A force-displacement correction method for instrumented impact testing

Abstract

The present invention discloses a force-displacement correction method for an instrumented impact test. The contact flexibility of the hammer blade and the specimen is obtained by the finite element method; a force-applying device and a laser interferometer are used to measure the flexibility of the anvil; an instrumented Charpy pendulum impact test is performed on a standard V-shaped impact specimen according to the standard, and force data during the pendulum impact on the specimen is obtained during the test. The deformation of the anvil and the hammer blade is corrected; based on the calculated corrected data, the force-displacement curve obtained from the instrumented impact test is redrawn. The method proposes an expression formula for contact flexibility, and obtains the specific parameters in this formula based on the finite element method. Based on this, the displacement error caused by the deformation of the hammer blade during the impact process is corrected; compared with the traditional method of treating the anvil and hammer blade as absolute rigid bodies, the present invention treats the hammer blade and anvil as elastic bodies, which is closer to the actual situation in principle, and the corrected data is more scientific and reasonable.

Description

Technical Field

[0001] The present invention belongs to the field of impact metrology and testing. Aiming at the practical characteristic that the anvil and hammer blade of an instrumented impact testing machine are not absolutely rigid, a correction method for the force-displacement curve in the instrumented impact test results based on the contact compliance of the two is proposed. The method provides a reference correction algorithm for more accurately evaluating the impact toughness of materials, thereby obtaining more accurate material impact performance data. Background Art

[0002] As a fundamental material property, impact toughness (i.e., the ability of a material to absorb energy during plastic deformation and fracture under impact loads) is a quantitative indicator of a material's ability to withstand impact loads in engineering applications. Specific experimental methods, depending on their service conditions, include the Charpy impact bending test under a simply supported beam (Charpy impact test), the Izod impact bending test under a cantilever beam (Izod impact test), and the impact tensile test. The Charpy impact test was established by French engineer Charpy around 1905, and has a history of over a century. This test method offers the advantages of simple specimen preparation, short testing time, and test data sensitive to material structure and metallurgical defects. It has become the most widely used traditional mechanical property test for evaluating the impact toughness of metal materials.

[0003] The traditional Charpy impact test uses a pendulum-type Charpy impact tester, which is designed and manufactured according to the principle of conservation of energy. It uses a pendulum design: after the pendulum is released from a static state at a certain high point, it performs a pendulum-like motion, contacts and breaks the test sample at the lowest point, and the residual energy after the break causes the pendulum to swing to the end position. The angle between the initial position and the end position is recorded by the dial. After the pendulum length is known, the height difference between the initial position and the end position is calculated. Combined with the weight of the pendulum, the energy consumed to break the sample can be calculated. This energy corresponds to the impact toughness of the sample.

[0004] The traditional Charpy impact test can, to a certain extent, meet the needs of testing and studying the impact toughness of materials. However, its test method determines that its only valid data is the impact energy required to break the specimen, and nothing else. During the impact test, the impact force acting on the specimen increases from zero to tens to hundreds of kilonewtons within (3-5) milliseconds and then drops back to zero. If two materials have different fracture mechanisms in the test (reflected by different force-displacement curves) but have the same impact energy test results, then the impact energy parameter alone cannot reflect the difference in impact resistance between the two. This simplification of parameters caused by the test method is a major obstacle to the research on the impact resistance of materials.

[0005] In order to deeply evaluate the fracture resistance of materials and conduct more detailed research on the impact process, scientific research departments and the industrial community have put forward the need to examine and analyze the stress conditions of materials during the entire impact process. To this end, with the support of the rapid development of electronic sampling technology in the past three or four decades, instrumented impact testing machines have emerged. The mechanical part of the instrumented impact testing machine is basically the same as that of the traditional impact testing machine, but a force sensor is installed at the hammer blade. After being matched with appropriate electronic instruments, the force sensor can continuously record the force signal acting on the hammer blade during the impact process, thereby realizing dynamic monitoring of the impact force value change. Based on the sampled force signal, calculations are performed to obtain the force-displacement curve, which is integrated to obtain the impact work. This solves the problem of "only result quantity but no process quantity" in traditional impact tests, and enables the real-time stress conditions of the impact specimen during the impact process to be recorded and analyzed.

