stress–depth profile analysis [20] revealed that the MHSed Ti has residual compressive stresses through the layers and a tensile stress at the NG layer/UFG core interface. The residual compressive stress in A/NC and NG layers act to arrest crack development and increase damage resistance, however the residual tensile stress at NG/UFG junction theoretically increases the propensity for crack initiation under contact loading. Given the absence of cracking at the NG/UFG interface, it appears the reduction of maximum stress and the attendant of redistribution of the stresses arising from multilayering and mechanical grading more

Improving Contact Load-Bearing Resistance of Ultrafine-Grained Materials…

http://dx.doi.org/10.5772/intechopen.72197

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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

(1) The MHSed Ti exhibited enhanced resistance to contact loading damage compared to the monolithic NG Ti. The multilayering and grading of UFG materials suppressed the

(2) The macroscopic indentation resistance of the MHSed Ti arises from the underlying micromechanics of the multilayered structure. The overall multilayered structure offers the effective macroscopic mechanical loading resistance, where the loading increasingly induces the more compliant structure to bear the deformation as the load increases.

(3) The mechanical gradation provides a transitional junction for stress redistribution and achieves a more gradual stress distribution between component layers. Such a graded stress distribution mitigates the interface failure and increases the interfacial toughness,

(4) The microstructural multilayering and grading of UFG metal can significantly modify the stress field and effectively reduce the maximum stress concentration within the material, thereby reduce the probability of cracks and shear localization which are commonly

formation of cracks and increased the loading damage resistance.

experienced in monolithic materials under indentation conditions.

thus providing strong resistance to loading damage.

than compensate for the residual tensile stress.

following conclusions can be drawn from this study:

**5. Summary and conclusions**

### **4.3. Cracks and stress concentrations**

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.
