A nanoindentation test method for indentation creep material hardness and elastic modulus

Abstract

The application discloses a nano-indentation test method for hardness and elastic modulus of indentation creep material, and relates to the technical field of solid material strength characteristic test. The method comprises the following steps: S1, fixing a sample to be tested on a sample table of a nano-indentation test device; S2, if high-temperature indentation test is performed, heating the sample and a sharp indenter, and performing temperature matching by using a temperature drift minimization method to achieve thermal equilibrium between the sharp indenter and the sample; S3, performing single-cycle or multi-cycle indentation test on the sample by using the sharp indenter, each single-cycle test process comprising a loading section, a load maintaining section, an unloading section and an indenter retraction section, and obtaining a curve of displacement and load change over time; and S4, processing and analyzing the curve of displacement and load change over time obtained in the step S3 to obtain the elastic modulus and hardness of the sample. The method provided by the application can process nano-indentation test of material hardness and elastic modulus under the condition of indentation creep.

Description

Technical Field

[0001] This invention belongs to the field of solid material strength property testing technology, specifically relating to a nano-indentation testing method for the hardness and elastic modulus of indented creep materials. Background Technology

[0002] Material hardness and elastic modulus are important mechanical properties of materials. Instrumented nanoindentation is a non-destructive micro / nano-scale material mechanical property testing technique. Under normal circumstances, the hardness and elastic modulus of a material can be obtained from the indentation and unloading curve of a conical indenter, and relevant standards exist both internationally and domestically.

[0003] Creep is the phenomenon of strain changing over time in a material under constant stress, and it intensifies with increasing test temperature. Indentation creep can also occur in materials under constant stress during indentation. High-temperature nanoindentation is an advanced technique for measuring the high-temperature mechanical properties of materials. However, with increasing test temperature, materials also face creep issues in high-temperature nanoindentation tests. The contact depth and indentation stiffness obtained from the indentation-unloading curve using conventional methods are affected by creep, leading to deviations in the calculation of the indenter contact area, thus affecting the calculation of hardness and elastic modulus. Therefore, current nanoindentation data processing methods are not suitable for extracting hardness and elastic modulus in the presence of creep, necessitating the development of a nanoindentation testing method capable of handling the hardness and elastic modulus of materials in the presence of indentation creep. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the present invention aims to provide a nano-indentation testing method for the hardness and elastic modulus of indented creep materials. This method can obtain the hardness and elastic modulus of materials under indentation creep conditions.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] A nano-indentation testing method for the hardness and elastic modulus of indented creep materials, the method being implemented using a nano-indentation testing device, and the method comprising the following steps:

[0007] S1. Fix the sample to be tested on the sample stage of the nano-indentation testing device;

[0008] S2. If a high-temperature indentation test is to be performed, the sample to be tested and the indenter configured in the device are heated, and the temperature is matched by the temperature drift minimization method so that the indenter and the sample to be tested reach thermal equilibrium.

[0009] S3. The sample to be tested is subjected to a single-cycle or multi-cycle indentation test using the pointed indenter. Each single-cycle test process includes a loading section, a holding section, an unloading section, and an indenter retraction section, to obtain curves of displacement and load changing over time.

[0010] S4. Process and analyze the curves of displacement and load change with time obtained in step S3 to obtain the elastic modulus and hardness of the sample to be tested.

[0011] Furthermore, in the nano-indentation test method for hardness and elastic modulus of creep materials as described above, if a high-temperature indentation test is performed, the nano-indentation test device has a dual heating mode for the indenter and the sample, and the equipped indenter can withstand high temperatures and does not react with the sample.

[0012] Furthermore, in the nano-indentation test method for hardness and elastic modulus of indented creep materials as described above, the test area of ​​the sample to be tested in step S1 should be flat and have low roughness. The test area that meets the requirements is obtained by grinding and polishing before the test. If a high-temperature indentation test is to be performed, the nano-indentation test device is placed on a constant temperature cold stage and the whole device is placed in a vacuum environment or an inert gas protective atmosphere.

[0013] Furthermore, in the nano-indentation test method for hardness and elastic modulus of indented creep materials as described above, the indicator for achieving thermal equilibrium between the pointed indenter and the sample to be tested in step S2 is that their respective temperatures do not change after they come into contact.

