rus
Issue #7-8/2023
I.V.Krasnogorov, A.A.Rusakov, V.N.Reshetov
USE OF A FORCE TRANSFORMER TO IMPROVE THE METROLOGICAL CHARACTERISTICS OF NANOHARDNESS TESTER
USE OF A FORCE TRANSFORMER TO IMPROVE THE METROLOGICAL CHARACTERISTICS OF NANOHARDNESS TESTER
DOI: https://doi.org/10.22184/1993-8578.2023.16.7-8.434.442
The equipment for instrumental nanoindentation traditionally represents a product containing a displacement sensor and a force-generating element operating in the nanoscale range of displacements and forces. At the same time, all working elements of the nanoindenter have a system of elastic attachment to a rigid body. However, part of the force generated by the actuator is spent on the deformation of the suspension system of the movable elements. This paper considers the design of a nanohardometer, in which a force cell is introduced that allows measuring the real value of the indentation force without the need to take into account the deformation losses of the elastic elements of the nanohardometer. Such modification of the product, according to the authors, allows to significantly increase the accuracy of measuring the mechanical properties of soft materials and thin coatings.
The equipment for instrumental nanoindentation traditionally represents a product containing a displacement sensor and a force-generating element operating in the nanoscale range of displacements and forces. At the same time, all working elements of the nanoindenter have a system of elastic attachment to a rigid body. However, part of the force generated by the actuator is spent on the deformation of the suspension system of the movable elements. This paper considers the design of a nanohardometer, in which a force cell is introduced that allows measuring the real value of the indentation force without the need to take into account the deformation losses of the elastic elements of the nanohardometer. Such modification of the product, according to the authors, allows to significantly increase the accuracy of measuring the mechanical properties of soft materials and thin coatings.
Теги: actuator capacitive sensor force transformer hardness instrumental indentation loading system modulus of elasticity nanoindenter power cell актюатор емкостной датчик инструментальное индентирование модуль упругости наноиндентор силовая ячейка система нагружения твердость трансформатор силы
INTRODUCTION
When designing force-loading assemblies in instruments for precision measurement of mechanical properties, called nanohardness testers or nanoindentors, one of the most common ways to control the load on the indenter is an electromagnetic actuator [1]. A capacitive differential sensor is often used to measure displacement of the movable part associated with the indenter. Used together, these solutions allow, with some limitations, to record the diagram of the dependence of the applied load on the indenter displacement during indentation into the sample surface and to measure mechanical properties by the tool indentation method [2, 3].
The technical novelty of the proposed solution is in the use of a combined measuring module, which allows to minimise the moving part mass of the device and to register with the help of capacitive sensors not only indenter movement, but also the force of interaction with the material under study. The introduction of a force-measuring cell included between the electromagnetic actuator and the diamond indenter in the device design allowed to significantly increase the resolving power of the nanohardness tester in the channel of pressure force while maintaining the range of available indentation depths at the level of at least 100 µm. The range of maximum indentation loads is about 100 mN, which is not critical for the use of such a device in the real nanoscale range of indentation depths and the microrange of pressing forces.
PECULIARITIES OF THE DYNAMIC NANOHARDNESS TESTER DESIGN
Hardness and modulus of elasticity are key characteristics of almost any structural material. The most common method of hardness measurement today is the Vickers hardness method. In this method, indentation with a given load is applied to the surface of a specimen, and after that, the geometric dimensions of this indentation (namely, the lengths of the diagonals) are measured using visualisation tools and the area is calculated [4]. The hardness of the material is calculated as the ratio of the applied load to the area of the residual indentation. Young’s modulus is usually determined by acoustic methods, based on the sound speed in a cylindrical specimen and density of the material [5].
The tool indentation method [2] was originally developed to measure hardness and Young’s modulus of materials at those load levels when measurement of the indentation area is impossible due to diffraction limitations of optical microscopy. However, it gradually spread not only to the area of microscopic loads, but also to the range of indentation loads up to 10 N, which noticeably exceeds the minimum loads of Vickers microhardness testers in the range of hundredths and tenths of Newton.
