rus
Issue #1/2016
А.Усеинов, В.Решетов, И.Маслеников, А.Русаков, Е.Гладких, В.Беспалов, Б.Логинов
Study of properties of thin films in dynamic mechanical analysis mode using NanoScan-4D scanning nano-hardness tester
Study of properties of thin films in dynamic mechanical analysis mode using NanoScan-4D scanning nano-hardness tester
The article describes the application of dynamic mechanical analysis to study the properties of thin films and presents
the experimental results of the surface topography measurement in the mode of resonant excitation
of the indenter suspension system
the experimental results of the surface topography measurement in the mode of resonant excitation
of the indenter suspension system
Теги: dynamic mechanical analysis indentation scanning nano-hardness tester динамический механический анализ индентирование сканирующий нанотвердомер
M
echanical testing of materials is an area of engineering materials science, whose task is to control the properties of the products during their manufacture and use. Dynamic mechanical analysis (DMA) as a kind of testing has firmly taken place among methods of measuring of hardness and real and imaginary parts of the elastic moduli, viscosity and creep of the material. Over the years many modifications of the devices for such methods, which operate with three-dimensional samples of special shape, mounted in special holders, have been developed. Dynamic methods of instrumental indentation, do not require the specialized test samples.
The basis of these methods is highly precise control of various characteristics of the interaction between the solid sharp tip (indenter) and the sample surface. The main parameters, which are used for determining the mechanical properties, are normal load applied to the indenter in contact with sample and the displacement of the indenter in the process of measurement. In addition, modern devices allow to control a number of additional characteristics, such as acoustic emission, electric current and lateral load.
Methods of measurement of mechanical properties based on the indentation, can be divided into static and dynamic. The most popular method of the static loading is the instrumental indentation, where indenter penetrates into the surface of the material with some speed, with followed monotonic unloading. The rate of penetration of the indenter is in the range from several tens of nanometers to tens of micrometers per second. During loading and unloading the values of normal load on the indenter and its displacement (introduction to the sample surface) are recorded. Next is the analysis of this diagrams using the methodology described in the standards GOST R 8.748-2011 [1] and ISO 14577 [2–4], and values of hardness, elastic modulus and other characteristics for the specified load or depth are calculated.
In dynamic method an oscillatory motion with a certain amplitude and frequency is superimposed on monotone implementation of the indenter. If the material has viscoelastic properties, then in the oscillatory system of "indenter-sample" effects arise that leading to change of the response amplitude and the phase difference between signal, which sets the oscillations, and the actual displacement of the indenter. Analysis of the amplitude and phase of forced oscillations allows to determine the elastic and viscous properties of the investigated sample depending on load, oscillation frequency and other parameters, such as temperature.
To determine the dependence of material properties on indentation depth, for most samples a single test using the dynamic method is more effective than multiple indentation cycles or multiple shots with partial unloading. During dynamic indentation the amplitude of oscillations of the indenter may be only a few nanometers, so this method allows to measure the properties of a very small near-surface volume of the material, which is impossible in the case of discrete unloading cycles [5].
Using load cycles of a sine wave at a high frequency, it is also possible to investigate the formation of cracks at the nanoscale by measuring of the contact stiffness, which changes indicate the micro-damages of the material [6].
Information about changing of the indentation depth during the recovery of the surface profile of the material allows to estimate the creep, the accuracy of which is higher when using the dynamic method because it is less sensitive to thermal drift than a standard instrumental indentation.
Dynamic mechanical analysis
A method of dynamic measurement presupposes the application of a sinusoidal force to the indenter during the indentation in the sample surface with subsequent measurement of the deformation response, which allows to determine the complex modulus of elasticity of the material.
Various materials can resist the applied load, as elastic or ductile substances. The former one store energy during the deformation and return to its original state when the load is removed. The latter remaining compressed after removal of the load and dissipate all the work of deformation as heat.
