Effects of water molecules on tribological behavior and property measurements in nano-indentation processes - a numerical analysis
© Wang and Shi; licensee Springer. 2013
Received: 23 August 2013
Accepted: 10 September 2013
Published: 17 September 2013
Nano/micro-manufacturing under wet condition is an important consideration for various tool-based processes such as indentation, scratching, and machining. The existence of liquids adds complexity to the system, changes the tool/work interfacial condition, and affects material behaviors. For indentation, it may also affect material property measurements. However, little effort has been made to study this challenging issue at nano- or atomistic scale. In this study, we tackle this challenge by investigating nano-indentation processes submerged in water using the molecular dynamics (MD) simulation approach. Compared with dry indentation in which no water molecules are present, the existence of water molecules causes the increase of indentation force in initial penetration, but the decrease of indentation force in full penetration. It also reduces the sticking phenomenon between the work and tool atoms during indenter retraction, such that the indentation geometry can be better retained. Meanwhile, nano-indentation under wet condition exhibits the indentation size effect, while dry nano-indentation exhibits the reverse indentation size effect. The existence of water leads to higher computed hardness values at low indentation loads and a smaller value of Young's modulus. In addition, the friction along the tool/work interface is significantly reduced under wet indentation.
Along with the rapid advancement of manufacturing technologies, the size of precision parts and the thickness of thin films have been significantly reduced. To identify the mechanical properties of work materials at small scales, nano-indentation is often adopted, in which an indenter with known geometry is driven into the work material. In fact, nano-indentation can also be regarded as a fundamental manufacturing process - the tool/material interaction in this process observed provides insight for other processes such as scratching and machining. Meanwhile, in any manufacturing process, the existence of a liquid between the tool and the work material will bring tribological changes to the tool/material interaction. For instance, the immediate benefits of applying lubricants in machining processes may include reduced friction on the tool/material interface, reduced cutting forces, and longer tool life. However, at nano/atomistic-scale sizes, there has been lack of investigation on the tribological effects of a liquid in tool-based manufacturing processes. As the first step, it makes sense to develop such understanding from the nano-indentation process.
In the literature, nano-indentation has been widely applied to determine the hardness values of bulk solid or thin films [1–3]. The Oliver-Pharr method  and work-of-indentation method  are the two popular approaches to determine hardness values based on load-depth curves. In the study of Zhou and Yao , for instance, the Oliver-Pharr method is adopted to calculate indentation hardness directly from the load-depth curve in the indentation process of single-crystal aluminum and single-crystal silicon using an atomic force microscope (AFM). A similar AFM indentation experiment was conducted by Beegan et al.  on sputter-deposited copper films, in which both the Oliver-Pharr method and the work-of-indentation method are used to analyze the results. Bhushan and Koinkar  also applied AFM to measure the hardness of ultra-thin films with an extremely small indentation depth of 1 nm by a specially prepared diamond tip. Nevertheless, the hardness measurement at the micro/nano-level exhibits strong indentation size effect (ISE), which means that the measured hardness decreases with increasing indentation depth. Especially, crystalline materials are known to have strong indentation size effect in micro-indentation hardness test. Oliver and Pharr  and Nix  performed a series of indentation tests with varying tip radii to examine the ISE. It was discovered that hardness values can be significantly affected by the indenter radius when a spherical indenter is applied. Xue et al.  established a model to study the effect of tip radius on micro-indentation hardness. The results show that the effect of the indenter tip radius disappears once the contact radius exceeds one half of the indenter tip radius. Moreover, to measure the indentation modulus and hardness of copper more precisely, McElhaney et al.  proposed a novel method to measure the contact area by taking into account the influence of inherent pile-up and sink-in in the indentation experiment of polycrystalline copper. Similarly, Ma and Clarke  investigated the relationship between size effect and crystal anisotropy in hardness measurement.
The existence of a liquid in nano-indentation is believed to be able to reduce the ISE. For example, Atkinson and Shi  investigated the apparent variation of the hardness of iron by varying the load from 15 g to 20 kg. It is found that the hardness variation is markedly reduced by liquid lubrication. This result suggests that the ISE is actually dependent upon friction condition. A similar experiment was performed by Ren et al. . The load varies from 0.125 to 1 kg in the indentation process of single-crystal MgO, but the ISE is seldom affected by the addition of a liquid for this material. Li et al.  studied the influence of a liquid on the friction between the micro-hardness indenter and the test material. It is claimed that the friction is the major reason for the increased hardness values under low loads and the ISE is related to the surface area-to-volume ratio. Moreover, Almond and Roebuck  discovered that the effect of lubrication on indentation hardness is significantly related to the indenter geometry. The existence of a liquid has little effect when the indenter's inclined angle is greater than 120°.
In this study, to investigate how the existence of a liquid affects the tool/material interaction in nano-indentation, as well indentation measurements, we adopt the technique of molecular dynamics (MD) simulation. This is an effective numerical approach for studying many intriguing issues such as material deformation, dislocation propagation, phase transformation, as well as material property evaluation. Many of these issues are beyond the capability of experimental approaches under very small scales. It should be noted that MD simulation has been widely adopted in studying various nano-manufacturing processes, such as nano-indentation , nano-machining [18, 19], and nano-forming . Nevertheless, the MD simulation literature on material processing that considers material deformation under wet condition is scarce. We believe that the results from this work on nano-indentation can also shed light on its tribological effects for other nano-manufacturing processes.