The indentation depths used today in nanohardness testers have fallen below 10 nm, and indentation sizes have become less than 100 nm, with a stable radius of curvature of the tip of the indenter pyramid tip less than 30 nm. Resolution of measuring systems of such devices in terms of displacement and force is fractions of nm and µN, the maximum depths of indenter immersion and pressing force are tens of µm and fractions of Newton. When working in the nanoscale range with clamping forces less than 50 mN and indentation depths up to 10 μm, electrostatic actuators combined with a capacitive displacement sensor are most often used [6]. In the micro range, the scheme with an electromagnetic actuator and a differential capacitor displacement sensor is the most popular [7]. The use of a force-measuring cell acting as a force transformer makes it possible to combine the advantages of a purely capacitive design with a combined design and, in devices with an electromagnetic actuator, to achieve a force resolution characteristic of purely capacitive circuits.
Instrument indentation devices are often referred to as nanoindenters or nanohardness testers. Nanoindenters are fitted on vibration-isolated platforms and placed inside thermally insulated boxes. Typically, it is the seismic noise level and temperature variations in the room that limit measurement accuracy and available indentation force level. To reduce influence of vibration interference, the mass of the moving elements associated with the diamond indenter is reduced, which makes it possible to increase the resonance frequency of the suspension system with unchanged stiffness of the membranes holding an indenter. The discussed technical solution with a power cell, minimising the weight of the moving indenter system, solves this problem as well.
The distinctive features of the developed design of the high-precision nanohardness tester are the use of a single electromagnetic actuator and two independent capacitive sensors measuring displacement of the actuator and a diamond indenter, as well as the presence of a power cell with a third differential capacitive displacement sensor, which allows measuring the clamping force.
The proposed design of the nanohardness tester consists of a rigid body 1 with an actuator 2 fixed on it with a moving coil 3 connected with a rod 4, a capacitive sensor 5 and an indenter 15 mounted on the free end of the rod 10. The measuring indentation module of the nanohardness tester is provided with a power cell 7 fixed inside the body 1 of the device on elastic hangers of membrane type 6 and 13, to the upper part of which is attached an intermediate movable rod 4 connected with the moving coil 3 of the actuator 2 and with the capacitive sensor 5 of the actuator 2, the movable lining 17 of which is fixed on the intermediate movable rod 4, for measuring the movement of the body of the power cell 7 in relation to the body 1 of the device. Inside the body of the power cell 7 are mounted flexible membranes 8 and 9, on which, coaxially with the intermediate rod 4, is fixed a working rod 10 with a diamond indenter 15 at the end and a capacitive force sensor 12, which measures interaction force between the indenter and the surface, controlling movement of the working rod 10 in relation to the body of the power cell 7. A capacitive sensor 14 is placed under the lower elastic suspension 9 to measure movement value of the working rod 10 in relation to the body 1 of the device and to determine the immersion depth of the indenter 15 in the material under test 16. The linings 18 and 19 of the capacitive force sensor 12 and the capacitive sensor 14 of the depth of movement are fixed on the moving working rod 10.
This kinematic scheme makes it possible to reduce the mass of the elements directly connected with the diamond indenter and separates the main heat-generating element of the nanohardness tester (electromagnetic actuator coil) from the capacitive sensors measuring force and embedding depth. A three-dimensional model and a photograph of the indentation module built in accordance with the principles described above are shown in Fig.2.
During loading and unloading under the action of the actuator 2 through the intermediate rod 4 there is a movement of the force measuring cell 7 and indenter 15 in direction of the tested material 16. After mechanical contact of the indenter 15 fixed on the working rigid rod 10 with the surface of the sample 16 there is deformation of the force cell 7 and with the help of the capacitive sensor 18 there is control of the pressing force of the indenter 15 during the process of tool indentation. The signal from the lower capacitive sensor 19 is used to measure depth of the indenter into the material. The signal from the upper capacitive sensor 17 is used to control movement of the power cell body. This measuring channel is redundant and serves for verification of data received from the sensors of plunging depth and pressing force. It also allows you to control the amplitude and phase of the oscillatory motion of the power cell when the instrument is operating in the dynamic contact stiffness measurement mode (DMA).
