Nowadays, instrumented indentation is routinely used in quality control as well as in many different areas of industrial and academic research. This technique is generally known as nanoindentation because the indentation depths are often much smaller than in traditional Vickers or Rockwell hardness measurements. In addition, the instrumented indentation method measures elastic modulus and hardness of a wide range of materials by applying load and determining the indentation depth.
Due to automated measurement including the analysis, a wide range of measurements can be carried out and examined automatically without any operator intervention. Thanks to the versatility of the Anton Paar nanoindentation systems and their related software, a variety of loading profiles can now be applied on specific materials to expose the unique material characteristics.
For instance, materials with surface coatings or with graded properties can be analyzed with cyclic loading to determine their gradient of hardness; polymers and other materials with time-dependent properties can be indented with various indentation rates or in constant strain rate mode in order to achieve their dynamic response. To observe the slip phenomena, certain indentation-related experiments such as micro pillar compression can be advantageously carried out in displacement control mode.
This article summarizes the variety of methods included in the Anton Paar Indentation software. All methods are comprehensively described and application examples are provided. The aim of this article is to guide nanoindenter users in their selection of the most appropriate indentation process.
The most common type of indentation is standard indentation that allows simple and efficient measurements of hardness and elastic modulus. This method is defined in the ISO 14577 standard. The maximum indentation load and the duration of the hold period have to be specified by the user. Figure 1a shows the load profile and Figure 1b shows the resulting load-displacement curve.
Figure 1. a) Standard indentation load profile, b) resulting load-displacement indentation curve.
Advanced Indentation Modes for Single Load Indentations
The advanced measurement mode is a technique of instrumented indentation that allows performing one single indentation measurement where the user independently defines the loading and the unloading rates. Due to this mode, different loading types can be selected making it possible to either speed up the total test time or to examine the response of different types of materials to different loading rates. The advanced measurement mode can be employed for most regular indentation testing applications.
Instrumented indentation (nanoindentation) testers from Anton Paar provide three key types of indentation loading:
- Constant Strain Rate
- Quadratic Loading
- Linear Loading
Test procedures based on Linear or a Constant Strain Rate type of loading can be either force-controller or displacement controlled.
Linear Loading with Various Loading Rates
This loading type of the advanced indentation mode can be employed for most of the standard indentation testing applications. Increased loading rate can result in reduced testing time, particularly when running large matrices. Also, it can be used on polymers to replicate step loading (fast load increase) and analyze stress or creep relaxation during the following hold period.
The process of indenter loading obeys the following formula: F=k×t (Figure 2), where k represents the loading rate in mN/minute. If the hardness is constant, the depth follows a square root evolution against time (F~√h)
Figure 2. Example of linear loading.
The loading and unloading rate, the maximum load to be reached and the duration of the holding period have to be specified by the user. By default, the acquisition rate is set to 10 Hz, but this can also be increased manually to record additional data during loading, to acquire better precision when determining the contact point.
When the linear loading rate is increased, the measurement can be accelerated. While the proposed loading time as recommended in ASTM 2808 and ISO 14577 is 30 seconds, this value can be reduced to a few seconds (typically 5 or 10 seconds) for time reducing purposes and when testing non-viscoelastic materials. However, the loading and the unloading time should not be brought down to less than 2 seconds and the acquisition rate should be increased in the same way to record sufficient data points so that the indentation process and contact point determination are properly controlled.
The following curves show the results acquired on fused silica when different loading periods (loading rates) were applied. Figure 3a shows three different load profiles and Figure 3b shows the three resulting load-displacement curve (Since silica lacks time-dependent properties, all the load-displacement curves are superimposed in spite of different loading rates).
Figure 3. Advanced indentation with different loading rates on fused silica: a) superimposed indentation load profiles, b) resulting load-displacement indentation curves (superimposed).
The loading of the indenter obeys the following formula: F=k×t∧2 (Figure 4), where k represents the loading rate in [mN/minute]. If the hardness is constant, the depth follows the evolution of time (h~t). This type of loading is routinely used with Continuous Multi Cycles (CMC) indentation mode in order to achieve uniformly spaced hardness and elastic modulus values in depth.
Figure 4. Force as a function of time in quadratic loading indentation.
This type of loading helps maintain a linear depth increase (contrary to linear loading where the depth increase follows a square root curve). The loading and unloading time, maximum load to be reached, and the holding period have to be specified by the user. By default, the acquisition rate is set to 10 Hz but this can also be increased manually.