[0014] Furthermore, in the nano-indentation test method for the hardness and elastic modulus of the indented creep material as described above, the holding time of the holding section in step S3 is set to more than 5 seconds to ensure that the steady-state creep rate can be extracted from the holding section; a constant load unloading rate is used in the unloading section; and a thermal drift measurement section is added between the unloading section and the indenter retraction section as needed.

[0015] Furthermore, in the nano-indentation test method for hardness and elastic modulus of indented creep materials as described above, the multi-cycle indentation test in step S3 refers to: setting multiple progressively increasing loads or indentation depths at the same indentation point and performing multiple single-cycle indentation tests; after completing the indentation test at one point, another indentation point can be selected on the sample to be tested, and sufficient spacing is maintained between the indentation points to ensure that the indentation points do not affect each other.

[0016] Furthermore, in the nano-indentation testing method for the hardness and elastic modulus of indented creep materials as described above, the data analysis and processing process in step S4 is specifically as follows:

[0017] S41. Apply data processing software to perform preliminary processing on the raw data obtained in step S3. After determining the zero point of indentation, deducting load drift and thermal drift, and deducting the additional displacement caused by frame flexibility, the time curves of preprocessed load P and displacement h are obtained.

[0018] S42. Linearly fit the displacement-time curve in the pre-treated load-holding section to obtain the creep rate of the steady-state creep of the load-holding section, and use the double exponential formula to fit the curve of the unloading section.

[0019] S43. Apply the corresponding formulas to calculate the contact stiffness and contact area at the unloading point after deducting creep, and then calculate the elastic modulus after deducting creep.

[0020] S44. Apply the corresponding formulas to calculate the contact stiffness and contact area at the creep initiation point after creep subtraction, and thus calculate the hardness after creep subtraction.

[0021] Furthermore, in the nano-indentation test method for the hardness and elastic modulus of indented creep materials as described above, step S42 specifically includes:

[0022] A linear fit was performed on the displacement-time curve of the load-holding section, and the slope of the fitted curve was equal to the creep rate of the load-holding section. The creep depth of the load-bearing section is expressed as:

[0023]

[0024] Where, Δt h The time difference between the start and end points of creep in the load-preserving section;

[0025] The load-time curve of the unloading section is fitted using a double exponential formula, and the fitting formula is as follows:

[0026]

[0027] Where h is the displacement, P is the load value, and h0 and A are... n and B m Both n and m are fitting parameters, and the range of m and n is set to 1 < m < 2 and n > 2.

[0028] Furthermore, in the nano-indentation test method for the hardness and elastic modulus of indented creep materials as described above, step S43 specifically includes:

[0029] The contact stiffness S is calculated based on the curve fitting formula (1) for the unloading section. n The calculation formula is:

[0030]

[0031] After deducting the effects of creep and substrate deformation, the true contact stiffness S′ is obtained, and the calculation formula is:

[0032]

[0033] in, The unloading rate of the load. To prevent creep in the load section, To maintain the steady-state creep rate of the load-bearing section, C ss For compliance correction caused by substrate deformation; for rigid and well-fixed sample C ss The contribution is negligible;

[0034] Contact depth h of elastic contact c Represented as:

[0035]

[0036] For a standard Berkovich indenter, ε = 0.75, the projected area of ​​the elastic contact, or simply the contact area A, is expressed as:

[0037] A = A(h) c (5)

[0038] For an ideal Berkovich indenter in a triangular pyramid, A(h) c The formula for calculating the zeroth-order term is:

[0039]

[0040] Where α is the included angle between the edges of the indenter. For a standard Berkovich indenter, α = 130.6°. In actual cases, the angle is calculated based on the parameters after calibration of the indenter area. The calculation formula is as follows:

[0041]

[0042] Calculate the composite response modulus E based on the contact stiffness S′ and the contact area A. r The calculation formula is:

[0043]

[0044] For the Berkovich indenter, β = 1.034;

[0045] The formula for calculating the elastic modulus E of the sample to be tested is:

[0046]

[0047] Where, v and v i E represents the Poisson's ratio of the sample and the indenter, respectively. iThis is the elastic modulus of the indenter.