Three differential capacitive sensors measuring the depth of the indenter immersion into the material under test, the level of deformation of the elastic elements of the force-loading cell and the movement of the electromagnetic actuator allow obtaining the values of mechanical properties not only in the quasi-static deformation mode, but also in the dynamic testing mode, when the mechanical properties are measured by superimposing sinusoidal deformation on the standard load-depth curve (DMA). As shown in laboratory tests, the proposed kinematic scheme achieves the following performance limits when performing mechanical property measurements:
working range of forces applied during indentation –
100 mN;
digital resolution of the force measurement channel – 0.01 µN;
working stroke of the diamond indenter during indentation – 100 µm;
digital resolution of the displacement measurement channel – 0.01 nm;
dimensions of the indentation module – about one cubic decimetre;
weight – less than one kilogram;
electrical power consumed by the module – about one watt.
The minimum loads and indentation depths described for this type of instrument are generally consistent with natural seismic noise conditions in absence of industrial interference and the use of a good vibration isolation system. The actual noise level of the force and displacement channels is dependent on the specific operating conditions of the instrument and is labelled "lab dependent". The digital resolution of the force and displacement channels is usually an order of magnitude lower than the declared "lab dependent" noise level.
The proposed technical solution consists in a lightweight system of diamond indenter suspension, control of the clamping force and measurement of the nanohardness tester oscillating system parameters during both conventional and dynamic tool indentation. At the same time, measuring accuracy of load-depth curve is increased and the functional capabilities of the nanohardness tester are expanded in terms of measuring the mechanical properties of viscoelastic materials, including polymeric and biological ones. This is achieved by increasing sensitivity to the force occurring in the area of contact of the indenter with the sample and absence of influence of the free stroke of the rod on the force-measuring cell signal.
Analysis of the dynamic model shows that elasticity coefficient of the suspension of the power cell can be 100 times greater than elasticity coefficient of the working rod suspension in the power cell. The weight of the working rod with the indenter is 10 times less than the weight of the power cell and the actuator coil. Thus, the resonant frequency of the suspension system of the power cell is 3 times higher than the resonant frequency of the system consisting of the rod with the indenter, the centre lining of the differential capacitor and the flexible membranes of the power cell.
The developed measuring module of the high-precision nanohardness tester has possibility to control dynamic behaviour of the indenter suspension system in the frequency band exceeding the frequency of the main resonance of the indenter. The control of the phase and amplitude of forced oscillations of the indenter is possible due to the joint processing of signals from three capacitive sensors measuring the movement of the main elements involved in the indentation process. The execution of the force-measuring cell in the form of a rigid body with flexible membranes located inside, on which a carbon rod with an indenter is fixed, provides movement of the rod inside the force cell along its axis due to elasticity of the membranes and makes it possible to carry out instrumental indentation of both soft and hard materials.
Installation of three capacitive sensors with ability to measure the immersion depth, pressure force and displacement of the power cell provides full control of the oscillating system included in the nanohardness tester, with ability to measure the dynamic characteristics of the indenter suspension system and isolation of viscoelastic forces arising in the interaction area between the indenter and the tested material. This capability is particularly relevant for mechanical property mapping and dynamic indentation, when a sinusoidal alternating force is applied to the progressive motion of the indenter. The presence of three capacitive sensors makes it possible to control behaviour of the actuator by controlling movements of the force-measuring cell through measurements of the cell’s displacement relative to the device body. Adding the capacitive sensor measuring the displacements of the force cell allows us to fully describe the behaviour of the paired resonant system of this nanohardness tester and to take into account changes in their behaviour during the indentation process due to the influence of contact stiffness on the resonant properties of the dynamic nanohardness tester. The movable system of a nanohardness tester for tool indentation consists of two coupled oscillating circuits – the suspension system of the power cell with its resonant frequency and the system consisting of the rod with the indenter and flexible membranes of the power cell with the other resonant frequency. Threefold separation of resonance frequencies facilitates measurements of dynamic characteristics of the materials under study. The use of different force-measuring cells as a mechanical transformer that transforms macroscopic displacement of the actuator into a microscopic force of the indenter pressing against the surface of the tested material, allows to produce devices adapted to the use when working with different materials according to a single design scheme. The use of a soft force cell is convenient when working with biological and polymeric materials that require measurement of small forces at large indenter displacements.