When using the dynamic method, the deformation ε depends on the frequency ω of the applied forces as follows:
ε = ε0 sin(tω). (1)
For a purely elastic body the Hooke's law is fair, and stress σ is proportional to the deformation (factor E is a Young's modulus):
σ = Eε, (2)
therefore, the load and deformation are cophased. In the viscous material, where there is no elastic deformation, the stress is given by Newton's law: σ = ηε and the stress arising in response to the load, differs from it in phase by δ = 90° [5]:
σ = σ0 sin(tω + δ). (3)
However, there are no absolutely elastic and absolutely inelastic bodies in nature. From the expressions (2) and (3), we obtain that the real and imaginary components of the Young's modulus E*=E'+iE'' are of the form:
. (4)
To describe the behavior of viscoelastic sample with stiffness S and damping ratio D two basic models presented in Fig.1 are usually applied:
Kelvin–Voigt model with spring (with stiffness coefficient S) and piston (with coefficient of viscous friction D) that are arranged in parallel;
Maxwell model with series-connected S- and D-elements.
In fact, only using a complex circuit with many connected components, which simulate the stiffness and damping, it is possible to describe the behavior of real viscoelastic material under load.
The polymers are materials with pronounced viscoelastic properties. The mechanical characteristics of the polymers depend on the microstructure and morphology. Compared with metals and ceramics, plastic, viscous and elastic properties of polymers vary within a wide range while changing the temperature and time of load. Such properties of polymers in the solid phase can be successfully investigated using dynamic mechanical analysis [7].
Experimental testing
The mode of dynamic mechanical analysis (DMA) is implemented and experimentally tested in the scanning nano-hardness tester "NanoScan-4D" (TISNCM, Russia). Nano-hardness tester "NanoScan-4D" is the only Russian measuring instrument, which allows to carry out complex studies of physical-mechanical properties of materials at submicron and nanometer scale of linear dimensions [8–11]. In the nano-hardness tester more than 30 various measuring techniques covering all known types of tests of mechanical properties are implemented. The field of application of NanoScan devices includes the studies of thin films, coatings and nanostructured materials ranging from soft polymers to superhard crystals and alloys. General view of the device is shown in Fig.2.
The oscillation frequency of the indenter in DMA mode typically vary from tenths to hundreds of hertz, while a typical amplitude is in the range from units to hundreds of nanometers. The applied load depends on the studied material and varies from several hundred of micronewton to tens of millinewton and even one of newton.
The frequency of the exciting force in a dynamic indentation mode is determined by the capabilities of the device and rarely is significantly higher than the resonance frequency of the suspension of indenter.
During the tests, using a standard sample of fused quartz, it was shown that for a homogeneous material, deformation of which does not depend on the loading rate, the dynamic method gives a constant value of hardness regardless of the embedding depth of the indenter. Within the error the hardness value coincides with the results of the static indentation.
To demonstrate the capabilities of the method a sample with a film of silver of a thickness of 180 nm on a glass substrate has been chosen. Fig.3 illustrates the change of hardness (a) and of real and imaginary part of elastic modulus (b) for the glass substrate (dotted line) and for silver film on the substrate depending on the contact depth. The obtained dependences show the decrease of Young's modulus and the increase of the hardness with increase of depth of embedding. Such behavior is typical for soft metal films on the glass surface, because the modulus of elasticity of metals is higher than that of glass, and the hardness is lower. Typical is the closeness to zero of the integrated component of the modulus of elasticity, since it is known that these materials are not viscous under deformation.
Natural application of a dynamic mode is obtaining images of the surface topography of the sample. To increase the sensitivity and performance of the device in this case, it is reasonable to excite oscillations at the resonant frequency of the suspension system. Fig.4 shows an example of profilograms of scratches on the surface of silver film at a load of 100 mn. It should be noted that the scratching and subsequent profiling are done with the same diamond indenter using scanning nano-hardness tester "NanoScan-4D".
For comparison Fig.5 shows an image of the same scratches, obtained by the atomic force microscopy using multifunctional device NTEGRA Prima (NT-MDT, Russia). In both images the characteristic piles arising during the scratching of metals are perfectly visible.
The possibility of imaging of the sample surface with nanometer spatial resolution enables to assess the level of roughness for choosing optimal parameters of mechanical test and, if necessary, for precise positioning of the indenter.