[0006] Generally, the displacement-time data in the instrumented impact test is calculated from the force-time data, and the impact energy is calculated from the force-displacement data. The specific calculation formula is given by the corresponding test method standard. The test methods involved are "GB / T 19748-2019 Metallic Materials Charpy V-notch pendulum impact test instrumented test method", "ISO14556-2015 Metallic materials—Charpy V-notch pendulum impact test—Instrumented test method" and "ASTM E2298–18 Standard Test Method for Instrumented Impact Testing of Metallic Materials". The calculation formulas used in the three are

[0007]

[0008] s(t)=∫0 t v(t)dt

[0009] Where t is the time independent variable, v(t) is the pendulum velocity at time t, v0 is the initial impact velocity of the pendulum, M is the effective impact mass of the pendulum, F(t) is the impact force at time t, and s(t) is the pendulum displacement at time t. It can be seen that the parameters related to the pendulum hammer blade and anvil do not appear in this calculation process. Generally speaking, the requirements for anvils and hammer blades in relevant standards are limited to a hardness of no less than 45HRC, while in reality, general impact testing machine manufacturers generally increase this to above 50HRC. This high hardness requirement will naturally result in the hammer blade and anvil being less deformed during the experiment, and accordingly, less energy absorbed during the impact. For this reason, the specifications of the three test methods mentioned above all choose to ignore the influence of the pendulum hammer blade and anvil on the experimental results.

[0010] But in fact, from a qualitative analysis, in terms of energy, the non-absolute rigid body property of the hammer blade and anvil makes the stress deformation of the hammer blade and anvil have the effect of absorbing energy, resulting in the measurement result being larger than the true value of the specimen toughness; in terms of displacement, the calculated displacement data will be the sum of the specimen deflection, the stress deformation of the anvil, and the contact deformation between the hammer blade and the specimen, which in turn affects the calculation of all displacement characteristic values, such as the yield displacement S gy , unstable crack extension starting displacement S iu′ , unstable crack growth termination displacement S a , displacement S at maximum force m and total displacement S t and certain force characteristic values, such as the yield strength F gy The evaluation of the energy characteristic value will affect the evaluation of the corresponding energy, such as the energy W at maximum force m , unstable crack growth starting energy W iu , unstable crack growth termination energy W a And the total impact energy W t .

[0011] Currently, there is no comprehensive study or compensation method for the effect of hammer blade and anvil compliance on instrumented Charpy impact test results. Furthermore, both the methods and data for measuring hammer blade and anvil compliance are lacking. To address this lack, the present invention provides a comprehensive set of methods for correcting the impact energy measurement errors caused by hammer blade and anvil compliance, as well as corresponding testing methods. These methods include an anvil compliance measurement method, a hammer blade compliance calculation method, and an algorithm for correcting the impact energy measurement errors caused by hammer blade and anvil compliance for impacts of specimens at different energy levels. This approach corrects the impact energy measured in instrumented impact tests and enables more accurate measurements of material impact toughness. Summary of the Invention

[0012] In response to the current problem that the influence of the flexibility of the hammer blade and anvil on the displacement calculation and impact energy measurement results in instrumented impact tests has not been considered, the present invention provides a complete set of methods for correcting the displacement calculation and impact energy measurement errors caused by the flexibility of the hammer blade and anvil. This method proposes an expression formula for contact flexibility, obtains the specific parameters in this formula based on the finite element method, and uses this as a basis to correct the displacement error caused by the deformation of the hammer blade during the impact process; and proposes a method and device for directly measuring the flexibility of the anvil (direct method) to measure and obtain the contact flexibility formula between the anvil and the specimen, and uses this as a basis to correct the displacement error caused by the deformation of the anvil during the impact process. For two types of fracture specimens, a targeted displacement correction method based on the contact flexibility of the anvil and hammer blade is proposed.

[0013] Specifically, the implementation steps of the present invention (an instrumented impact test force-displacement correction method) are as follows:

[0014] Step 1: Obtain the contact compliance between the hammer blade and the specimen by the finite element method. Perform 3D modeling based on the hammer blade size and the standard V-type impact specimen size (the standard specimen refers to the relevant provisions on the hammer blade and specimen size in the national standard GB / T 229 and the European standard ISO 148-1). Then, divide the grid in the finite element simulation analysis module (the recommended grid size is not more than 1mm). Set the boundary condition as the specimen is fixed and the hammer blade can only move along the impact direction. Load the hammer blade with 500N as the first level, simulate multiple levels of loads, and draw the deformation-force diagram ( Figure 2 ), and the hammer blade deformation δ an The relationship between the force F, δ ss (F ss );