CONCLUSIONS
The new design of a highly sensitive nanohardness tester considered in this work demonstrates possibility of achieving working loads at indentation at the level of micronewtons. This range of the main operating characteristic of the device will allow to carry out studies of mechanical properties with spatial resolution in the sample plane better than 50 nm, and in depth about 10 nm, will allow to operate with heterogeneous materials and thin functional coatings on both soft and hard substrates.
Instrumentation for tool indentation has reached the development level at it is relevant to use it both in scientific laboratories and in real production conditions for the control of machine-building products. The main technical difficulties of the instrumental implementation of the tool indentation method have been successfully overcome, the data obtained are well interpreted, the level of automation of the measurement process is high, and one operator can operate several instruments at once. Regular international comparisons and availability of a domestic standard in the field of tool indentation and standard samples with assigned characteristics make this method convenient for wide application.
PEER REVIEW INFO
Editorial board thanks the anonymous reviewer(s) for their contribution to the peer review of this work. It is also grateful for their consent to publish papers on the journal’s website and SEL eLibrary eLIBRARY.RU.
Declaration of Competing Interest. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
When designing force-loading assemblies in instruments for precision measurement of mechanical properties, called nanohardness testers or nanoindentors, one of the most common ways to control the load on the indenter is an electromagnetic actuator [1]. A capacitive differential sensor is often used to measure displacement of the movable part associated with the indenter. Used together, these solutions allow, with some limitations, to record the diagram of the dependence of the applied load on the indenter displacement during indentation into the sample surface and to measure mechanical properties by the tool indentation method [2, 3].
The technical novelty of the proposed solution is in the use of a combined measuring module, which allows to minimise the moving part mass of the device and to register with the help of capacitive sensors not only indenter movement, but also the force of interaction with the material under study. The introduction of a force-measuring cell included between the electromagnetic actuator and the diamond indenter in the device design allowed to significantly increase the resolving power of the nanohardness tester in the channel of pressure force while maintaining the range of available indentation depths at the level of at least 100 µm. The range of maximum indentation loads is about 100 mN, which is not critical for the use of such a device in the real nanoscale range of indentation depths and the microrange of pressing forces.
PECULIARITIES OF THE DYNAMIC NANOHARDNESS TESTER DESIGN
Hardness and modulus of elasticity are key characteristics of almost any structural material. The most common method of hardness measurement today is the Vickers hardness method. In this method, indentation with a given load is applied to the surface of a specimen, and after that, the geometric dimensions of this indentation (namely, the lengths of the diagonals) are measured using visualisation tools and the area is calculated [4]. The hardness of the material is calculated as the ratio of the applied load to the area of the residual indentation. Young’s modulus is usually determined by acoustic methods, based on the sound speed in a cylindrical specimen and density of the material [5].
The tool indentation method [2] was originally developed to measure hardness and Young’s modulus of materials at those load levels when measurement of the indentation area is impossible due to diffraction limitations of optical microscopy. However, it gradually spread not only to the area of microscopic loads, but also to the range of indentation loads up to 10 N, which noticeably exceeds the minimum loads of Vickers microhardness testers in the range of hundredths and tenths of Newton.
The indentation depths used today in nanohardness testers have fallen below 10 nm, and indentation sizes have become less than 100 nm, with a stable radius of curvature of the tip of the indenter pyramid tip less than 30 nm. Resolution of measuring systems of such devices in terms of displacement and force is fractions of nm and µN, the maximum depths of indenter immersion and pressing force are tens of µm and fractions of Newton. When working in the nanoscale range with clamping forces less than 50 mN and indentation depths up to 10 μm, electrostatic actuators combined with a capacitive displacement sensor are most often used [6]. In the micro range, the scheme with an electromagnetic actuator and a differential capacitor displacement sensor is the most popular [7]. The use of a force-measuring cell acting as a force transformer makes it possible to combine the advantages of a purely capacitive design with a combined design and, in devices with an electromagnetic actuator, to achieve a force resolution characteristic of purely capacitive circuits.
Instrument indentation devices are often referred to as nanoindenters or nanohardness testers. Nanoindenters are fitted on vibration-isolated platforms and placed inside thermally insulated boxes. Typically, it is the seismic noise level and temperature variations in the room that limit measurement accuracy and available indentation force level. To reduce influence of vibration interference, the mass of the moving elements associated with the diamond indenter is reduced, which makes it possible to increase the resonance frequency of the suspension system with unchanged stiffness of the membranes holding an indenter. The discussed technical solution with a power cell, minimising the weight of the moving indenter system, solves this problem as well.