[0048] Furthermore, in the nano-indentation test method for the hardness and elastic modulus of indented creep materials as described above, step S44 specifically includes:

[0049] The contact stiffness S″ at the starting point of the load-bearing section is calculated using the following formula:

[0050]

[0051] Calculate the contact depth h′ corresponding to the starting point of the load-bearing section. c The calculation formula is:

[0052]

[0053] The contact area A(h) corresponding to the starting point of the load-bearing section is calculated using equation (5). c The material hardness H is expressed as:

[0054]

[0055] Compared with existing technologies, the nano-indentation testing method for the hardness and elastic modulus of indented creep materials provided by this invention has the following advantages:

[0056] This invention utilizes a highly stable nano-indentation testing device. It employs a pointed indenter to obtain indentation curves showing load and displacement over time. After determining the zero-point of indentation, deducting load drift and thermal drift, and subtracting additional displacement caused by frame compliance, the displacement-time curve in the load-holding segment is linearly fitted to obtain the creep rate of steady-state creep. A double-exponential formula is used to fit the unloading curve, and the contact stiffness and contact depth at the unloading point and creep initiation point are calculated using these formulas. Furthermore, the elastic modulus and hardness after creep subtraction are calculated. The testing method provided by this invention can obtain the material hardness and elastic modulus under indentation creep conditions. Attached Figure Description

[0057] Figure 1 This is a flowchart of a nano-indentation test method for the hardness and elastic modulus of indented creep materials provided in an embodiment of the present invention;

[0058] Figure 2 The load-time curves of a high-temperature solder sample under nano-indentation tests at 50℃ and 100℃ are shown.

[0059] Figure 3 The load-indentation depth curves of a high-temperature solder sample under nano-indentation tests at 50℃ and 100℃ are shown.

[0060] Figure 4 The load-time curve of a ferritic / martensitic steel sample subjected to a multi-cycle indentation test at 600℃ is shown.

[0061] Figure 5 The test curve of a ferritic / martensitic steel sample subjected to multiple cycles of indentation at 600℃ is shown.

[0062] Figure 6 The elastic modulus is given by a multi-cycle indentation test at 600℃ for a ferritic / martensitic steel sample.

[0063] Figure 7 The hardness is given by a multi-cycle indentation test at 600℃ for a ferritic / martensitic steel sample. Detailed Implementation

[0064] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0065] Figure 1 This invention provides a flowchart of a nano-indentation testing method for the hardness and elastic modulus of indented creep materials, implemented on a nano-indentation testing device. The method includes the following steps:

[0066] S1. Fix the sample to be tested on the sample stage of the nanoindentation test device.

[0067] The nanoindentation testing device should possess high temperature and mechanical stability. For high-temperature indentation testing, the device should also feature dual heating modes for both the indenter and the sample, with the indenter capable of withstanding high temperatures and not reacting with the sample. To prevent oxidation of the indenter and sample, this invention places the nanoindentation device on a constant-temperature cooling stage, and the entire device is placed in a vacuum environment or an inert gas protective atmosphere. At high temperatures, a constant-temperature cooling stage is used to obtain a highly stable nanoindentation testing device.

[0068] The sample to be tested is fixed to the sample stage of the nano-indentation testing device using high-temperature adhesive or clamps, and the sample chamber of the testing device is evacuated. The test area of ​​the sample should be flat with low roughness, which can be achieved by grinding and polishing before testing. The indentation test uses a pointed indenter, such as a standard Berkovich indenter or a Vickers indenter.

[0069] S2. The sample to be tested and the indenter configured in the device are heated, and the temperature is matched by the temperature drift minimization method so that the indenter and the sample to be tested reach thermal equilibrium.

[0070] This step can be omitted if measuring room temperature hardness and elastic modulus.

[0071] If a high-temperature indentation test is to be performed, first turn on the constant temperature cold stage system and use the nano-indentation device to heat the sample to be tested and the indenter. After the system stabilizes, apply the temperature drift minimization method to match the temperature of the sample to be tested and the indenter so that the indenter and the sample to be tested reach thermal equilibrium. The indicator that the indenter and the sample to be tested reach thermal equilibrium is that their respective temperatures do not change after they come into contact.