[0015] Step 2: Use the force device and laser interferometer to measure the anvil compliance. Figure 3 , Figure 4 Set up the anvil flexibility test equipment: install the support baffle (support), force sensor, force oil pump, force transmission rod, etc. in series. Place a laser reflector at the contact position between the force transmission rod and the anvil, and the local effect is as follows Figure 5 As shown. Use the force pump to apply force. Every time the force value increases by 500N, record the displacement data measured by the laser interferometer and the force value data measured by the force sensor, and then draw the deformation-force diagram ( Figure 6 ), and the anvil deformation δ is obtained an The relationship between the force F, δ an (F an );

[0016] Step 3: Perform an instrumented Charpy pendulum impact test on the standard V-type impact specimen according to the standard, obtain the force data during the test when the pendulum impacts the specimen, and use the formula provided in the standard, that is,

[0017]

[0018] s(t)=∫0 t v(t)dt

[0019] Calculation is performed to obtain the uncorrected force-displacement diagram of the impact process.

[0020] Step 4: According to the formula

[0021] F an (t) = F up (t)+F low (t)-F st (t)

[0022] and formula

[0023] F an (t) = 2 × F ne (t)-F st (t)

[0024] Force F on the anvil an Perform calculations;

[0025] Step 5: According to the formula

[0026]

[0027] Corrections are made to the deformation of the anvil and hammer blade. The force-displacement curves obtained from the instrumented impact test are replotted based on the calculated corrected data.

[0028] This method is also applicable to non-standard impact specimens.

[0029] The present invention has the following advantages:

[0030] 1. Compared with the traditional method of treating the anvil and the hammer blade as absolutely rigid bodies, the present invention treats the hammer blade and the anvil as elastic bodies, which is closer to the actual situation in principle.

[0031] 2. Regarding the previously unstudied influence of the anvil and hammer blade's inherent flexibility on the instrumented impact test results, the present invention provides a calculation method that can correct the two, making the obtained experimental results closer to reality and the corrected data more scientific and reasonable.

[0032] 3. This method is practical, reliable, simple and feasible. It can correct the test results without modifying the instrument or affecting the experiment itself. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 : Finite element simulation diagram of contact deformation between hammer blade and specimen.

[0034] Figure 2 : Simulation results of hammer blade deformation and total deformation of hammer blade and specimen under different forces.

[0035] Figure 3 : Actual picture of the anvil compliance measurement system (force measurement part).

[0036] Figure 4 : Overall picture of the anvil compliance measurement system.

[0037] Figure 5 : Schematic diagram of laser incident position.

[0038] Figure 6 : Anvil compliance measurement results.

[0039] Figure 7 : Schematic diagram of the force and deformation of each part of the hammer blade, specimen and anvil.

[0040] Figure 8 : Schematic diagram of anvil force estimation (brittle fracture).

[0041] Figure 9 : Schematic diagram of anvil force estimation (ductile fracture).

[0042] Figure 10 : Force-displacement diagrams before and after correction (brittle fracture).

[0043] Figure 11 : Force-displacement diagrams before and after correction (ductile fracture). DETAILED DESCRIPTION

[0044] The present invention is described in detail below with reference to specific implementation examples.

[0045] In order to solve the calculation error caused by ignoring the flexibility of the anvil and hammer blade in the existing instrumented impact test displacement calculation method, the present invention provides a complete set of correction methods for the two, including deriving and calculating the contact flexibility of the hammer blade and the specimen based on the finite element method, making a force-applying device according to the experimental method to apply horizontal force to the anvil and using a laser interferometer to measure the deformation of the anvil to measure the flexibility of the anvil, and using the above-mentioned algorithm to correct the displacement data of the instrumented impact test according to the flexibility of the hammer blade and anvil.

[0046] An instrumented impact test force-displacement correction method, the calculation steps of the method are as follows:

[0047] Step 1: Obtain the contact compliance between the hammer blade and the specimen by the finite element method. Perform 3D modeling based on the hammer blade size and the standard V-type impact specimen size (the standard specimen refers to the relevant provisions on the hammer blade and specimen size in the national standard GB / T 229 and the European standard ISO 148-1). Then, divide the grid in the finite element simulation analysis module (the recommended grid size is not more than 1mm). Set the boundary condition as the specimen is fixed and the hammer blade can only move along the impact direction. Load the hammer blade with 500N as the first level, simulate multiple levels of loads, and draw the deformation-force diagram ( Figure 2 ), and the hammer blade deformation δ an The relationship between the force F, δ ss (F ss );