The distinctive features of the developed design of the high-precision nanohardness tester are the use of a single electromagnetic actuator and two independent capacitive sensors measuring displacement of the actuator and a diamond indenter, as well as the presence of a power cell with a third differential capacitive displacement sensor, which allows measuring the clamping force.
The proposed design of the nanohardness tester consists of a rigid body 1 with an actuator 2 fixed on it with a moving coil 3 connected with a rod 4, a capacitive sensor 5 and an indenter 15 mounted on the free end of the rod 10. The measuring indentation module of the nanohardness tester is provided with a power cell 7 fixed inside the body 1 of the device on elastic hangers of membrane type 6 and 13, to the upper part of which is attached an intermediate movable rod 4 connected with the moving coil 3 of the actuator 2 and with the capacitive sensor 5 of the actuator 2, the movable lining 17 of which is fixed on the intermediate movable rod 4, for measuring the movement of the body of the power cell 7 in relation to the body 1 of the device. Inside the body of the power cell 7 are mounted flexible membranes 8 and 9, on which, coaxially with the intermediate rod 4, is fixed a working rod 10 with a diamond indenter 15 at the end and a capacitive force sensor 12, which measures interaction force between the indenter and the surface, controlling movement of the working rod 10 in relation to the body of the power cell 7. A capacitive sensor 14 is placed under the lower elastic suspension 9 to measure movement value of the working rod 10 in relation to the body 1 of the device and to determine the immersion depth of the indenter 15 in the material under test 16. The linings 18 and 19 of the capacitive force sensor 12 and the capacitive sensor 14 of the depth of movement are fixed on the moving working rod 10.
This kinematic scheme makes it possible to reduce the mass of the elements directly connected with the diamond indenter and separates the main heat-generating element of the nanohardness tester (electromagnetic actuator coil) from the capacitive sensors measuring force and embedding depth. A three-dimensional model and a photograph of the indentation module built in accordance with the principles described above are shown in Fig.2.
During loading and unloading under the action of the actuator 2 through the intermediate rod 4 there is a movement of the force measuring cell 7 and indenter 15 in direction of the tested material 16. After mechanical contact of the indenter 15 fixed on the working rigid rod 10 with the surface of the sample 16 there is deformation of the force cell 7 and with the help of the capacitive sensor 18 there is control of the pressing force of the indenter 15 during the process of tool indentation. The signal from the lower capacitive sensor 19 is used to measure depth of the indenter into the material. The signal from the upper capacitive sensor 17 is used to control movement of the power cell body. This measuring channel is redundant and serves for verification of data received from the sensors of plunging depth and pressing force. It also allows you to control the amplitude and phase of the oscillatory motion of the power cell when the instrument is operating in the dynamic contact stiffness measurement mode (DMA).
Three differential capacitive sensors measuring the depth of the indenter immersion into the material under test, the level of deformation of the elastic elements of the force-loading cell and the movement of the electromagnetic actuator allow obtaining the values of mechanical properties not only in the quasi-static deformation mode, but also in the dynamic testing mode, when the mechanical properties are measured by superimposing sinusoidal deformation on the standard load-depth curve (DMA). As shown in laboratory tests, the proposed kinematic scheme achieves the following performance limits when performing mechanical property measurements:
working range of forces applied during indentation –
100 mN;
digital resolution of the force measurement channel – 0.01 µN;
working stroke of the diamond indenter during indentation – 100 µm;
digital resolution of the displacement measurement channel – 0.01 nm;
dimensions of the indentation module – about one cubic decimetre;
weight – less than one kilogram;
electrical power consumed by the module – about one watt.
The minimum loads and indentation depths described for this type of instrument are generally consistent with natural seismic noise conditions in absence of industrial interference and the use of a good vibration isolation system. The actual noise level of the force and displacement channels is dependent on the specific operating conditions of the instrument and is labelled "lab dependent". The digital resolution of the force and displacement channels is usually an order of magnitude lower than the declared "lab dependent" noise level.