Conclusion
Dynamic mechanical analysis is a powerful research tool for many tasks. It is of particular interest in the study of mechanical properties of layered materials and multilayer structures because it allows to determine changes in the contact stiffness, elastic modulus, hardness and viscous losses as functions of the indentation depth. In addition, the continuous dynamic indentation can be used to measure the viscous properties and to determine conditions of the transition from elastic to plastic deformation. There is no doubt that the dynamic method is promising for obtaining three-dimensional images of the studied materials, and is more informative compared to the multi-cyclic indentation and to applying of series of pricks. Further development of the DMA will be associated with its use for spatial volumetric mapping (tomograms) of mechanical, elastic and viscous properties of near-surface volumes of materials. ■
The project was implemented with the financial support of the Ministry of education and science of the Russian Federation under the agreement No.14.577.21.0088 (unique identifier of project RFMEFI57714X0088).
echanical testing of materials is an area of engineering materials science, whose task is to control the properties of the products during their manufacture and use. Dynamic mechanical analysis (DMA) as a kind of testing has firmly taken place among methods of measuring of hardness and real and imaginary parts of the elastic moduli, viscosity and creep of the material. Over the years many modifications of the devices for such methods, which operate with three-dimensional samples of special shape, mounted in special holders, have been developed. Dynamic methods of instrumental indentation, do not require the specialized test samples.
The basis of these methods is highly precise control of various characteristics of the interaction between the solid sharp tip (indenter) and the sample surface. The main parameters, which are used for determining the mechanical properties, are normal load applied to the indenter in contact with sample and the displacement of the indenter in the process of measurement. In addition, modern devices allow to control a number of additional characteristics, such as acoustic emission, electric current and lateral load.
Methods of measurement of mechanical properties based on the indentation, can be divided into static and dynamic. The most popular method of the static loading is the instrumental indentation, where indenter penetrates into the surface of the material with some speed, with followed monotonic unloading. The rate of penetration of the indenter is in the range from several tens of nanometers to tens of micrometers per second. During loading and unloading the values of normal load on the indenter and its displacement (introduction to the sample surface) are recorded. Next is the analysis of this diagrams using the methodology described in the standards GOST R 8.748-2011 [1] and ISO 14577 [2–4], and values of hardness, elastic modulus and other characteristics for the specified load or depth are calculated.
In dynamic method an oscillatory motion with a certain amplitude and frequency is superimposed on monotone implementation of the indenter. If the material has viscoelastic properties, then in the oscillatory system of "indenter-sample" effects arise that leading to change of the response amplitude and the phase difference between signal, which sets the oscillations, and the actual displacement of the indenter. Analysis of the amplitude and phase of forced oscillations allows to determine the elastic and viscous properties of the investigated sample depending on load, oscillation frequency and other parameters, such as temperature.
To determine the dependence of material properties on indentation depth, for most samples a single test using the dynamic method is more effective than multiple indentation cycles or multiple shots with partial unloading. During dynamic indentation the amplitude of oscillations of the indenter may be only a few nanometers, so this method allows to measure the properties of a very small near-surface volume of the material, which is impossible in the case of discrete unloading cycles [5].
Using load cycles of a sine wave at a high frequency, it is also possible to investigate the formation of cracks at the nanoscale by measuring of the contact stiffness, which changes indicate the micro-damages of the material [6].
Information about changing of the indentation depth during the recovery of the surface profile of the material allows to estimate the creep, the accuracy of which is higher when using the dynamic method because it is less sensitive to thermal drift than a standard instrumental indentation.
Dynamic mechanical analysis
A method of dynamic measurement presupposes the application of a sinusoidal force to the indenter during the indentation in the sample surface with subsequent measurement of the deformation response, which allows to determine the complex modulus of elasticity of the material.
Various materials can resist the applied load, as elastic or ductile substances. The former one store energy during the deformation and return to its original state when the load is removed. The latter remaining compressed after removal of the load and dissipate all the work of deformation as heat.
When using the dynamic method, the deformation ε depends on the frequency ω of the applied forces as follows:
ε = ε0 sin(tω). (1)
For a purely elastic body the Hooke's law is fair, and stress σ is proportional to the deformation (factor E is a Young's modulus):
σ = Eε, (2)
therefore, the load and deformation are cophased. In the viscous material, where there is no elastic deformation, the stress is given by Newton's law: σ = ηε and the stress arising in response to the load, differs from it in phase by δ = 90° [5]:
σ = σ0 sin(tω + δ). (3)
However, there are no absolutely elastic and absolutely inelastic bodies in nature. From the expressions (2) and (3), we obtain that the real and imaginary components of the Young's modulus E*=E'+iE'' are of the form:
. (4)
To describe the behavior of viscoelastic sample with stiffness S and damping ratio D two basic models presented in Fig.1 are usually applied:
Kelvin–Voigt model with spring (with stiffness coefficient S) and piston (with coefficient of viscous friction D) that are arranged in parallel;
Maxwell model with series-connected S- and D-elements.