[0048] Step 2: Use the force device and laser interferometer to measure the anvil compliance. Figure 3 , Figure 4 Set up the anvil flexibility test equipment: install the support baffle (support), force sensor, force oil pump, force transmission rod, etc. in series. Place a laser reflector at the contact position between the force transmission rod and the anvil, and the local effect is as follows Figure 5 As shown. Use the force pump to apply force. Every time the force value increases by 500N, record the displacement data measured by the laser interferometer and the force value data measured by the force sensor, and then draw the deformation-force diagram ( Figure 6 ), and the anvil deformation δ is obtained an The relationship between the force F, δ an (F an );

[0049] Step 3: Perform an instrumented Charpy pendulum impact test on the standard V-type impact specimen according to the standard, obtain the force data during the test when the pendulum impacts the specimen, and use the formula provided in the standard, that is,

[0050]

[0051] s(t)=∫0 t v(t)dt

[0052] Calculation is performed to obtain the uncorrected force-displacement diagram of the impact process.

[0053] Step 4: According to the formula

[0054] F an (t) = F up (t)+F low (t)-F st (t)

[0055] and formula

[0056] F an (t) = 2 × Fne (t)-F st (t)

[0057] Force F on the anvil an Perform calculations;

[0058] Step 5: According to the formula

[0059]

[0060] The deformations of the anvil and hammer blade were calculated and corrected, and the force-displacement curves obtained from the instrumented impact test were redrawn based on the corrected data.

[0061] Taking the T-shaped hammer blade of a certain instrumented impact testing machine as an example, the contact deformation of the hammer blade itself and the overall contact deformation of the hammer blade and the specimen under different impact forces are obtained through finite element analysis. According to the simulation results ( Figure 1 、 2 ), the fitting formula for the overall contact deformation of the hammer blade and the specimen is obtained as

[0062] δ ss (F)=0.006822atan(0.1423F)+0.001854F

[0063] The unit of force F is kN, and the overall contact deformation of the hammer blade and the specimen is δ ss The unit is mm. The R 2 The value is 0.9998 and the RMSE value is 0.0004353.

[0064] There are two points to note about displacement measurement: First, before each measurement, the fixed position of the laser reflector needs to be adjusted so that it is close to the anvil. This is because after the force application and unloading cycle, the position of the laser reflector relative to the force transmission rod will change to a certain extent, and there will be a gap between the two. Second, the position of the laser reflector should be close to the anvil, and the laser injection position on the laser reflector should be aligned with the chamfer of the anvil, such as Figure 5 The second reason is that, in general, the impact process can be regarded as a three-point bending process, so the flexibility of the anvil is mainly reflected in the force-displacement relationship at its chamfer position.

[0065] When fitting the flexibility measurement data in steps 1 and 2, the following fitting formula can be used:

[0066] δ(F)=a×atan(b×F)+c×F

[0067] Where δ is the deformation of the anvil or hammer blade, and a, b, and c are the fitting coefficients to be determined. This fitting formula has a relatively good fitting effect.

[0068] The formula in step 5 is derived as follows

[0069] The anvil, specimen and hammer blade are connected in series, so

[0070] δ ss =δ1-δ2

[0071] δ s =δ2-δ3

[0072] δ an =δ3

[0073] where δ an is the deformation of the anvil; δ ss is the contact deformation between the hammer blade and the specimen; δ s is the deformation of the specimen; δ1 is the displacement of the hammer blade; δ2 is the displacement of the contact point between the specimen and the hammer blade; δ3 is the displacement of the contact point between the specimen and the anvil. Obviously, the displacement s(t) calculated in the traditional method without correction is δ s , δ an and δ ss of

[0074] s(t)=δ1=(δ1-δ2)+(δ2-δ3)+δ3=δ s +δ an +δ ss

[0075] After substituting and discretizing, we can get

[0076]

[0077] Among them F an is the force on the anvil, F ss is the force on the hammer blade, which is the original force data obtained in the instrumented impact test, δ an (F) is the anvil flexibility, δ ss (F) is the contact compliance between the specimen and the hammer blade, with the subscripts representing the i-th and i+1-th data points. This formula is the core formula of this correction method.

[0078] The force sensor in an instrumented impact tester is a strain gauge force sensor located at the hammer blade. Therefore, the force data collected is the force applied to the hammer blade during the impact. However, the specimen vibration caused by the impact causes a 180° phase difference between the forces acting on the anvil and the hammer blade. During the impact, the specimen is first accelerated by the hammer blade to the initial pendulum impact velocity. During this acceleration, which accounts for the majority of the initial peak force, the specimen is not in contact with the anvil. After the anvil, specimen, and hammer blade make contact, the specimen continues to vibrate, causing the forces acting on the anvil and hammer blade to be asynchronous, until the specimen undergoes brittle fracture (usually occurring in low-energy specimen tests) or yields, causing the vibration to decay (usually occurring in medium- and high-energy specimen tests). Therefore, the force acting on the anvil can be determined using the following method.