[0072] The process for temperature matching between the sample and the indenter using the temperature drift minimization method is as follows: The temperature change of the indenter is used as an indicator of the temperature difference between the sample and the indenter, and heating is controlled using a PID controller. First, the sample temperature and indenter temperature are set. The indenter temperature is set to sample temperature - Δ, with Δ ranging from 15 to 20°C. After the sample and indenter temperatures, as well as the system displacement and load sensors, stabilize, the PID controller for the indenter temperature is turned off, maintaining a constant indenter heating current. Indentation is then performed according to the temperature matching indentation procedure, yielding the first temperature drift of the indenter during contact. Next, the PID controller for the indenter temperature is turned on, keeping the sample temperature setting unchanged. The indenter temperature is set to sample temperature + Δ, and indentation is performed according to the temperature matching indentation procedure, yielding the second temperature drift of the indenter during contact. The optimal temperature for temperature matching between the indenter and the sample is obtained from the temperature drift of the indenter at these two temperatures. At this temperature, the temperatures of the indenter tip and the sample surface are essentially the same, minimizing thermal drift. The specific calculation method has been explained in detail in "CN202310323177.4 A micro-nano scale indentation test method for high temperature yield strength of a material", and will not be described in detail here.

[0073] S3. Use the pointed indenter to perform single-cycle or multi-cycle indentation tests on the sample to be tested. Each single-cycle indentation test process includes a loading section, a holding section, an unloading section, and an indenter retraction section, to obtain the curves of displacement and load changing over time.

[0074] Each single-cycle indentation test typically includes an indentation phase, a hold phase, an unloading phase, and a head retraction phase. A thermal drift measurement phase can be added between the unloading phase and the head retraction phase as needed. The hold time for the highest load phase is generally set to at least 5 seconds to ensure that the steady-state creep rate can be extracted from the hold phase. A constant load unloading rate is used in the unloading phase.

[0075] Multi-cycle indentation test refers to setting multiple progressively increasing loads or indentation depths at the same indentation point and performing multiple single-cycle indentations.

[0076] After completing the indentation test at one point, another indentation point can be selected on the sample to be tested, and the single-cycle indentation test of step S3 can be repeated. Sufficient spacing should be maintained between the indentation points to ensure that they do not affect each other.

[0077] S4. Process and analyze the displacement and load curves obtained in step S3 over time to obtain the elastic modulus and hardness of the sample under test. The data analysis and processing process specifically includes:

[0078] S41. Apply data processing software to perform preliminary processing on the raw data obtained in step S3. After determining the zero point of indentation, deducting load drift and thermal drift, and deducting the additional displacement caused by frame flexibility, the time curves of preprocessed load P and displacement h are obtained.

[0079] S42. Linearly fit the displacement-time curve in the pre-processed load-holding section to obtain the creep rate of steady-state creep in the load-holding section, and use the double exponential formula to fit the curve of the unloading section.

[0080] Linear fitting is performed on the displacement-time curve of the load-holding section. The fitting should exclude data where the sample continues to deform due to the ongoing loading. The slope of the fitted curve represents the creep rate of the load-holding section. The creep depth of the load-bearing section can be expressed as: Where Δt h This is the time difference between the start and end points of creep in the load-bearing section.

[0081] Considering the influence of creep on the unloading curve, the following double exponential formula is used to fit the unloading curve:

[0082]

[0083] Where h is displacement, P is load, and h0 and A are... n and B m Both n and m are fitting parameters, with m and n taking values ​​ranging from 1 < m < 2 and n > 2, respectively. When using the above formula for fitting, the 98% P-value on the unloading curve is generally taken. max Up to 20% P max The region can also be selected from a segment of the unloading curve based on data quality, but it cannot be selected only from 50% P. max The above areas.

[0084] S43. Apply the corresponding formulas to calculate the contact stiffness and contact area at the unloading point after deducting creep, and then calculate the elastic modulus after deducting creep.