Constant Strain Rate Loading
The loading of the indenter obeys the following formula: dP/dt×1/P=const. (Figure 5).
Figure 5. Force as function of time in constant strain rate loading indentation.
This loading type is proposed for viscoelastic materials whose mechanical properties depend on strain rate. The use of different loading rates can be favorably used to observe the creep response after different strain rate loading as well as to find optimal indentation conditions to lower the effects of loading rate on the elastic modulus when testing viscoelastic materials.
The minimum and maximum load (in load control) or minimum and maximum depth (in depth control) to be reached, the strain rate as well as the duration of the hold period have to be specified by the user. By default, the acquisition rate is set to 10 Hz but this can be manually increased.
The response of the indentation depth as a function of the strain rate is shown in Figure 6. For all indentations, the maximum applied normal load was maintained constant while the strain rate was gradually increased from 0.05/s to 1/s.
Figure 6. Illustration of indentation depth versus time plots for different values of constant strain rate indentation.
It is a well-known fact that the classic Oliver and Pharr method used for determining the elastic modulus by depth sensing indentation employs the unloading response of the material which is believed to be elastic. Yet, the viscous behavior of the material can affect the unloading of viscoelastic materials and thus affect the elastic modulus, which is measured from the unloading part of the indentation curve. While a number of corrective formulae exist in the literature, the influence of creep on the measured elastic modulus can be reduced easily by simply introducing sufficiently long holding period at the maximum load.
Indentations with Cyclic Loading
During a procedure with cyclic loading during one procedure (loading-partial unloading) can be particularly useful for obtaining depth profiles of hardness or elastic modulus of materials with graded mechanical properties such as functionally graded materials (FGM). The mechanical properties of these types of materials are differing from the surface toward the substrate or inner material. Through cyclic indentation procedures, discrete characterization of elastic modulus and hardness as a function of indentation depth can be realized. Instrumented indentation testers from Anton Paar provide three types of cyclic indentation procedures:
- Progressive Multi Cycle
- Continuous Multi Cycle (CMC)
- Constant Multicycle
The indenter, in all these procedures, remains in contact with the sample and the material’s entire mechanical properties are acquired from each partial unload. Several cyclic indentations (even of different types) can certainly be combined in Visual or Advanced matrix.
Continuous Multi Cycle
The CMC process involves repeated loading and partial unloading as schematically illustrated in Figure 7a. The maximum load in the first cycle, the maximum load in the last cycle, the number of cycles (typically 10 to 20), hold periods and the type of maximum load increment (typically quadratic to achieve results at equally spaced depths) have to be specified by the user. In each cycle, the unloading is performed to a percentage of the maximum load in the given cycle (typically 20% of the maximum load is used). Consequently, each unload yields discrete value of hardness and elastic modulus and thus a depth profile is obtained, as seen in Figure 7b. This depth profile, in turn, reveals the evolution of elastic modulus and hardness as a function of indentation depth. Such a profile can show a gradient in mechanical properties or help determine the highest indentation depth on coated materials where there is no effect of substrate. In the CMC depth profiles, about 10 to 20 cycles are usually used and the indentation loading and unloading times are shorter to lower the testing time.
Figure 7. a) Typical Continuous Multi Cycle (CMC) load and depth profile, b) resulting depth profile of hardness of standard material and material with graded properties.
Progressive Multi Cycle
Progressive multicycle is practically the same as the CMC profile, but the unloading in each cycle is performed to specified load rather than a percentage of the maximum load in each cycle.
Constant Multi Cycle
For some materials with porous structure such as thermally sprayed coatings, other cyclic methods can be useful. Constant Multicycle (CM) is the most common method, which is based on cyclic loading at the same spot between two load levels (Figure 8).
Just like the CMC measurement, the indenter is allowed to remain in contact with the surface during the entire duration of the cyclic indentation. When it comes to testing the response of a material to a compacting cyclic loading, the CM method is particularly useful. This method is thus suitable for porous materials where repeated indentation results in the closing of pores. A key advantage provided by the CM method is that increased indentation depth can be observed as a function of the number of cycles, and therefore the material’s ability to recover can be assessed easily.
The Constant Multicycle (CM) is predominantly carried out in Load control mode, but Depth control mode is also available. In the Constant Multicycle, the minimum and load that needs to be reached in each cycle, loading and unloading rate, number of cycles and hold period have to be specified by the user.
Figure 8a shows typical CM load profile and Figure 8b shows the typical results acquired on porous ceramics.
