Design and Analysis of Key Components in the Nanoindentation and Scratch Test Device

In recent years, nanomechanics as an important branch of nanotechnology has been an effective method to study mechanical properties of structures and materials from microto nano-scale. It has been widely used to study mechanical behaviour and damage mechanism of nanotube, nanobelt as well as other nanostructures (Zhu & Espinosa, 2005; Han et al., 2007). Some researchers studied biomechanics properties of tissues and organs of human body, such as the red cell (Suresh, 2007; Lim et al., 2006) and bone (Tai et al., 2007; Hansma et al., 2006; Thurner, 2009; Zheng & Mak, 1996; Koff et al., 2010; Huja et al., 2010; Diez-Perez et al., 2010; Zhang et al., 2010) by means of experimental nanomechanics approaches, to reveal occurrence rules, prevention and control methods of some diseases. Compared with tensile, torsion, bend and hardness tests etc. during which samples are usually in condition of simple stress state, nanoindentation and scratch test can obtain more parameters of materials including hardness, modulus, fracture toughness, creep property, fatigue, adhesion and so on (Doerner & Nix, 1986; Oliver & Pharr, 1992) because samples are in condition of complex stress state. So, it has been widely used in fields of materials science (Lucas & Oliver, 1999; Yang et al., 2007; Tao et al., 2010), nanotechnology, surface engineering (Jardret & Morel, 2003 ), semiconductor (Michler et al., 2005; Zhao et al., 2009), MEMS/NEMS (Abdel-Aal et al., 2005; Bhushan, 2007), biomedicine (Suresh, 2005), biomechanics (Bruet et al., 2008) and so on. In addition, it is a useful method to study multiphysical field coupled performance of materials (Bradby et al., 2003; Schuh et al., 2005; Nowak et al., 2009). So in past years, nanoindentation and scratch test gave a big boost to the development of related fields and also it was given huge attention in all over the world. With further development of materials science and nanomechanics, more and more researchers tried to study principle of deformation and damage of materials (De Hosson et al., 2006; Rabe, 2006; Zhou & Komvopoulos, 2006). Nanoscale deformation: Seeing is believing (Hemker & Nix, 2008). So research on in situ nanoindentation and scratch test was proposed, through which process of deformation and damage of samples can be observed. However, because of large size and complex structure of existing commercial equipments (MTS NanoIndenter; Hysitron Incorporated; CSIRO.UMIS; Micro Materials Ltd.; CSM instruments), they can not be installed on the stage of SEM or TEM to realize in situ nanoindentation and scratch test. So, novel nanoindentation and scratch test devices are required. And this is advanced technology and up to now there is no mature product for in situ nanoindentation and scratch test.