[0085] Calculate the contact stiffness S from the fitting formula of the unloading curve. n The calculation formula is:

[0086]

[0087] The actual contact stiffness should account for the effects of creep and substrate deformation. The calculation formula is as follows:

[0088]

[0089] in, The unloading rate of the load. To prevent creep in the load section, Let C be the steady-state creep rate of this segment. ss This is a compliance correction caused by substrate deformation; its contribution to rigid and well-fixed samples is negligible.

[0090] Contact depth h of elastic contact c It can be represented as:

[0091]

[0092] For a standard Berkovich indenter, ε = 0.75, the projected area of ​​the elastic contact, or simply the contact area A, is expressed as:

[0093] A = A(h) c (5) For an ideal Berkovich indenter, A(h) c The zero-level term is The calculation formula is:

[0094]

[0095] Where α = 130.6° is the included angle between the edges of the Berkovich indenter. In practice, this can be calculated using the parameters after indenter area calibration, and the calculation formula is:

[0096]

[0097] To calculate the elastic modulus E, first calculate the composite response modulus E from the contact stiffness and contact area. r The calculation formula is:

[0098]

[0099] For the Berkovich indenter, β = 1.034.

[0100] The formula for calculating the elastic modulus E of a sample is:

[0101]

[0102] Where ν and v i E represents the Poisson's ratio of the sample and the indenter, respectively. i This is the elastic modulus of the indenter.

[0103] S44. Apply the corresponding formulas to calculate the contact stiffness and contact area at the creep initiation point after creep subtraction, and thus calculate the hardness after creep subtraction.

[0104] Because creep occurs in the load-holding section, the creep section should be deducted from the hardness calculation. Furthermore, since the indentation depth differs between the start and end points of the load-holding section, the contact stiffness corresponding to the end point of the load-holding section cannot be used when calculating the hardness; instead, the contact stiffness corresponding to the start point should be used. Since contact stiffness is proportional to contact depth, and contact depth is approximately proportional to indentation depth, the contact stiffness S″ corresponding to the start point of the load-holding section can be calculated using the following formula:

[0105]

[0106] The contact depth h′ used to calculate material hardness c That is:

[0107]

[0108] The contact area A(h′) is calculated using equation (5). c The material hardness H is expressed as:

[0109]

[0110] Example 1

[0111] This embodiment provides an example of measuring the creep, hardness, and elastic modulus of a material at different temperatures.

[0112] The sample to be tested was a lead-free high-temperature solder sheet with a smooth surface. The sample was fixed to the sample stage with high-temperature resistant adhesive and tested on an in-situ high-temperature nanoindentation instrument for scanning electron microscopy. A standard Berkovich indenter was used, which is made of cubic boron nitride (cBN) material and is resistant to high temperatures. The sample chamber of the scanning electron microscope was evacuated.

[0113] The temperature change of the indenter is used as an indicator of the temperature difference between the sample and the indenter. A temperature drift minimization method is applied to match the temperature of the sample and the indenter. The sample and indenter are heated using PID control, with the sample temperature set at 50℃ and the indenter temperature at 35℃. After the sample and indenter temperatures, as well as the system displacement and load sensors, stabilize, the PID control for the indenter temperature is turned off, maintaining a constant indenter heating current. Indentation is then performed according to the temperature-matched indentation procedure, and the temperature drift of the indenter during contact is obtained. The PID control for the indenter temperature is then turned on, and the indenter temperature is set at 65℃. Indentation is performed according to the temperature-matched indentation procedure, and the temperature drift of the indenter during contact is obtained. The optimal temperature for temperature matching between the indenter and sample is determined by the temperature drift at 35℃ and 65℃, at which the temperatures of the indenter tip and the sample surface are essentially the same, with minimal thermal drift.

[0114] Using the imaging capabilities of a scanning electron microscope, a suitable location was selected for a high-temperature indentation experiment. The loading curves for this experiment are shown below. Figure 2The loading rate was set to 20 mN / s, the maximum load was 100 mN, the holding time of the load holding section (i.e. the creep measurement section) was 300 s, the unloading rate was 20 mN / s, and after unloading to 10 mN, the load was held for 60 s as the thermal drift measurement section, and finally the load was completely unloaded.

