Method for calculating maximum high-temperature tensile strength
By welding thermocouples and combining them with the force-time curve in a high-temperature tensile test, the minimum cross-sectional radius of the necking zone of the specimen is calculated, which solves the problem of inaccurate cross-sectional area changes in the prior art and realizes the accurate calculation of the maximum tensile strength at high temperatures.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- ANGANG STEEL CO LTD
- Filing Date
- 2026-02-09
- Publication Date
- 2026-05-12
AI Technical Summary
Existing high-temperature tensile testing equipment cannot accurately obtain the change in cross-sectional area of materials during high-temperature tensile testing, resulting in inaccurate stress calculations, especially with large deviations in results under non-uniform deformation conditions.
By welding a thermocouple at the middle of the specimen and conducting a high-temperature tensile test using a thermal simulation testing machine, the force value and the tensile length of the specimen are collected, the force-time curve is plotted, and the minimum cross-sectional radius and maximum strength of the necking zone of the specimen are calculated.
The maximum strength of the specimen during high-temperature tensile testing was accurately calculated, which solved the stress calculation error caused by inaccurate changes in cross-sectional area and improved the accuracy of the test data.
Smart Images
Figure CN122016505A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of materials testing technology, and in particular to a method for calculating the maximum tensile strength at high temperatures. Background Technology
[0002] High-temperature tensile testing can reflect the combined effects of external force and temperature on the properties of metallic materials. In scientific experiments or accident analysis, it is necessary to know the characteristic values and curves of materials at various temperatures, such as maximum stress and true stress-true strain curves. However, generally, tests only provide force values and engineering stress-strain curves at various temperatures, making it difficult to analyze the causes of material deformation and failure. For example, in the continuous casting process of steel, surface cracks often appear on the billet within certain specific temperature ranges. Analyzing the cause of these cracks requires understanding the strength of the billet within that temperature range and the true stress-true strain curve of the billet under tensile stress. This necessitates a corresponding transformation of the high-temperature tensile test results, and the key to this transformation lies in determining the cross-sectional area of the high-temperature tensile specimen.
[0003] Currently, high-temperature tensile tests are mainly conducted using thermal simulation testing machines and material mechanics testing machines. The data from these tests is used to study the high-temperature mechanical properties of materials, crack generation during continuous casting, and to predict rolling forces. These testing devices are equipped with force sensors that can directly acquire the force values experienced by the material throughout the test. However, these devices lack a mechanism to directly acquire the changes in the cross-sectional area of the material during the test. During the test, the testing machine can obtain parameters such as temperature, deformation, force, and stress values through corresponding sensors. For stress, a crucial parameter in high-temperature tensile test data, the equipment can only accurately acquire the load force borne by the specimen, making it difficult to obtain the changes in the cross-sectional area of the specimen during the tensile process. Therefore, it is assumed that the material deforms uniformly during tensile testing. However, the deformation of the specimen during high-temperature tensile testing is often non-uniform. Therefore, the stress obtained under this assumption is inaccurate, and the more non-uniform the specimen deformation, the greater the deviation in the result.
[0004] To obtain tensile test data of materials through high-temperature tensile testing and to study the high-temperature mechanical properties of materials based on this data, it is necessary to find a method for calculating the maximum tensile strength at high temperatures. Summary of the Invention
[0005] This invention provides a method for calculating the maximum tensile strength at high temperatures, accurately finding the maximum force value that the specimen bears during high-temperature tensile process and the corresponding minimum cross-sectional area of the specimen, thereby accurately calculating the maximum strength of the specimen during high-temperature tensile process.
