**3.2. Mechanical gradations**

Microstructural and damage observations were conducted using a field-emission gun scanning electron microscope (SEM) Zeiss Supra 55VP operated at 10 kV and a transmission elec-

**Figure 1.** (a) Schematic illustration of the surface load-bearing and cross-sectional nanoindentation testing. The black ball represents the load-bearing testing indenter and the black triangle represents the indent of nanoindentation testing.

A two-dimensional axisymmetric model was developed to simulate the ball indentation using Abaqus v6.10. The specimens were modeled as isotropic, elastic–perfectly plastic following the large-deformation theory. The finite element mesh contained 42,163 four-node bilinear axisymmetric quadrilateral elements (CAX4R), with a refined mesh in the indentation region (**Figure 1b**). Mesh convergence was verified by comparing load–depth curves and stress contours using models with element number ranging from 11,183 to 42,163. A user subroutine UMAT was developed to take into account the gradation of material properties, in which the discrete and gradient model parameters were assigned to elements based on their distance from the surface (see later for further details). The ball indenter was modeled as a rigid body, and the contact between the indenter and specimen was assumed frictionless. A maximum load of 1000 N was applied to indent the samples at a loading rate of 1000 N/s. The finite element analysis (FEA) of the microindentation adopted a similar methodology to the axisymmetric nanoindentation simulations. The Vickers indenter was modeled to be a conical rigid indenter with an apex angle of 70.3° and tip radius of 3.4 μm, which approximates a Vickers indenter tip.

A SEM cross-sectional view of the MHSed Ti surface shows three-layered structure without sharp interfaces between the successive layers (**Figure 2a**). TEM analysis revealed that the ∼30 μm thick top layer was composed of a bright phase matrix and a discrete darker nanostructure (**Figure 2b**).

tron microscope (TEM) Jeol JEM 2100 operated at 200 kV.

(b) Finite element mesh of the ball indentation model.

82 Contact and Fracture Mechanics

**3. Results**

**3.1. Microstructure**

Nanoindentation was used to measure the elastic and plastic mechanical properties spatially through the cross-section of the MHSed Ti. The elastic mismatch and delamination, commonly existed in other multilayered systems produced by deposition or coating, are two critical factors controlling crack confinement [23]. In contrast, due to the gradients in both the strain and strain rate induced by the cryorolling and SMAT process from the top surface to the inner core, the reported MHSed Ti is free from elastic mismatch and delamination between layers.

**Figure 2.** Microstructural characteristic of the MHSed Ti: (a) SEM cross-sectional image. (b) TEM bright-field (BF) image of the microstructure situated 20 μm below the top surface. The upper right and lower left insets are the selected-area diffraction (SAD) patterns of the bright region the dark region, respectively; (c) TEM BF image of the microstructure located 60 μm below the top surface. The inset shows the corresponding SAD pattern; (d) TEM BF image of the innermost core. The inset shows the corresponding SAD pattern; (e and f) histogram of the grain size distribution in the NG layer (e) and UFG core (f). The grain size *D* was defined by *D* = √ \_\_\_\_\_\_\_ *dT* × *dL*, *dT* is the transverse length of the grain and *dL* is the longitudinal length. 300 grains were statistical measured from several TEM dark-field (DF) images.

Moreover the MHSed Ti possesses mechanical gradations within and between each successive layer. The Oliver–Pharr [24] indentation hardness *H*O–P (ranging from ∼5.3 to ∼3.2 GPa) and modulus *E*O–P (ranging from ∼137 to ∼113 GPa) gradually decreased with the distance from the top surface to the core (**Figure 3a** and **b**). The highest average indentation hardness (∼5.2 GPa) of the top A/NC layer is consistent with its microstructure which is composed of amorphous and nanocrystalline phases. The NG layer has nanograins compared with the A/ NC layer, but reduced grain size relative to the UFG core, consistent with the mechanical trend observed in **Figure 3a** and **b**. The UFG core, consists of ultrafine equiaxed grains with average grain size of ∼180 nm, thus has the lowest average indentation hardness (∼3.2 GPa). **Figure 3c** shows the SEM image of the residual indents after indentation unloading. The absence of radial or circumferential cracks confirms the plastic nature of the material layers. The mechanical gradations were calculated as the slope of datasets presented in **Figure 3a**. With the distance from the outer surface to inner core, approximately negative linear gradations in both *E*O–P and *H*O–P were obtained within the top A/NC and the NG layers beneath. The UFG core, however, show no detectable gradation. **Table 1** summarizes the gradations of *E*O–P and *H*O–P in each layer.

for the MHSed Ti is expected due to the high hardness and strength of the top A/NC layer. The residual impression radius for the MHSed Ti and the monolithic NG were measured to be 424 and 488 μm (**Figure 4a** and **b**), respectively. A complete suppression of cracks in the MHSed material was clearly substantiated by SEM observations (**Figure 4c**). In contrast, cracks (marked by white arrows) appeared to initiate at the contact edge of the indentation and propagate through the region in the monolithic NG Ti, most likely due to local stress

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

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

85

**Components (layer) Gradation** *E***O–P (GPaμm−1) Gradation** *H***O–P (GPaμm−1)**

A/NC −0.57 −0.013 NG −0.25 −0.014 UFG 0 0

**Table 1.** Mechanical gradations in each component layer.

Most of the plastic deformations of the tested materials occur within a semi-circular area as revealed by optical microscopy observation on the cross sections (**Figure 4e**–**h**). The semi-circle represents an elastic–plastic deformation border and the semi-circular area can be considered as the plastic strain zone. The overall through-thickness impact impression of the MHSed Ti is comparatively much lower (**Figure 4c**) than the monolithic NG Ti (**Figure 4d**), however, the MHSed Ti yields a significant compliance and the elastic–plastic deformation border occurs at a greater depth compared with the monolithic NG material (**Figure 4e** and **f**). The radius of the plastic strain zone for the MHSed Ti and monolithic NG Ti was established to be ∼530 μm and ∼460 μm, respectively. High magnification observations on the elastic–plastic strain boundary revealed that the MHSed Ti achieves more gradual strain redistribution than the monolithic NG Ti in which intense shear localization were found (**Figure 4g** and **h**). The smooth transitional region for elastic–plastic deformation in the MHSed materials is the direct result of the multilayered structure accommodating the imposed load. These results suggest that the multilayered structure and the associated mechanical gradations in the material offer