[0115] The raw data is preliminarily processed using data processing software, including finding the zero-point of the load, deducting load drift and thermal drift, and deducting the additional displacement caused by the frame flexibility, to obtain the time curves of load P and displacement h.

[0116] The unloading curve was fitted using a double exponential formula, and the stiffness was calculated to be 267.5 mN / μm according to equation (2). The steady-state creep rate of the load-holding section was calculated to be 0.00154 μm / s and the creep amount was 0.463 μm using processing software. The stiffness after considering creep was calculated to be 256.8 mN / μm according to equation (3), and the corrected contact depth was calculated to be 2.07 μm according to equation (4). The Poisson's ratio of the indenter was 0.12 and the elastic modulus was 960 GPa. The composite response modulus and elastic modulus of the sample at 50℃ were obtained to be 22.1 GPa and 20.6 GPa respectively according to equations (8) and (9). The contact depth before the load-holding section was calculated to be 1.70 μm according to equation (11), and the hardness of the sample at 50℃ was calculated to be 1.41 GPa according to equation (12).

[0117] Adjust the sample temperature to 100℃ and perform temperature matching between the indenter and the sample. The matching process is similar to that of pressing at 50℃. Set the indenter temperature to 80℃ and 120℃ respectively. After the temperature matching is completed, set the indenter to the matching temperature.

[0118] Using the imaging function of a scanning electron microscope, a suitable location was selected for a high-temperature indentation experiment. The loading curve was the same as that at 50℃. The load-displacement time curve was obtained after the test. Data processing software was used to perform preliminary processing of the raw data; the processed curve is shown below. Figure 3 The unloading curve was fitted using a double exponential formula, and the stiffness was calculated to be 183.6 mN / μm according to equation (2). The steady-state creep rate of the load-holding section was calculated to be 0.00300 μm / s and the creep amount was 0.899 μm using processing software. The stiffness after considering creep was calculated to be 174.1 mN / μm according to equation (3), and the corrected contact depth was calculated to be 3.00 μm according to equation (4). The Poisson's ratio of the indenter was 0.12 and the elastic modulus was 960 GPa. The composite response modulus and elastic modulus of the sample at 100℃ were obtained to be 10.4 GPa and 9.54 GPa respectively according to equations (8) and (9). The contact depth before the load-holding section was calculated to be 2.37 μm according to equation (11), and the hardness of the sample at 100℃ was calculated to be 0.724 GPa according to equation (12).

[0119] Example 2

[0120] This embodiment provides an example of measuring the hardness and elastic modulus of a ferritic / martensitic steel at different depths at high temperatures.

[0121] Before testing, the samples underwent mechanical grinding and polishing. Grinding was done with sandpaper, specifically 400#, 800#, 1200#, 2000#, and 3000# sandpaper, respectively. After grinding, polishing was performed sequentially with 3μm and 1μm diamond polishing slurries, and finally with Al2O3 polishing slurry with a particle size of 0.05μm.

[0122] The sample to be tested was fixed to the sample stage with high-temperature adhesive and tested on an in-situ high-temperature nanoindentation instrument for scanning electron microscopy. This nanoindentation instrument is equipped with a constant-temperature cooling water system with a temperature control accuracy of 0.1℃. The sample chamber of the scanning electron microscope was evacuated until the vacuum reached ~10℃. -4 Pa, turn on the heating of the sample and the indenter, turn on the temperature control PID, set the sample temperature to 600℃, set the indenter temperature to 580℃, and set the heating rate to 10℃ / min.

[0123] Once the system temperature stabilized and the load and displacement drift rates measured over 30 seconds were below 0.1 mN / min and 0.01 μm / min, respectively, the indentation experiment began, employing a multi-cycle indentation mode. Due to the relatively long overall test time, the load-time curves of the experiment are shown below. Figure 4 Each loop contains a loading segment, a holding segment, and an unloading segment, with a thermal drift correction segment set in the first and last push loops.