Introduction
In recent years, nanomechanics as an important branch of nanotechnology has been an effective method to study mechanical properties of structures and materials from micro-to nano-scale. It has been widely used to study mechanical behaviour and damage mechanism of nanotube, nanobelt as well as other nanostructures (Zhu & Espinosa, 2005;Han et al., 2007). Some researchers studied biomechanics properties of tissues and organs of human body, such as the red cell (Suresh, 2007;Lim et al., 2006) and bone (Tai et al., 2007;Hansma et al., 2006;Thurner, 2009;Zheng & Mak, 1996;Koff et al., 2010;Huja et al., 2010;Diez-Perez et al., 2010;Zhang et al., 2010) by means of experimental nanomechanics approaches, to reveal occurrence rules, prevention and control methods of some diseases. Compared with tensile, torsion, bend and hardness tests etc. during which samples are usually in condition of simple stress state, nanoindentation and scratch test can obtain more parameters of materials including hardness, modulus, fracture toughness, creep property, fatigue, adhesion and so on (Doerner & Nix, 1986;Oliver & Pharr, 1992) because samples are in condition of complex stress state. So, it has been widely used in fields of materials science (Lucas & Oliver, 1999;Yang et al., 2007;Tao et al., 2010), nanotechnology, surface engineering (Jardret & Morel, 2003 ), semiconductor (Michler et al., 2005;Zhao et al., 2009), MEMS/NEMS (Abdel-Aal et al., 2005;Bhushan, 2007), biomedicine (Suresh, 2005), biomechanics (Bruet et al., 2008) and so on. In addition, it is a useful method to study multiphysical field coupled performance of materials (Bradby et al., 2003;Schuh et al., 2005;Nowak et al., 2009). So in past years, nanoindentation and scratch test gave a big boost to the development of related fields and also it was given huge attention in all over the world. With further development of materials science and nanomechanics, more and more researchers tried to study principle of deformation and damage of materials (De Hosson et al., 2006;Rabe, 2006;Zhou & Komvopoulos, 2006). Nanoscale deformation: Seeing is believing (Hemker & Nix, 2008). So research on in situ nanoindentation and scratch test was proposed, through which process of deformation and damage of samples can be observed. However, because of large size and complex structure of existing commercial equipments (MTS NanoIndenter; Hysitron Incorporated; CSIRO.UMIS; Micro Materials Ltd.; CSM instruments), they can not be installed on the stage of SEM or TEM to realize in situ nanoindentation and scratch test. So, novel nanoindentation and scratch test devices are required. And this is advanced technology and up to now there is no mature product for in situ nanoindentation and scratch test.
In this chapter, we introduced principle of nanoindentation. A new method of indentation measurement through two displacement sensors and a displacement amplification structure was proposed. This measuring method was different from many commercial devices. Two key components of the proposed device including precise driving and precise measuring units were designed and analyzed. Hysteresis of two kinds of piezoelectric stacks were measured and analyzed. Here piezoelectric stacks and flexure hinges were used to realize precise positioning and precise loading and unloading of the diamond indenter. Flexure hinges with multi-structure forms were proposed and analyzed by finite element method. Based on the previous work, the prototype of nanoindentation and scratch device was designed and fabricated. Calibration experiments of sensors and displacement amplification structure were carried out and output performances of designed flexure hinges were measured and discussed. At last, nanoindentation experiments of optical glass were carried out. The relation curves between penetration load and depth were obtained, from which hardness of the glass was figured out. Nanoindentation morphology was obtained through high resolution optical microscope. Nanoindentation results indicated that the device presented in this chapter can realize the high precise nanoindentation test, but the testing resolution should be improved and the device also should be calibrated precisely. Though the accuracy was required to improve, this work was a bold attempt to combine the piezoelectric-driven mechanism and flexure hinge to realize precise motion in nanoindentation device. This transmission mode is very simple and can be used easily to realize miniaturization of the device and in situ nanoindentation test which is our future work.

Principle of nanoindentation test technology---the Oliver-Pharr method
Nanoindentation is a useful method to test the mechanical behavior and damage mechanism of materials from micro-to nano-scale. When a diamond indenter with sharp tip is penetrating into and then withdrawing from a sample surface, the load P and displacement h is continuously monitored by high resolution sensors. The load and displacement data is sent to processor during the indentation process and then converted to P-h curve which contains abundant information of material such as hardness, elastic modulus, yield stress and so on. Fig.1 is a typical P-h curve of nanoindentation. It mainly consists of two portions, loading and unloading process. Sometimes, in order to study creep of materials, holding portion (holding for a certain time at maximum load) between loading and unloading is added. Fig.2 is cross-section of indentation and the related parameters. Up to now, the Oliver-Pharr method (Oliver & Pharr, 1992) based on results by Sneddon (Sneddon, 1965) is most commonly used to analyze the load and penetration depth for nanoindentation measurements.