Figure 8. a) Typical Constant Multicycle (CM) load and depth profile, b) evolution of maximum indentation depth as a function of number of cycles.
Indentation in Depth Control Mode
In certain cases, indentation measurements in Depth (displacement) control mode are preferred over Load control mode. A classic example is the study of pop-in (slipping of the shear bands) when compressing micro pillars, as shown in Figure 9.
In these measurements, the pillar suddenly deforms, which generates a large drop of the compressing load while just a slight decrease in depth is noted. Depth control mode is also favored in finite element simulations against Load control mode. Also, the Full depth control mode enables measuring relaxation for materials that have time-dependent properties such as hydrogels or polymers by holding the Maximum depth constant: the load on the indenter decreases as the material relaxes. Therefore, the Full Depth control mode makes it possible to measure relaxation of materials.
Figure 9. An example of Full Depth control mode indentation (compression) of gold micro pillar. Note drops in force due to pop in effects when compressing the micro pillar.
There are two possible controls of the Depth mode:
- Full Depth control mode allows the ability to reach a specified Maximum penetration depth by managing the displacement (depth) rate (in nm/minutes) of the indenter
- Maximum Depth with load control mode allows reaching the Maximum depth by managing the loading and unloading rates
In the Maximum depth mode with load control, the loading/unloading rate in mN/minutes, the maximum depth and duration of the hold period have to be specified by the user. In the Full Depth control mode, the penetrating displacement rate, displacement unloading rate in nm/minutes and duration of the hold period have to be specified by the operator.
The Maximum depth with load control mode is used predominantly for experiments, where certain indentation depth has to be reached; however, the user prefers load control over displacement control. Full Depth control mode is employed in those applications where there is a need for displacement control such as studies of pop-in events, or for stress relaxation experiments on materials with time-dependent properties. Indentation curves achieved with a Full depth control and a Maximum depth control indentation modes are compared in Figure 10.
Figure 10. Full depth mode (a) and Maximum depth mode with load control (b) and their resulting load vs. penetration depth curves (c, d).
To properly set up the Full Depth control mode as well as the Maximum depth with load control mode parameters, uses are advised to conduct a standard indentation with load control mode. In this manner, the Loading rate required to reach the specified Maximum depth can be set to practical values so that too slow or too fast rates are prevented. For the Full Depth control mode, it is advised to alter the displacement rate proximal to the Indenter approach speed during the surface approach. The load needed to reach the specified Maximum depth should not exceed the instrument’s load range.
User Defined Profile
The User defined profile, a unique method of instrumented indentation, enables the user to generate a specific indentation profile by combining loadings, unloading and holds. Using this technique, the indentation procedure can be fully customized to match the user’s precise application. This type of indentation is mainly used in applications where measurement has to be made at various temperatures and subsequent stabilization times are required prior to the corresponding segments of the indentation cycle, or segments with varying loading rates within the same cycle.
In the User defined profile, a single indentation measurement is split into segments that are user-programmable with each segment including loading, hold period and unloading portions. In addition, each segment can be separately programmed for different hold times or loading/unloading rates. During the entire duration of indentation, the indenter is allowed to remain in contact with the tested material.
There are three main types of user segments: load control, depth (with depth control) and depth (with load control) which allow choosing the maximum penetration depth or the maximum applied load. During each unloading segment, hardness and elastic modulus are measured.
This indentation mode makes it possible to create a non-conventional indentation cycle to be carried out on the same spot. An example of a user-defined test protocol conducted on a tin sample is shown in Figure 11.
Figure 11. An example of User defined indentation profile.
This indentation profile includes three successive indentations at various maximum applied loads and between each of these three indentations, the temperature was increased. Due to the segment definition, the holding period may be selected to make sure that there is adequate thermal stabilization following the change in temperature.
Instrumented indentation systems make it possible to use a wide variety of testing loading protocols for many different purposes. The Anton Paar Indentation software includes different loading profiles that respond to most of the customers’ requests on nanoindentation processes, whether the user’s interest concerns creep properties, simple hardness and elastic modulus values, or other mechanical properties.
All the presented indentation profiles can be used in visually selected matrix or in automatic matrix measurement. All measurements use the key feature of instrumented indentation, i.e., automatic analysis of the results without the need for user intervention. The user can even export the data in ASCII format in order to apply custom analysis to the indentation data.
This information has been sourced, reviewed and adapted from materials provided by Anton Paar TriTec SA.
For more information on this source, please visit Anton Paar.