In fact, only using a complex circuit with many connected components, which simulate the stiffness and damping, it is possible to describe the behavior of real viscoelastic material under load.
The polymers are materials with pronounced viscoelastic properties. The mechanical characteristics of the polymers depend on the microstructure and morphology. Compared with metals and ceramics, plastic, viscous and elastic properties of polymers vary within a wide range while changing the temperature and time of load. Such properties of polymers in the solid phase can be successfully investigated using dynamic mechanical analysis [7].
Experimental testing
The mode of dynamic mechanical analysis (DMA) is implemented and experimentally tested in the scanning nano-hardness tester "NanoScan-4D" (TISNCM, Russia). Nano-hardness tester "NanoScan-4D" is the only Russian measuring instrument, which allows to carry out complex studies of physical-mechanical properties of materials at submicron and nanometer scale of linear dimensions [8–11]. In the nano-hardness tester more than 30 various measuring techniques covering all known types of tests of mechanical properties are implemented. The field of application of NanoScan devices includes the studies of thin films, coatings and nanostructured materials ranging from soft polymers to superhard crystals and alloys. General view of the device is shown in Fig.2.
The oscillation frequency of the indenter in DMA mode typically vary from tenths to hundreds of hertz, while a typical amplitude is in the range from units to hundreds of nanometers. The applied load depends on the studied material and varies from several hundred of micronewton to tens of millinewton and even one of newton.
The frequency of the exciting force in a dynamic indentation mode is determined by the capabilities of the device and rarely is significantly higher than the resonance frequency of the suspension of indenter.
During the tests, using a standard sample of fused quartz, it was shown that for a homogeneous material, deformation of which does not depend on the loading rate, the dynamic method gives a constant value of hardness regardless of the embedding depth of the indenter. Within the error the hardness value coincides with the results of the static indentation.
To demonstrate the capabilities of the method a sample with a film of silver of a thickness of 180 nm on a glass substrate has been chosen. Fig.3 illustrates the change of hardness (a) and of real and imaginary part of elastic modulus (b) for the glass substrate (dotted line) and for silver film on the substrate depending on the contact depth. The obtained dependences show the decrease of Young's modulus and the increase of the hardness with increase of depth of embedding. Such behavior is typical for soft metal films on the glass surface, because the modulus of elasticity of metals is higher than that of glass, and the hardness is lower. Typical is the closeness to zero of the integrated component of the modulus of elasticity, since it is known that these materials are not viscous under deformation.
Natural application of a dynamic mode is obtaining images of the surface topography of the sample. To increase the sensitivity and performance of the device in this case, it is reasonable to excite oscillations at the resonant frequency of the suspension system. Fig.4 shows an example of profilograms of scratches on the surface of silver film at a load of 100 mn. It should be noted that the scratching and subsequent profiling are done with the same diamond indenter using scanning nano-hardness tester "NanoScan-4D".
For comparison Fig.5 shows an image of the same scratches, obtained by the atomic force microscopy using multifunctional device NTEGRA Prima (NT-MDT, Russia). In both images the characteristic piles arising during the scratching of metals are perfectly visible.
The possibility of imaging of the sample surface with nanometer spatial resolution enables to assess the level of roughness for choosing optimal parameters of mechanical test and, if necessary, for precise positioning of the indenter.
Conclusion
Dynamic mechanical analysis is a powerful research tool for many tasks. It is of particular interest in the study of mechanical properties of layered materials and multilayer structures because it allows to determine changes in the contact stiffness, elastic modulus, hardness and viscous losses as functions of the indentation depth. In addition, the continuous dynamic indentation can be used to measure the viscous properties and to determine conditions of the transition from elastic to plastic deformation. There is no doubt that the dynamic method is promising for obtaining three-dimensional images of the studied materials, and is more informative compared to the multi-cyclic indentation and to applying of series of pricks. Further development of the DMA will be associated with its use for spatial volumetric mapping (tomograms) of mechanical, elastic and viscous properties of near-surface volumes of materials. ■
The project was implemented with the financial support of the Ministry of education and science of the Russian Federation under the agreement No.14.577.21.0088 (unique identifier of project RFMEFI57714X0088).
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