[0124] The raw data was initially processed using data processing software, including identifying the zero-point indentation, subtracting load drift and thermal drift, and subtracting additional displacement caused by frame compliance, resulting in the time curves of load P and displacement h. The load-displacement curves are shown below. Figure 5 The steady-state creep rate and creep strain during the load-bearing segment in each cycle were determined. The unloading curve for each cycle was fitted using a double-exponential formula, yielding the stiffness considering creep; its reciprocal is the compliance given by the indentation test. The corrected contact depth is obtained using equation (4), and the compliance correction C caused by substrate deformation is calculated. ss Based on the property that the modulus does not change with depth, it is determined by the following formula.

[0125]

[0126] The Poisson's ratio of the indenter is 0.12, and the elastic modulus is 960 GPa. The composite response modulus and elastic modulus are obtained from equations (8) and (9), where the elastic modulus varies with the indentation depth as shown in [reference needed]. Figure 6For this ferritic / martensitic steel sample, the elastic modulus at 600℃ using the traditional tensile testing method was 124 GPa. It can be seen that the elastic modulus obtained from the original data gradually decreases with depth, and at the deepest indentation depth, the elastic modulus is already far lower than the tensile test value. Even considering only the matrix compliance correction, it is still difficult to obtain an elastic modulus that does not change with depth, and the result is significantly greater than the tensile test value. Only after considering indentation creep and then performing matrix compliance correction can the elastic modulus obtained show only a certain degree of fluctuation with depth, with an average elastic modulus of 129 ± 5 GPa at all depths, which is close to the tensile test value.

[0127] The hardness of the ferritic / martensitic steel sample obtained after multiple cycles of indentation at 600°C is shown in the figure. Figure 7 Compared with the elastic modulus, the effect of creep correction on hardness is not significant, indicating that the indentation test method proposed in this invention is applicable to the following situations: extraction of elastic modulus under creep conditions and extraction of hardness and elastic modulus under high indentation creep rate conditions.

[0128] This invention provides a nano-indentation testing method for the hardness and elastic modulus of indented creep materials. Based on a highly stable nano-indentation testing device, it uses a pointed indenter to obtain indentation curves of load and displacement over time. After determining the zero-point of indentation, deducting load drift and thermal drift, and deducting additional displacement caused by frame compliance, the displacement-time curve in the load-holding segment is linearly fitted to obtain the creep rate of steady-state creep. A double-exponential formula is used to fit the unloading curve, and the contact stiffness and contact depth at the unloading point and the creep initiation point are calculated using the formulas. Furthermore, the elastic modulus and hardness after deducting creep are calculated. The method provided by this invention can handle nano-indentation testing of material hardness and elastic modulus under indentation creep conditions.

[0129] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention is also intended to include these modifications and variations.

Claims

1. A nano-indentation testing method for the hardness and elastic modulus of indented creep materials, the method being implemented using a nano-indentation testing device, the method comprising the following steps: S1. Fix the sample to be tested on the sample stage of the nano-indentation testing device; S2. If a high-temperature indentation test is to be performed, the sample to be tested and the indenter configured in the device are heated, and the temperature is matched by the temperature drift minimization method so that the indenter and the sample to be tested reach thermal equilibrium. S3. The sample to be tested is subjected to a single-cycle or multi-cycle indentation test using the pointed indenter. Each single-cycle test process includes a loading section, a holding section, an unloading section, and an indenter retraction section, to obtain curves of displacement and load changing over time. S4. The displacement and load curves obtained in step S3 are processed and analyzed to obtain the elastic modulus and hardness of the sample under test, specifically: S41. Apply data processing software to perform preliminary processing on the raw data obtained in step S3. After determining the zero point of indentation, deducting load drift and thermal drift, and deducting the additional displacement caused by frame flexibility, the time curves of preprocessed load P and displacement h are obtained. S42. Linearly fit the displacement-time curve in the pre-treated load-holding section to obtain the creep rate of the steady-state creep of the load-holding section, and use the double exponential formula to fit the curve of the unloading section. S43. Apply the corresponding formulas to calculate the contact stiffness and contact area at the unloading point after deducting creep, and then calculate the elastic modulus after deducting creep. S44. Apply the corresponding formulas to calculate the contact stiffness and contact area at the creep initiation point after creep deduction, and thus calculate the hardness after creep deduction. Step S42 is as follows: A linear fit was performed on the displacement-time curve of the load-holding section, and the slope of the fitted curve was equal to the creep rate of the load-holding section. The creep depth of the load-preserving section is expressed as: Where, Δt h The time difference between the start and end points of creep in the load-preserving section; The load-time curve of the unloading section is fitted using a double exponential formula, and the fitting formula is as follows: Where h is the displacement, P is the load value, and h0 and A are... n and B m Both n and m are fitting parameters, and the range of m and n is set to 1 < m < 2 and n > 2.