[0006] To achieve the above objectives, the present invention employs the following technical solution: A method for calculating the maximum tensile strength at high temperatures includes the following steps: S1. A rod-shaped tensile specimen with a circular cross-section is subjected to a high-temperature tensile test. The radius of the circular cross-section of the specimen is... , length is ; S2, Correspondence between maximum force value and specimen elongation; Based on the collected force values and the tensile length of the specimen, plot the force versus time curve and the tensile length versus time curve on the same coordinate system. Keeping the time interval constant, identify the maximum force value within the same time period. Corresponding sample elongation ; S3. Determination of parameters of high-temperature tensile specimens before and after deformation; The tensile specimen fractured into two segments after a high-temperature tensile test. The total length of the two segments was [missing information]. When the sample breaks under tension, the total elongation is ,but ; One of the two fractured specimens was analyzed, and the length of the necking region along the specimen axis was measured and recorded as . , The portion of the specimen involved in deformation, at its original length 2 before deformation. Calculated using the following formula: 2 ; S4. Calculation of the minimum cross-sectional area of the necking region of the specimen: ; in, The minimum cross-sectional radius of the necking region of the specimen; S5. Maximum strength calculation: .
[0007] Furthermore, step S1 specifically includes: taking a rod-shaped tensile specimen with a circular cross-section, welding a thermocouple at the middle position of the specimen, and then installing the specimen on a thermal simulation testing machine to conduct a high-temperature tensile test, during which the force value and the length of the specimen being stretched are collected.
[0008] Furthermore, the minimum cross-sectional radius of the necking region of the specimen is the value of the force the specimen can withstand. The radius of the minimum cross-sectional circle of the specimen is calculated as follows: The force that the specimen endured during the high-temperature tensile process was... At that time, the elongation of the sample was When the sample bears the force value The radius of the minimum cross-sectional circle of the specimen is The elongation of the specimen on the side of the smallest cross-section circle is Let the line containing the diameter of the smallest cross-section circle be the x-axis and the line containing the axis of the specimen be the y-axis. Then, the equation corresponding to the curve of the side surface of the specimen on the smallest cross-section circle within this established rectangular coordinate system is expressed by the following formula: ; in, These are undetermined constants; The equation of the curve passes through two points with coordinates of ( , ( ) ,0), ( , + Solve for the undetermined constants. : ; ; Based on the principles of calculus, and considering the invariant volume of the tensile specimen before and after deformation in the deformed portion, the following formula applies: ; The left end shows the volume calculation formula for the specimen involved in deformation, and the right end shows the volume calculation formula for this part of the specimen after deformation, thus obtaining the minimum cross-sectional radius of the necking region of the specimen: .
[0009] Compared with the prior art, the beneficial effects of the present invention are: This invention has found a functional relationship between the tensile deformation of the specimen and the radius of the necking section, which reflects that as the elongation of the specimen increases during the tensile process, the cross section gradually decreases. This accurately identifies the cross-sectional area corresponding to the maximum force the specimen can withstand, thereby accurately calculating the maximum strength of the specimen under high-temperature tension. Attached Figure Description
[0010] Figure 1 This is a graph showing the change of tensile force and elongation of the high-temperature tensile specimen described in this invention over time.
[0011] In the figure: 1. Curve showing the change of tensile force on the high-temperature tensile specimen over time; 2. Curve showing the change of elongation of the high-temperature tensile specimen over time; 3. Location of the high-temperature tensile specimen bearing the maximum force; 4. Location of the elongation corresponding to the maximum force on the high-temperature tensile specimen. Detailed Implementation
[0012] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings: This invention provides a method for calculating the maximum tensile strength at high temperatures, comprising the following steps: S1, High-temperature tensile test; Take a rod-shaped tensile specimen with a circular cross-section, the radius of which is... , length is A thermocouple is welded to the middle of the specimen, and then the specimen is installed on a thermal simulation testing machine for a high-temperature tensile test. During the test, parameters such as force value, the length of the specimen being stretched, and temperature are collected.
[0013] S2, Correspondence between maximum force value and specimen elongation; Based on the force values and tensile length of the specimen collected in step S1, plot the force versus time curve in the same coordinate system, see... Figure 1 1 is the curve showing the change of tensile force on the high-temperature tensile specimen over time; 2 is the curve showing the change of elongation of the high-temperature tensile specimen over time; 3 is the location of the maximum force on the high-temperature tensile specimen; 4 is the location of the elongation corresponding to the maximum force on the high-temperature tensile specimen. The curves show the change of the specimen's stretched length over time. By keeping the time interval constant, the maximum force value within the same time period is identified. Corresponding sample elongation .