Fig. 2. Cross-section of indentation
According to Oliver-Pharr method, nanoindentation hardness is defined as the indentation load divided by the projected contact area of the indentation. In Fig.1, indentation hardness (H) can be obtained at the peak load given by where P max is the peak load and A c is the projected contact area. And the projected contact area can be calculated from the relation as following where h c is the contact depth which is given by where ε is a constant and depends on the geometry of the indenter (ε=0.72 for cone indenter, ε=0.75 for paraboloid of revolution, and ε=1.00 for flat indenter) (Sneddon, 1965). h max is the maximum penetration depth and S is the contact stiffness. The contact stiffness S can be calculated from the slope of the initial portion of the unloading curve and S=dP/dh, which can be obtained by curve fitting of 25%-50% unloading data. Based on relationships developed by Sneddon, the contact stiffness S can also be expressed by where is a constant and depends on geometry of the indenter ( =1.034 for a Berkovich indenter, =1.012 for a Vickers indenter and =1.000 for a cylinder indenter). Because both the sample and the indenter have elastic deformation during the indentation process, the reduced modulus E r is defined by where E and are the elastic modulus and Poisson's ratio for the sample; E i and i are the elastic modulus and Poisson's ratio for the indenter, respectively. For a diamond indenter, E i =1141GPa, i =0.07. According to the Oliver-Pharr method mentioned above, the nanoindentation hardness, the contact stiffness and the elastic modulus of materials can be obtained. Fig.3 is the schematic diagram of indentation device which will be designed in this chapter. It mainly consists of two portions, precise driving unit including z-axis precise driving unit (4), x, y precise positioning platform (8) and precise measuring unit including capacitance displacement sensor (5), displacement amplification structure (9) and laser displacement sensor (10). Compared with most of commercial indentation equipments, the principle is different. Penetration load is not measured directly by a load sensor but it is obtained with the help of displacement amplification structure and laser displacement sensor. When the indenter is pushing into and withdrawing the sample located on the left of displacement amplification structure, the amplification structure will deform and the right will output enlarged displacement which is measured by high resolution laser displacement sensor. At the same time, displacement of the indenter is measured by the capacitance displacement sensor. Because deformation of displacement amplification structure is very small, it is elastic deformation. Fig. 3. Schematic diagram of the device which will be designed in this chapter 1 Base; 2(12) Supporting plates; 3(11) Macro-adjusting mechanism; 4 z-axis precise driving unit; 5 Capacitance displacement sensor; 6 Indenter; 7 Sample; 8 x, y precise positioning platform; 9 Displacement amplification structure; 10 Laser displacement sensor Calculation model and related parameters are shown in Fig.4. P is penetration load and h 3 is left deformation of displacement amplification structure corresponding to the load P. h 1 and www.intechopen.com h 2 are right deformation and displacement of the indenter measured by laser displacement sensor and capacitance displacement sensor, respectively. P, h 1 , h 2 , h 3 and penetration depth h have relationships as follows

Idea of device design
where and are calibration coefficients. According to equations (6)-(8), penetration load P and depth h can be obtained, and material parameters can be calculated by the Oliver-Pharr method.

Design and analysis of precise driving units
Nanoindentation and scratch test technology mainly involves precise driving and precise measuring technology. For precise driving, there are many choices, for example, electromagnetic driver, shape memory alloy driver, micro-film, micro-beam and so on. Up to now, most of indentation devices are large because of using of electromagnetic and electrostatic drivers which also need complex control. Due to size limitation of SEM and TEM, these large indentation devices can not be used to realize in situ indentation test. So it is necessary to find more suitable driving mechanism to ensure miniaturization of indentation device. In this section, based on early research foundation on the piezoelectricdriven and flexure hinge, kinds of precise driving units realized by piezoelectric actuator and flexure hinge were designed.

Piezoelectric actuator
Principle of piezoelectric actuator is shown in Fig.5 which is based on the inverse piezo effect. The piezoelectric actuator will deform when an electric voltage signal is applied to it. The amount of movement is a function of the polarity of the voltage applied and the direction of the polarization vector. Piezoelectric actuator takes many advantages of small size, unlimited resolution, large force generation, fast response, low power consumption and no wear. So it is widely used in fields of actuators, micro-and nano-positioning, laser tuning, active vibration damping, micropumps, and so on. In this chapter, two kinds of piezoelectric actuator are selected, PT200/10*10/40 piezoelectric stack used for z axis and AE0505D16F for x-y axis. Hysteresis is an inherent property of piezoelectric ceramic. Hysteresis of the two kinds of piezoelectric stacks was measured and shown in Fig.6 and Fig.7. In Fig.6 and Fig.7, there are two curves, respectively. One is the output displacement when voltage increases and the other is the output displacement when the voltage decreases. It is obvious that the displacement is different at the same voltage and the two curves are not symmetrical. The hysteresis H can be expressed where D DMAX is the maximum difference of displacement at the same voltage; D S is the total output displacement. In Fig.6, the maximum difference of displacement is about 1.15μm at voltage 45V and the total output displacement is 12.91μm. According to equation (9), the hysteresis is about 8.91% for AE0505D16F. In Fig.7, the maximum difference of displacement is about 5.49μm at voltage 45V and the total output displacement is 35.92μm. According to equation (9), the hysteresis is about 15.28% for PT200/10*10/40 piezoelectric stack. So hysteresis is different for different kinds of piezoelectric stacks and some measurements for example close-loop control should be taken to decrease the hysteresis for special application.