[0079] For brittle fracture (low energy level) specimens, the upper and lower limits of the hammer blade vibration force can be determined by the peak and valley values ​​through you, such as Figure 8 As shown. Since the anvil and hammer blade have a 180° phase difference in the force corresponding to the vibration, the force on the anvil can be calculated as follows:

[0080] F an (t) = F up (t)+F low (t)-F st (t)

[0081] Among them F an is the force on the anvil, F up is the value of the upper edge, F low is the lower limit value, F st is the force applied to the hammer blade, i.e., the measured force value (=F(t)). This formula applies to the second stage. In the first stage, i.e., at the initial peak, there is no contact between the specimen and the anvil. However, it is certain that from the first valley of the hammer blade force, the hammer blade, specimen, and anvil are in contact. Therefore, the force applied to the anvil in the first stage is the line connecting the intersection of the force applied to the anvil at the first valley of the hammer blade and the lower limit along the same time axis. This line is the force applied to the anvil in the first stage. In the third stage, since the specimen breaks, the force applied to the anvil equals the force applied to the hammer blade.

[0082] For ductile fracture specimens, Figure 11 As shown in the figure, the first stage of the anvil force calculation is the same as that of the brittle fracture specimen. Due to its significant material yield effect, the second stage of the ductile fracture specimen can be divided into two parts for calculation. The overall idea is the same as the second stage calculation of brittle fracture. However, since the peak points of the force climbing part (the first part of the second stage) may be too few, the neutral line fitting can be used instead of the peak point fitting, and the following formula can be used to calculate the anvil force

[0083] Fan (t) = 2 × F ne (t)-F st (t)

[0084] Among them F ne is the value of the neutral line. In the third stage, yielding causes the vibration to decay, making the force on the anvil equal to the force on the hammer blade.

[0085] The force-displacement curves before and after correction are as follows: Figure 10 、 11 shown.

[0086] The above description is a detailed description of an embodiment of the present invention and is not intended to limit the present invention in any form. Those skilled in the art may make a series of optimizations, improvements, and modifications based on the present invention. Therefore, the scope of protection of the present invention shall be defined by the appended claims.

Claims

1. An instrumented impact test force-displacement correction method, characterized by: The implementation steps of this method are as follows: Step 1: Obtain the contact compliance between the hammer blade and the specimen using the finite element method; perform 3D modeling based on the hammer blade size and the standard V-shaped impact specimen size, then divide the mesh in the finite element simulation analysis module, set the boundary conditions as the specimen is fixed and the hammer blade can only move along the impact direction; load the hammer blade, with 500N as the first level, perform multiple simulations for multiple levels of load, draw the deformation-force diagram, and obtain the hammer blade deformation δ ss The relationship between the force F, δ ss (F ss ); Step 2: Use a force device and a laser interferometer to measure the anvil's flexibility; install the support baffle, force sensor, force oil pump, and force transmission rod in series; place a laser reflector at the contact position between the force transmission rod and the anvil; use the force oil pump to apply force. For every 500N increase in force, record the displacement data measured by the laser interferometer and the force data measured by the force sensor, and then draw a deformation-force diagram to obtain the anvil deformation δ an The relationship between the force F, δ an (F an ); Step 3: Perform an instrumented Charpy pendulum impact test on the standard V-type impact specimen according to the standard, obtain the force data during the test when the pendulum impacts the specimen, and use the formula provided in the standard, that is, Calculation is performed to obtain the uncorrected force-displacement diagram of the impact process; Where v(t) is the velocity of the pendulum during the impact, s(t) is the displacement of the pendulum during the impact, t is time, M is the effective impact mass of the pendulum, and v0 is the initial pendulum impact velocity; Step 4: According to the formula F an (t)=F up (t)+F low (t)-F st (t) and formula F an (t)=2×F ne (t)-F st (t) Force F on the anvil an Perform calculations; F an is the force on the anvil, F ss The force on the hammer blade; F up is the value of the upper edge, F low is the lower limit value, F st is the force on the hammer blade, F ne is the value of the neutral line; Step 5: According to the formula Correct the deformation of the anvil and hammer blade; redraw the force-displacement curve obtained from the instrumented impact test based on the calculated corrected data; δ an (F) is the anvil flexibility, δ ss (F) is the contact compliance between the specimen and the hammer blade, with the subscripts representing the i-th and i+1-th data points; where s is the displacement of the pendulum during the impact process.