[0014] S3. Determination of parameters of high-temperature tensile specimens before and after deformation; After step S1, the tensile specimen fractured into two segments under high temperature tensile stress, with a total length of [missing information]. When the sample breaks under tension, the total elongation is ,but ; One of the two fractured specimens was analyzed, and the length of the necking region along the specimen axis was measured and recorded as . The portion of the specimen involved in deformation, at its original length of 2 before deformation. Calculated using the following formula: (1) S4. Calculation of the minimum cross-sectional area of the necking region of the specimen: The force that the specimen endured during the high-temperature tensile process was... At that time, the elongation of the sample was When the sample bears the force value The radius of the minimum cross-sectional circle of the specimen is The specimens on both sides of the minimum cross-section circle are symmetrical; therefore, the elongation of the specimen on one side of the minimum cross-section circle is... If we establish a rectangular coordinate system with the line containing the diameter of the smallest cross-section circle as the x-axis and the line containing the axis of the specimen as the y-axis, then the equation corresponding to the curve of the side surface of the specimen on the smallest cross-section circle within the established rectangular coordinate system can be expressed by the following formula: (2) in, These are undetermined constants; The equation of the curve passes through two points with coordinates of ( , ( ) ,0), ( , + Substituting these two data points into formula (2) yields the following formula: (3) (4) By combining equations (3) and (4), the undetermined constants can be solved. : (5) (6) From formulas (5) and (6), it can be seen that the undetermined constants In elongation Original length before deformation 2 Under certain conditions, It will vary with the radius of the cross-section circle It changes with the changes, that is The value is related to the radius of the smallest cross-sectional circle of the specimen. Closely related; Based on the principles of calculus, and considering the invariant volume of the tensile specimen before and after deformation in the deformed portion, the following formula applies: (7) The left side of formula (7) is the formula for calculating the volume of the specimen involved in deformation, and the right side is the formula for calculating the volume of the specimen after deformation. Combining formulas (5), (6), and (7), we can obtain: (8) As can be seen from formula (8), when the specimen is subjected to the maximum tensile force At that time, the minimum cross-sectional radius of the necking region of the sample is The cross-sectional area can be calculated using formula (8): (9) The maximum strength is: .
[0015] The following embodiments are implemented based on the technical solution of the present invention, providing detailed implementation methods and specific operation processes. However, the scope of protection of the present invention is not limited to the following embodiments. Unless otherwise specified, the methods used in the following embodiments are conventional methods.
[0016] Example 1 A method for calculating the maximum tensile strength at high temperatures includes the following steps: S1, High-temperature tensile test; A low-carbon microalloyed steel billet was processed into a circular bar-shaped tensile specimen with dimensions of Φ10×125mm. A thermocouple was welded to the center of the specimen. The specimen was then mounted on a thermal simulation testing machine for a high-temperature tensile test at 950℃ and a tensile rate of 2×10⁻⁶. -3 During the experiment, parameters such as force value, the length of the sample being stretched, and temperature were collected.
[0017] S2, Correspondence between maximum force value and specimen elongation; Based on the force values and tensile lengths of the specimen collected in step S1, plot the force versus time curves and the tensile length versus time curves of the specimen in the same coordinate system. Keeping the time interval constant, identify the maximum force value within the same time period. =5321N, corresponding to the elongation of the sample. =2.23mm.
[0018] S3. Determination of parameters of high-temperature tensile specimens before and after deformation; After step S1, the tensile specimen fractured into two segments under high temperature tensile stress, with a total length of [missing information]. =130mm, when the specimen breaks under tension, the total elongation is =5mm; One of the two fractured specimens was analyzed, and the length of the necking region along the specimen axis was measured and recorded as . =9mm, the part of the sample that participated in the deformation, 2 in the original length before deformation. 2 is calculated from formula (1) =13mm.