Flexure hinges
Materials and structures will deform under the external load and the deformation is usually very small and linear. Those are the working principle of flexure hinges. Compared to conventional mechanisms with sliding and rolling bearings, the flexure hinge takes many advantages of simple and compact structure, no lubrication and high positioning accuracy. For these reasons, flexure hinges have been widely used in fields of micro-positioning, micromanipulation, micro-gripper and so on. Stiffness and output displacement of flexure hinges are contradictory to each other. Larger elastic deformation is hoped to ensure output displacement. On the other hand, enough stiffness is also very important to ensure the device having good dynamic characteristic and the anti-interference ability. Also internal stress of materials should not exceed permissible stress. Currently, there are four kinds of materials-beryllium bronze, aluminium, steel and titanium alloy to be used to fabricate flexure hinges. For these four kinds of materials, titanium alloy has the highest inherent frequency and best anti-interference ability, while the displacement is too small. In contrast, beryllium bronze has larger elastic deformation, but cost of these two kinds of materials is too high, and they are not suitable to make flexure hinges. Here, 65Mn was chosen to process them, which had numerous advantages of cheap price, high sensitivity, low elastic lag, high fatigue resistance, etc.

Z-axis flexure hinge
Z-axis precise driving unit consists of z-axis flexure hinge and z-axis piezoelectric actuator, and it is used to realize the precise loading and unloading of the indenter. Z-axis piezoelectric actuator was PT200/10*10/40 piezoelectric stack. Large output displacement was given to z-axis flexure hinge realized by the level-type enlarging structure as shown in Fig.8, which was convenient to estimate the initial contact point. Static and modal analysis was carried out to evaluate strength and dynamic performance of z-axis flexure hinge by finite element method. Displacement load of 10μm was applied to the area where piezoelectric actuator was located. And analysis results were shown in Fig.9 and Fig.10. As shown in Fig.9, displacement of 42μm was obtained at the output end which indicated that magnification of the flexure hinge was about 4, while the maximum stress was 33MPa, which was less than permissible stress of 65Mn being 432MPa. The first three natural frequencies of the flexure hinge were about 1133.7Hz、1366.7Hz、4243.5Hz which indicated that z-axis flexure hinge had good stability in the indentation device working at low frequency condition.

x-y precise positioning hinge
x-y precise positioning platform including y-axis macro-adjusting mechanism, x-y precise positioning hinge and x-y piezoelectric actuators, is used to realize precise positioning of sample during indentation test and to realize precise motion of the sample during the scratch test. y-axis macro-adjusting mechanism as well as another two macro-adjusting mechanisms was bought directly and the models were GCM-1253001BM. x-y piezoelectric actuators were AE0505D16F piezoelectric stacks. The designed x-y precise positioning hinge was shown in Fig.11. Static and modal analysis results were shown in Fig.12 and Fig.13. The maximum stress was 158.6MPa, which was less than permissible stress of 65Mn being 432MPa. The first three natural frequencies of the flexure hinge were about 2669.5 Hz, 4831.0 Hz, 6281.8 Hz and the hinge had good dynamic performance.