2. The instrumented impact test force-displacement correction method according to claim 1, characterized in that: Before each displacement measurement, the fixed position of the laser reflector needs to be adjusted so that it is close to the anvil; the position of the laser reflector is close to the anvil, and the laser injection position on the laser reflector should be aligned with the chamfer of the anvil. The flexibility of the anvil is reflected in the force-displacement relationship at its chamfer position.

3. The instrumented impact test force-displacement correction method according to claim 1, characterized in that: When fitting the flexibility measurement data in steps 1 and 2, the following fitting formula is used: δ(F)=a×atan(b×F)+c×F where δ is the deformation of the anvil or hammer blade, and a, b, and c are fitting coefficients to be determined.

4. The instrumented impact test force-displacement correction method according to claim 1, characterized in that: The formula in step 5 is derived as follows The anvil, specimen and hammer blade are connected in series, so d ss =δ1-δ2 d s =δ2-δ3 d an =δ3 where δ an is the deformation of the anvil; δ ss is the contact deformation between the hammer blade and the specimen; δ s is the deformation of the specimen; δ1 is the displacement of the hammer blade; δ2 is the displacement of the contact point between the specimen and the hammer blade; δ3 is the displacement of the contact point between the specimen and the anvil; Obviously, the displacement s(t) calculated without correction is δ s ,δ an and δ ss The sum of: s(t)=δ1=(δ1-δ2)+(δ2-δ3)+δ3=δ s +d an +d ss After substituting and discretizing, we can get Among them F an is the force on the anvil, F ss is the force on the hammer blade, which is the original force data obtained in the instrumented impact test, δ an (F) is the anvil flexibility, δ ss (F) is the contact compliance between the specimen and the hammer edge, and the subscripts are the i-th and i+1-th data points.

5. The instrumented impact test force-displacement correction method according to claim 1, characterized in that: The force sensor of the instrumented impact tester is a strain gauge force sensor, which is located at the hammer blade. Therefore, the force data collected is the force applied to the hammer blade during the impact process. The vibration of the specimen caused by the impact will cause the anvil and the hammer blade to have a 180° phase difference in the force corresponding to the vibration: during the impact process, the specimen will first be accelerated by the hammer blade to the initial pendulum impact speed. During the acceleration process, which is the vast majority of the first peak force, the specimen has no contact with the anvil. After the anvil, specimen and hammer blade come into contact, the specimen continues to vibrate, causing the anvil and hammer blade to be subjected to asynchronous force until the specimen undergoes brittle fracture or the specimen bends and yields, causing the vibration to attenuate.

6. The instrumented impact test force-displacement correction method according to claim 1, characterized in that: The force on the anvil is obtained by the following method; For brittle fracture specimens, the upper and lower limits of the hammer blade vibration force can be determined by fitting the peak and valley values. Since the anvil and hammer blade have a 180° phase difference in the force corresponding to the vibration, the anvil force is calculated as follows: F an (t)=F up (t)+F low (t)-F st (t) Among them F an is the force on the anvil, F up is the value of the upper edge, F low is the lower limit value, F st is the force applied to the hammer blade, i.e., the measured force value F(t). This formula is applicable to the second stage. In the first stage, i.e., at the first peak position, there is no contact between the specimen and the anvil. Starting from the first valley of the force applied to the hammer blade, the hammer blade, specimen, and anvil are in contact. Therefore, the force applied to the anvil in the first stage is the line connecting the intersection of the force applied to the anvil at the first valley of the hammer blade and the lower limit along the same time axis. This line is the force applied to the anvil in the first stage. In the third stage, since the specimen breaks at this time, the force applied to the anvil is equal to the force applied to the hammer blade. For ductile fracture specimens, the first stage of anvil force calculation is the same as that of brittle fracture specimens. Due to its significant material yield effect, the second stage of ductile fracture specimens is divided into two parts. The neutral line fitting is used instead of the peak point fitting, and the following formula is used to calculate the anvil force F an (t)=2×F ne (t)-F st (t) Among them F ne is the value of the neutral line; in the third stage, yielding causes the vibration to attenuate, which makes the force on the anvil the same as that on the hammer blade, so at this time the force on the anvil is equal to the force on the hammer blade.

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