[0019] S4. Calculation of the cross-sectional area of the specimen; The specimen experiences the greatest force during high-temperature tensile testing. When the strength is 5321 N, the elongation of the sample is: =2.23mm, when the sample bears a force value The radius of the minimum cross-sectional circle of the specimen is The specimens on both sides of the minimum cross-section circle are symmetrical; therefore, the elongation of the specimen on one side of the minimum cross-section circle is... =1.115mm, with the line containing the diameter of the smallest cross-section circle as the x-axis and the line containing the axis of the specimen as the y-axis, a rectangular coordinate system is established. Then, the equation corresponding to the curve of the side of the specimen on the smallest cross-section circle in the established rectangular coordinate system can be expressed by formula (2), where, These are undetermined constants; The equation of the curve passes through two points with coordinates of ( , ( ) Substituting these two data points (0, 5, 7.615) into formula (2) yields the following formula: (11) (12) By combining equations (11) and (12), the undetermined constants can be solved. : (13) (14) From formulas (13) and (14), it can be seen that the undetermined constants In elongation Original length before deformation 2 Under certain conditions, It will vary with the radius of the cross-section circle It changes with the changes, that is The value is related to the radius of the specimen cross-section circle. Closely related; According to the principle of calculus, and the relationship between the volume of the tensile specimen before and after deformation and the volume of the part involved in deformation remains unchanged, formula (7) holds. The left side of formula (7) is the formula for calculating the volume of the specimen involved in deformation, and the right side is the formula for calculating the volume of the specimen after deformation. Combine formulas (13), (14), and (7), and then determine the... =2.23mm, 2 Substituting 13mm, we get: (15) As can be seen from formula (15), when the specimen is subjected to the maximum tensile force When the strength is 5321 N, the minimum cross-sectional radius of the necking region of the sample is: =4.2mm, which can be calculated according to formula (9), the cross-sectional area is mm 2 The maximum strength calculated according to formula (10) is 95.93 MPa.
[0020] Example 2 A method for calculating the maximum tensile strength at high temperatures includes the following steps: S1, High-temperature tensile test; A low-carbon microalloyed steel billet was processed into a circular bar-shaped tensile specimen with dimensions of Φ10×125mm. A thermocouple was welded to the center of the specimen. The specimen was then mounted on a thermal simulation testing machine for a high-temperature tensile test at 1000℃ and a tensile rate of 2×10⁻⁶. -3 During the experiment, the force value and the length of the sample being stretched were collected.
[0021] S2, Correspondence between maximum force value and specimen elongation; Based on the force values and tensile lengths of the specimen collected in step 1, plot the force versus time curves and the tensile length versus time curves on the same coordinate system. Keeping the time interval constant, identify the maximum force value within the same time period. =2368N, corresponding to the elongation of the sample. =3.23mm.
[0022] S3. Determination of parameters of high-temperature tensile specimens before and after deformation; After step S1, the tensile specimen fractured into two segments under high temperature tensile stress, with a total length of [missing information]. =132mm, the total elongation at tensile fracture of the specimen is =7mm; One of the two fractured specimens was analyzed, and the length of the necking region along the specimen axis was measured and recorded as . =10mm, the part of the sample that participated in the deformation, 2 in the original length before deformation. 2 is calculated from formula (1) =13mm.