Precise measuring unit
Parameters of materials are calculated by the penetration load and depth data. Because it is on very small scales, very high accuracy and resolution is required for sensors. As mentioned in section 3, penetration load and depth is obtained by indirect measurement method. The displacement amplification structure and two displacement sensors are used to realize measurement. The laser displacement sensor LK-G10 which has resolution of 10nm is used to measure the output end (the right) of the displacement amplification structure, and the capacitance displacement sensor MDSL-0500M6-1 which has resolution of 10nm is used to  In this section, we will focus on design and analysis of the displacement amplification structure which plays an important role in measuring unit as well as entire indentation device. The designed displacement amplification structure with a lever amplification mechanism is shown in Fig.14. The sample is located on point A during the indentation test. Work principle is shown in Fig.15. Assumptions are as follows: 1. The upper thin plate rotates around the point O and the rotation angle is so small that the plate can be thought to be horizontal; 2. There is no bend deformation for the upper thin plate during the rotation.  As shown in Fig.15, the displacement amplification structure not only works as a sample stage but also has the function of amplifying displacement signal. According to Fig.4 and Fig.15, the magnification factor is given by where a is the horizontal distance between point A and the rotation point O; b is the horizontal distance between point B and the rotation point O.
In this chapter, the magnification factor k was designed to be 4. Static and modal analysis was carried out to evaluate the strength, output displacement and dynamic performance of displacement amplification structure. Displacement load of 10μm was applied to point A. Output displacement of point B was 38.2μm shown in Fig.16, and the maximum stress was 6.04MPa which was less than permissible stress of 65Mn being 432MPa. Fig.17 was the first three mode shapes and the first three natural frequencies were 170.53Hz, 407.42Hz, and 909.51Hz. The displacement amplification structure would bend or rotate at the structure' first three natural frequencies which were a little low. So the work frequency of the indentation device should be away from natural frequencies to avoid sympathetic vibration and also it is better to take measures to alleviate and isolate the vibration existing in the surroundings.  1mN and 1mN, respectively. Analysis results were shown in Fig.18 and Fig.19 respectively. In these two figures, the amplification structure had 43.3nm and 433nm output displacements corresponding to the loads 0.1mN and 1mN. The magnifications of input loads and output displacements were coincident which indicated that the structure had good linear output performance. Output displacement of 43.3nm can be detected easily by laser displacement sensor with the resolution of 10nm. That was to say the load resolution of the displacement amplification structure was higher than 0.1mN.

Prototype design
According to the analysis in the previous sections, the catia model of designed indentation device was shown in Fig.20. Parts were fabricated and the prototype was assembled as shown in Fig.21. The brief work processes are as follows: 1. Clear the sample surface; 2. Install the sample on the displacement amplification structure; 3. Install the indenter and lock it with the lock screw; 4. Adjust the macro-adjusting mechanism to make the laser displacement sensor in the suitable measuring range( the indicator light will be green); 5. Apply voltage to electronic components and wait for a moment to make the components stabilization; 6. Adjust the z-axis macro-adjusting mechanism to make the indenter close to the sample surface. When it is very close to the surface, stop macro-adjusting mechanism and apply voltage to the z-axis piezoelectric stack. Use the change of the read of the laser displacement sensor to judge the contact between the indenter and the sample surface; 7. Choose suitable voltage step to load and unload the indenter. During the process, use software to record the data sent by the A/D card. And then, process the data and obtain parameters of the sample.

Experiments
In this section, experiments of the designed indentation device were carried out to evaluate its performances. These experiments mainly include calibration of laser and capacitance displacement sensors as well as the displacement amplification structure, output performance test of the designed x-y precise positioning hinge and z-axis precise driving hinge and indentation test of optical glass.

Calibration experiments of the sensors
Use z-axis precise driving unit to generate precise displacement signal. Use the laser and capacitance displacement sensors to measure the signal, respectively. And then, record the reading and the output voltage, respectively. The experiment data was processed with the criteria of least squares. Curves and equations of linear fitting were obtained, which were shown in Fig.22 and Fig.23. From these two figures, relation between measured Fig. 22. Calibration curve of the laser displacement sensor www.intechopen.com displacement h 1 /μm and output voltage X 1 /V of the laser displacement sensor was h 1 =9.967×X 1 -17.887 and relation between measured displacement h 2 /μm and output voltage X 2 /V of the capacitance displacement sensor was h 2 =49.538×X 2 -194.27. Their linear correlation coefficients R 2 were both close to 1, which showed the two sensors had high linearity. So the equations of linear fitting can be used in the experiment without correction.   From these two figures, relation between the load P/mN and output displacement h 1 /μm of point B of the displacement amplification structure was P=1.1227Xh 1 -0.426, and relation between deformation h 3 /μm of point A and output displacement h 1 /μm of point B is h 3 =0.2783×h 1 +0.5153. Their linear correlation coefficients R 2 were 0.9998 and 0.9991, which indicated that output of the structure was linear. Also equations of linear fitting can be used in the experiment without correction.