To better understand how the structural multilayering and grading influences the contact loadbearing behavior of the MHSed materials, an elastic–perfectly plastic finite element analysis (FEA) computational model was developed. Here the three-dimensional indenter geometry represented as two dimensional, axisymmetric and rigid has been simulated to fit the experimental nanoindentation loading-depth data for each layer. The extensive study showed that incorporating the post yield strain hardening (linear isotropic, linear kinematic and Ramberg– Osgood isotropic hardening) into the models had a minimal effect on improving the prediction of the simulated data and the estimated yield strength [10]. Consequently, we assume zero hardening for plastic behavior and that the material deformation is elastic–perfectly plastic. This is a simple and effective approach to describe the mechanical behavior of the material.

an advantageous mechanism for contact damage resistance.

concentrations (**Figure 4d**).

**3.4. Computational simulations**

#### **3.3. Contact load-bearing response**

The experimental contact load-bearing response of the MHSed Ti and the monolithic NG Ti is shown in **Figure 4**. For the same contact load (1000 N), a relatively small contact impression

**Figure 3.** Mechanical gradations of the MHSed Ti. (a) Hardness and modulus through the cross-section of MHSed Ti using a 20 mN maximum load; (b) average indentation hardness and modulus for each of the layers; and (c) SEM images of the residual indents on the cross-section of each layer. From left to right: A/NC, NG, and UFG.


**Table 1.** Mechanical gradations in each component layer.

Moreover the MHSed Ti possesses mechanical gradations within and between each successive layer. The Oliver–Pharr [24] indentation hardness *H*O–P (ranging from ∼5.3 to ∼3.2 GPa) and modulus *E*O–P (ranging from ∼137 to ∼113 GPa) gradually decreased with the distance from the top surface to the core (**Figure 3a** and **b**). The highest average indentation hardness (∼5.2 GPa) of the top A/NC layer is consistent with its microstructure which is composed of amorphous and nanocrystalline phases. The NG layer has nanograins compared with the A/ NC layer, but reduced grain size relative to the UFG core, consistent with the mechanical trend observed in **Figure 3a** and **b**. The UFG core, consists of ultrafine equiaxed grains with average grain size of ∼180 nm, thus has the lowest average indentation hardness (∼3.2 GPa). **Figure 3c** shows the SEM image of the residual indents after indentation unloading. The absence of radial or circumferential cracks confirms the plastic nature of the material layers. The mechanical gradations were calculated as the slope of datasets presented in **Figure 3a**. With the distance from the outer surface to inner core, approximately negative linear gradations in both *E*O–P and *H*O–P were obtained within the top A/NC and the NG layers beneath. The UFG core, however, show no detectable gradation. **Table 1** summarizes the gradations of

The experimental contact load-bearing response of the MHSed Ti and the monolithic NG Ti is shown in **Figure 4**. For the same contact load (1000 N), a relatively small contact impression

**Figure 3.** Mechanical gradations of the MHSed Ti. (a) Hardness and modulus through the cross-section of MHSed Ti using a 20 mN maximum load; (b) average indentation hardness and modulus for each of the layers; and (c) SEM images

of the residual indents on the cross-section of each layer. From left to right: A/NC, NG, and UFG.

*E*O–P and *H*O–P in each layer.

84 Contact and Fracture Mechanics

c

500nm

Epox y

**3.3. Contact load-bearing response**

A/NC NG UFG

a b

for the MHSed Ti is expected due to the high hardness and strength of the top A/NC layer. The residual impression radius for the MHSed Ti and the monolithic NG were measured to be 424 and 488 μm (**Figure 4a** and **b**), respectively. A complete suppression of cracks in the MHSed material was clearly substantiated by SEM observations (**Figure 4c**). In contrast, cracks (marked by white arrows) appeared to initiate at the contact edge of the indentation and propagate through the region in the monolithic NG Ti, most likely due to local stress concentrations (**Figure 4d**).

Most of the plastic deformations of the tested materials occur within a semi-circular area as revealed by optical microscopy observation on the cross sections (**Figure 4e**–**h**). The semi-circle represents an elastic–plastic deformation border and the semi-circular area can be considered as the plastic strain zone. The overall through-thickness impact impression of the MHSed Ti is comparatively much lower (**Figure 4c**) than the monolithic NG Ti (**Figure 4d**), however, the MHSed Ti yields a significant compliance and the elastic–plastic deformation border occurs at a greater depth compared with the monolithic NG material (**Figure 4e** and **f**). The radius of the plastic strain zone for the MHSed Ti and monolithic NG Ti was established to be ∼530 μm and ∼460 μm, respectively. High magnification observations on the elastic–plastic strain boundary revealed that the MHSed Ti achieves more gradual strain redistribution than the monolithic NG Ti in which intense shear localization were found (**Figure 4g** and **h**). The smooth transitional region for elastic–plastic deformation in the MHSed materials is the direct result of the multilayered structure accommodating the imposed load. These results suggest that the multilayered structure and the associated mechanical gradations in the material offer an advantageous mechanism for contact damage resistance.