[0023] S4. Calculation of the cross-sectional area of the specimen; The specimen experiences the greatest force during high-temperature tensile testing. When the strength is 2368 N, the elongation of the sample is: =3.23mm, when the sample bears a force value The radius of the minimum cross-sectional circle of the specimen is The specimens on both sides of the minimum cross-section circle are symmetrical; therefore, the elongation of the specimen on one side of the minimum cross-section circle is... =1.615mm. Using the line containing the diameter of the smallest cross-section circle as the x-axis and the line containing the axis of the specimen as the y-axis, a rectangular coordinate system is established. The equation corresponding to the curve of the side surface of the specimen on the smallest cross-section circle within the established rectangular coordinate system can be expressed by formula (2), where, These are undetermined constants; The equation of the curve passes through two points with coordinates of ( , ( ) Substituting these two data points (0, 5, 8.115) into formula (2) yields the following formula: (16) (17) By combining equations (16) and (17), the undetermined constants can be solved. : (18) (19) From formulas (18) and (19), it can be seen that the undetermined constants are... In elongation Original length before deformation 2 Under certain conditions, It will vary with the radius of the specimen cross-section circle It changes with the changes, that is The value is related to the radius of the specimen cross-section circle. Closely related; According to the principle of calculus, and the relationship between the volume of the tensile specimen before and after deformation and the volume of the part involved in deformation remains unchanged, formula (7) holds. The left side of formula (7) is the formula for calculating the volume of the specimen involved in deformation, and the right side is the formula for calculating the volume of the specimen after deformation. Combine formulas (18), (19), and (7), and then determine the... =3.23mm, 2 Substituting 13mm, we get: (20) As can be seen from formula (20), when the specimen is subjected to the maximum tensile force When the strength is 2368 N, the minimum cross-sectional radius of the necking region of the sample is: =3.88mm, which can be calculated according to formula (9), and the cross-sectional area is mm 2 The maximum strength calculated according to formula (10) is 50.01 MPa.
Claims
1. A method for calculating the maximum tensile strength at high temperatures, characterized in that, Includes the following steps: S1. A rod-shaped tensile specimen with a circular cross-section is subjected to a high-temperature tensile test. The radius of the circular cross-section of the specimen is... , length is ; S2, Correspondence between maximum force value and specimen elongation; Based on the collected force values and the tensile length of the specimen, plot the force versus time curve and the tensile length versus time curve on the same coordinate system. Keeping the time interval constant, identify the maximum force value within the same time period. Corresponding sample elongation ; S3. Determination of parameters of high-temperature tensile specimens before and after deformation; The tensile specimen fractured into two segments after a high-temperature tensile test. The total length of the two segments was [missing information]. When the sample breaks under tension, the total elongation is ,but ; One of the two fractured specimens was analyzed, and the length of the necking region along the specimen axis was measured and recorded as . , The portion of the specimen involved in deformation, at its original length 2 before deformation. Calculated using the following formula: 2 ； S4. Calculation of the minimum cross-sectional area of the necking region of the specimen: ； in, The minimum cross-sectional radius of the necking region of the specimen; S5. Maximum strength calculation: 。 2. The method for calculating the maximum tensile strength at high temperatures according to claim 1, characterized in that, Step S1 specifically includes: taking a rod-shaped tensile specimen with a circular cross-section, welding a thermocouple at the middle position of the specimen, and then installing the specimen on a thermal simulation testing machine to conduct a high-temperature tensile test, collecting the force value and the length of the specimen being stretched during the test.
3. The method for calculating the maximum tensile strength at high temperatures according to claim 1, characterized in that, The minimum cross-sectional radius of the necking region of the specimen is the value of the force the specimen can withstand. The radius of the minimum cross-sectional circle of the specimen is calculated as follows: The force that the specimen endured during the high-temperature tensile process was... At that time, the elongation of the sample was When the sample bears the force value The radius of the minimum cross-sectional circle of the specimen is The elongation of the specimen on the side of the smallest cross-section circle is Let the line containing the diameter of the smallest cross-section circle be the x-axis and the line containing the axis of the specimen be the y-axis. Then, the equation corresponding to the curve of the side surface of the specimen on the smallest cross-section circle within this established rectangular coordinate system is expressed by the following formula: ； in, These are undetermined constants; The equation of the curve passes through two points with coordinates of ( , ( ) ,0), ( , + Solve for the undetermined constants. : ； ； Based on the principles of calculus, and considering the invariant volume of the tensile specimen before and after deformation in the deformed portion, the following formula applies: ； The left end shows the volume calculation formula for the specimen involved in deformation, and the right end shows the volume calculation formula for this part of the specimen after deformation, thus obtaining the minimum cross-sectional radius of the necking region of the specimen: 。