Output performance of x-y precise positioning hinge and z-axis precise driving hinge
Output performances of x-y precise positioning hinge and z-axis precise driving hinge were tested by laser displacement sensor. The range of applied voltage was form 0V to 120V for x and y piezoelectric stacks with step of 5V while the range was from 0V to 90V for z axis piezoelectric stack with step of 5V or various steps (5V to 1V). The testing results were shown in Fig.26 -Fig.29.  As shown in Fig.26 and Fig.27, the output performances were large different for x and y axis. The maximum output displacement was 1.86μm in x direction while it was 8.92μm in y direction. For 24 steps, the total output displacement was 77.5nm and 371.7nm in x and y directions respectively. So it had different output displacement resolution in the two directions. These differences were caused by different stiffness of flexure hinges in x and y directions. Fig.28 was the output curve of z-axis precise driving hinge when applied voltage was from 0V to 90V with step of 5V. The maximum output displacement was about 60μm at voltage of 90V, which was large than the maximum output displacement of z piezoelectric stack about 40μm. So the z-axis precise driving hinge had the function of displacement magnification. Fig.29 was the output curve of z-axis precise driving hinge with various steps from 5V to 1V. Due to the hysteresis of piezoelectric stack, the curve was asymmetrical. Through the manner of various steps, it was convenient to realize the judgement of contact between the indenter and the sample with large step and to realize loading and unloading process with small step. Also it can be used to research the mechanical performance of materials under different steps. In order to evaluate performance of the unit, parameters were defined as follows. D s was the maximum output displacement. D r was the residual displacement. was the absolute error. α was the average error of each step. And then, and can be expressed where n was the total steps in a test circle. According to equations (11) and (12), parameters were obtained and listed in Table 4. When the voltage step decreases, higher resolution will be obtained and unlimited resolution will be possible under ideal conditions.
x axis y axis z axis

Indentation test of optical glass
Indentation experiments of optical glass were carried out and the P-h curves were shown in Fig.30 and Fig.31. www.intechopen.com The three polynomial fitting was used to fit the curve of partial unloading data. Fig.32 was fitted curves and equations corresponding to Fig.30, and Fig.33 was fitted curves and equations corresponding to Fig.31. As shown in Fig.32 and Fig.33, the correlation coefficients were close to 1 which indicated that the selected order was suitable. So the relation between load P and the depth of partial unloading for the two experiments were given： Compared with the result by commercial indentation device shown in Fig.36 (Zhao et al., 2009), the measured penetration depth was larger at a same load which was caused by structure compliance, indenter installation as well as the sample surface process, and it would be reduced and eliminated in our future work. The indentation morphology was obtained through high resolution optical microscope shown in Fig.37. The material generated some cracks which had significant value to analyze the damage mechanism especially that the full measuring process was monitored by SEM, TEM as well as other monitoring methods. The designed indentation device integrating flexure hinges and piezoelectric actuators is smaller than commercial indentation devices but can realize high precise measurement which gives solid foundation for our future work. We will make the device more precise and design smaller indentation device that can be located on the platform of SEM to realize in situ measurement.

Conclusions
A new kind of indentation measurement method through two displacement sensors and a displacement amplification structure was proposed and established. Based on this method, a miniaturization indentation device was designed and analyzed. Hysteresis of two kinds of piezoelectric stacks were measured and analyzed. The hysteresis was different for different piezoelectric stacks.
Two key components of the device, the precise driving and precise measuring units, were designed and analyzed. Results from static and modal analysis indicated that designed hinges and amplification structure had enough strength. The dynamic performances of flexure hinges were good but the natural frequencies of the amplification structure were low. So the work frequency of the indentation device should be away from the natural frequencies of the amplification structure to avoid sympathetic vibration and also it is better to take measures to alleviate and isolate the vibration existing in the surroundings. Calibration experimental results of the two displacement sensors and the amplification structure showed that they all had high linearity. The amplification structure had functions of stage and load-sensing, and can be used to realize precise load measurement. Output performances of flexure hinges were measured and obtained. They all had stable output displacement and the output resolution was related with the voltage step applied to the piezoelectric stack. Indentation experiments of optical glass were carried out. Relation curves between load and penetration depth were obtained. Contact stiffness and hardness were discussed. Curves obtained from the designed device and commercial device were compared and analyzed. The designed indentation device had smaller volume and can realize indentation test but the accuracy should be improved more.
The future work will focus on designing smaller indentation device and realizing in situ experiments.