The remainder of the paper is arranged as follows. The next section briefly explains the construction of MD simulation models and introduces the indentation process parameters for the simulation cases. Thereafter, the simulation results under dry indentation and wet indentation are compiled. They include the comparisons of load–displacement curves, calculated hardness and Young's modulus values, the distributions of friction and normal forces along the indenter/work interface, and stress distribution within the work material. Finally, conclusions are drawn in the final section.
Nano-indentation parameters for the six simulation cases
Depth of indentation (Å)
Indentation speed (m/s)
Retraction speed (m/s)
LJ potential parameters for O-O, O-Cu, O-C, C-H, and Cu-H atom pairs
Equilibrium distance (σ, Å)
Cohesive energy (ϵ, 10−3 eV)
Cutoff distance (Å)
Bond length (Å)
H-O-H angle (deg)
Morse potential parameters for the C-Cu pair interaction
Cutoff distance (Å)
Equilibrium distance r0 (Å)
Elastic modulus α (Å)
Cohesive energy D (eV)
EAM potential parameters for the interaction among Cu atoms
Δ(Ebcc − Efcc)
Δ(Ehcc − Efcc)
Stacking fault energy
where N T is the number of carbon atoms in the diamond indenter and f ij is the individual interaction force from atom j acting on atom i.
Results and discussion
Indentation morphology and force
However, for both 10 and 100 m/s speeds, the indentation force for dry indentation starts to overtake that for wet indentation when the indentation depth reaches 3.3 nm. This phenomenon can be attributed to the change of friction force between the indenter and the work material due to the addition of water. When the indentation depth is less than a critical value, the resultant reduction of indentation force is too small to compensate the resistant force of water molecules between the indenter and the work material. When the indentation depth is beyond the critical value, the beneficial tribological effect is sufficient to compensate the resistant force. As a result, the indentation force in the late stage for wet indentation is smaller than that for dry indentation.
Hardness and Young's modulus
The hardness curve for wet indentation demonstrates the ISE, which means that the calculated hardness decreases with the increase of loading/penetration. On the other hand, the hardness-depth curve for dry indentation exhibits the reverse ISE, which means that the hardness increases with the increase of loading/penetration. These findings are not very common for numerical studies in the literature, but they are fairly consistent with experimental studies in the literature at larger scales. For instance, the reverse ISE in dry indentation is reported in several studies [30–32], and the regular ISE in lubricated indentation is also reported [14–16]. In particular, the reverse ISE phenomenon has not been fully understood. Speculated reasons include the existence of a distorted zone near the crystal-medium interface , the applied energy loss due to specimen chipping around the indentation , and the generation of median or radial cracks during indenter loading half-cycle .
Comparison of MD simulation results with the literature
Young's modulus (GPa)
Case 1 of this study - wet indentation
19.5 to 25.5
Case 2 of this study - dry indentation
12.7 to 21.7
MD simulation by Fang et al. 
20.4 to 43.4
283.4 to 444.9
MD simulation by Leng et al. 
Nano-indentation experiment 
7.1 to 10
116 to 126 
Note that the mechanisms of dislocation development with the presence of imperfections and grain boundaries in nano-indentation processes are investigated by numerical approaches in the literature. In this regard, the representative studies cover the typical research topics of dislocation nucleation and defect interactions , vacancy formation and migration energy, interstitial formation energy, stacking fault energy , coherent twin boundaries and dislocations , and the effect of grain boundary on dislocation nucleation and intergranular sliding . In addition, Shi and Verma  compared the nano-machining processes of a monocrystalline copper and a polycrystalline copper by MD simulation. The results indicate that the presence of grain boundaries significantly reduces the cutting force and stress accumulation inside the workpiece by up to 40%. However, the focuses of these studies are not about the calculation of hardness and Young's modulus, and certainly they do not tackle the tribological effects of any liquid. As such, it will be interesting to carry out such investigation on nano-indentation simulation of polycrystalline structures in the near future.
Friction along the tool/work interface
where F x and F y are the average horizontal and vertical force components of each group, respectively.
Influence of indentation speed
This research investigates nano-indentation processes with the existence of water molecules by using the numerical approach of MD simulation. The potential tribological benefits of water or other liquids, as well as the influence on material property measurements, are intriguing to nano-indentation. This also applies to other tool-based precision manufacturing processes. By configuring 3D indentation of single-crystal copper with a diamond indenter, six simulation cases are developed. Based on the results, the major findings can be summarized as follows:
Compared with dry indentation, wet indentation incurs higher indentation force during the initial penetration of the indenter, but lower force during the full penetration period.
Wet indentation can effectively reduce the adhesion between the atoms of the work material and the atoms of the indenter. It helps preserve the final indentation shape and geometry after the indenter is retracted.
In dry indentation, the hardness-indentation depth curve exhibits the reverse indentation size effect. In wet indentation, the curve exhibits the regular indentation size effect.
By analyzing the force distributions along the indenter/work interface, it is found that the existence of water molecules can significantly reduce the friction force, but not the normal force.
In dry indentation, the maximum indentation force increases from 468.0 to 549.7 eV/Å as the indentation speed increases from 10 to 100 m/s. In wet indentation, the maximum indentation force increases from 423.2 to 565.6 eV/Å with the same increase of speed. However, the increase of indentation force is much less significant when the speed increases from 1 to 10 m/s.
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