The proposed technical solution consists in a lightweight system of diamond indenter suspension, control of the clamping force and measurement of the nanohardness tester oscillating system parameters during both conventional and dynamic tool indentation. At the same time, measuring accuracy of load-depth curve is increased and the functional capabilities of the nanohardness tester are expanded in terms of measuring the mechanical properties of viscoelastic materials, including polymeric and biological ones. This is achieved by increasing sensitivity to the force occurring in the area of contact of the indenter with the sample and absence of influence of the free stroke of the rod on the force-measuring cell signal.
Analysis of the dynamic model shows that elasticity coefficient of the suspension of the power cell can be 100 times greater than elasticity coefficient of the working rod suspension in the power cell. The weight of the working rod with the indenter is 10 times less than the weight of the power cell and the actuator coil. Thus, the resonant frequency of the suspension system of the power cell is 3 times higher than the resonant frequency of the system consisting of the rod with the indenter, the centre lining of the differential capacitor and the flexible membranes of the power cell.
The developed measuring module of the high-precision nanohardness tester has possibility to control dynamic behaviour of the indenter suspension system in the frequency band exceeding the frequency of the main resonance of the indenter. The control of the phase and amplitude of forced oscillations of the indenter is possible due to the joint processing of signals from three capacitive sensors measuring the movement of the main elements involved in the indentation process. The execution of the force-measuring cell in the form of a rigid body with flexible membranes located inside, on which a carbon rod with an indenter is fixed, provides movement of the rod inside the force cell along its axis due to elasticity of the membranes and makes it possible to carry out instrumental indentation of both soft and hard materials.
Installation of three capacitive sensors with ability to measure the immersion depth, pressure force and displacement of the power cell provides full control of the oscillating system included in the nanohardness tester, with ability to measure the dynamic characteristics of the indenter suspension system and isolation of viscoelastic forces arising in the interaction area between the indenter and the tested material. This capability is particularly relevant for mechanical property mapping and dynamic indentation, when a sinusoidal alternating force is applied to the progressive motion of the indenter. The presence of three capacitive sensors makes it possible to control behaviour of the actuator by controlling movements of the force-measuring cell through measurements of the cell’s displacement relative to the device body. Adding the capacitive sensor measuring the displacements of the force cell allows us to fully describe the behaviour of the paired resonant system of this nanohardness tester and to take into account changes in their behaviour during the indentation process due to the influence of contact stiffness on the resonant properties of the dynamic nanohardness tester. The movable system of a nanohardness tester for tool indentation consists of two coupled oscillating circuits – the suspension system of the power cell with its resonant frequency and the system consisting of the rod with the indenter and flexible membranes of the power cell with the other resonant frequency. Threefold separation of resonance frequencies facilitates measurements of dynamic characteristics of the materials under study. The use of different force-measuring cells as a mechanical transformer that transforms macroscopic displacement of the actuator into a microscopic force of the indenter pressing against the surface of the tested material, allows to produce devices adapted to the use when working with different materials according to a single design scheme. The use of a soft force cell is convenient when working with biological and polymeric materials that require measurement of small forces at large indenter displacements.
CONCLUSIONS
The new design of a highly sensitive nanohardness tester considered in this work demonstrates possibility of achieving working loads at indentation at the level of micronewtons. This range of the main operating characteristic of the device will allow to carry out studies of mechanical properties with spatial resolution in the sample plane better than 50 nm, and in depth about 10 nm, will allow to operate with heterogeneous materials and thin functional coatings on both soft and hard substrates.
Instrumentation for tool indentation has reached the development level at it is relevant to use it both in scientific laboratories and in real production conditions for the control of machine-building products. The main technical difficulties of the instrumental implementation of the tool indentation method have been successfully overcome, the data obtained are well interpreted, the level of automation of the measurement process is high, and one operator can operate several instruments at once. Regular international comparisons and availability of a domestic standard in the field of tool indentation and standard samples with assigned characteristics make this method convenient for wide application.
PEER REVIEW INFO
Editorial board thanks the anonymous reviewer(s) for their contribution to the peer review of this work. It is also grateful for their consent to publish papers on the journal’s website and SEL eLibrary eLIBRARY.RU.
Declaration of Competing Interest. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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