2. The nano-indentation test method for the hardness and elastic modulus of indented creep materials according to claim 1, characterized in that, If a high-temperature indentation test is performed, the nano-indentation test device has a dual heating mode for the indenter and the sample. The indenter is equipped with high temperature resistance and does not react with the sample.

3. The nano-indentation test method for the hardness and elastic modulus of indented creep materials according to claim 2, characterized in that, In step S1, the test area of ​​the sample to be tested should be flat and have low roughness. Before testing, the test area that meets the requirements is obtained by grinding and polishing. If a high-temperature indentation test is to be performed, the nano-indentation test device is placed on a constant temperature cold stage and the whole device is placed in a vacuum environment or an inert gas protective atmosphere.

4. The nano-indentation test method for the hardness and elastic modulus of indented creep materials according to claim 3, characterized in that, The indicator for achieving thermal equilibrium between the indenter and the sample to be tested in step S2 is that their respective temperatures do not change after they come into contact.

5. The nano-indentation test method for the hardness and elastic modulus of indented creep materials according to any one of claims 1-4, characterized in that, In step S3, the holding time of the load-holding section is set to more than 5 seconds to ensure that the steady-state creep rate can be extracted from the load-holding section; a constant load unloading rate is used in the unloading section; and a thermal drift measurement section is added between the unloading section and the pressure head retraction section as needed.

6. The nano-indentation test method for the hardness and elastic modulus of indented creep materials according to claim 5, characterized in that, The multi-cycle indentation test mentioned in step S3 refers to setting multiple progressively increasing loads or indentation depths at the same indentation point and performing multiple single-cycle indentations. After completing the indentation test at one point, another indentation point can be selected on the sample to be tested for indentation testing. Sufficient spacing is maintained between the indentation points to ensure that they do not affect each other.

7. The nano-indentation test method for the hardness and elastic modulus of indented creep materials according to claim 6, characterized in that, Step S43 is as follows: The contact stiffness S is calculated based on the curve fitting formula (1) for the unloading section. n The calculation formula is: After deducting the effects of creep and substrate deformation, the true contact stiffness S′ is obtained, and the calculation formula is: in, The unloading rate of the load. To prevent creep in the load section, To maintain the steady-state creep rate of the load-bearing section, C ss For compliance correction caused by substrate deformation; for rigid and well-fixed sample C ss The contribution is negligible; Contact depth h of elastic contact c Represented as: For a standard Berkovich indenter, ε = 0.75, the projected area of ​​the elastic contact, or simply the contact area A, is expressed as: A=A(h c ) (5) For an ideal Berkovich indenter in a triangular pyramid, A(h) c The formula for calculating the zeroth-order term is: Where α is the included angle between the edges of the indenter. For a standard Berkovich indenter, α = 130.6°. In actual cases, the angle is calculated based on the parameters after calibration of the indenter area. The calculation formula is as follows: Calculate the composite response modulus E based on the contact stiffness S′ and the contact area A. r The calculation formula is: For the Berkovich indenter, β = 1.034; The formula for calculating the elastic modulus E of the sample to be tested is: Among them, ν and ν i E represents the Poisson's ratio of the sample and the indenter, respectively. i This is the elastic modulus of the indenter.

8. The nano-indentation test method for the hardness and elastic modulus of indented creep materials according to claim 7, characterized in that, Step S44 is as follows: The contact stiffness S″ at the starting point of the load-bearing section is calculated using the following formula: Calculate the contact depth h corresponding to the starting point of the load-bearing section. c The calculation formula is: The contact area A(h) corresponding to the starting point of the load-bearing section is calculated using equation (5). c The material hardness H is expressed as:

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