Method for determining high-temperature tensile true stress-strain curve
By analyzing the material deformation characteristics and the law of constant volume, the cross-sectional area of the necking region of the high-temperature tensile specimen was calculated, which solved the problem of inaccurate stress value measurement in the existing technology and enabled the plotting of the true stress-strain curve during the high-temperature tensile process.
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 technologies make it difficult to accurately measure the true stress-strain curve of materials in high-temperature tensile tests, especially when the specimen deformation is uneven, making it difficult to obtain the change in the cross-sectional area of the specimen, resulting in inaccurate stress value measurement.
By analyzing the deformation characteristics of the material and using the law of constant volume, the minimum cross-sectional area of the necking region of the specimen is calculated. Combined with the stress value and strain relationship, the true stress-strain curve is plotted.
It enables accurate acquisition of the true stress-strain curve of materials during high-temperature tensile processes, thereby improving the accuracy of stress value measurement.
Smart Images
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Abstract
Description
Technical Field
[0001] This invention relates to the field of materials testing technology, and in particular to a method for determining the true stress-strain curve of high-temperature tensile stress. Background Technology
[0002] High-temperature tensile tests 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 characteristic curves of materials at various temperatures, such as maximum stress and true stress-true strain curves.
[0003] Plasticity and toughness are important performance parameters reflecting a material's properties, while the true stress-strain curve accurately reflects the plastic deformation during tensile testing and is crucial for determining the material's true breaking strength and resistance to deformation. Research on high-temperature mechanical properties and rolling force prediction based on high-temperature tensile test data primarily utilizes thermodynamic simulation testing machines and material mechanics testing machines. Typical testing equipment incorporates force sensors to directly acquire the force values experienced by the material throughout the test. However, these machines lack devices capable of directly acquiring 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. Stress is a critical parameter in high-temperature tensile test data; however, the equipment can only accurately acquire the load force borne by the specimen, making it difficult to obtain the changes in the specimen's cross-sectional area during tensile testing. This difficulty is further compounded when uneven deformation occurs during high-temperature tensile testing. Since stress is the ratio of the load force to the corresponding cross-sectional area of the specimen, accurate measurement of stress values during tensile testing is challenging with current technologies.
[0004] In studying the high-temperature strength of materials and predicting the rolling force of rolling mills, one approach is to obtain tensile test data through high-temperature tensile testing. Based on this data, regression fitting is performed to obtain a stress-strain curve, taking into account the influence of deformation rate and deformation temperature on rheological stress to obtain a highly accurate predicted rolling force value. However, traditional methods have always had limitations in measuring the true stress-strain curve. Therefore, developing a method for determining the true stress-strain curve of tensile tests is of great significance. Summary of the Invention
[0005] This invention provides a method for determining the true stress-strain curve of a high-temperature tensile test. By analyzing the deformation characteristics of the material, the cross-sectional area of the specimen corresponding to the force value during the deformation process is found, so as to effectively obtain the true stress-strain curve of the material during the high-temperature tensile test.
[0006] To achieve the above objectives, the present invention employs the following technical solution: A method for determining the true stress-strain curve of high-temperature tensile stress 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 force value and specimen elongation; Based on the force values and the tensile length of the specimen collected in the experiment, plot the force versus time curve and the tensile length of the specimen versus time curve on the same coordinate system. Keeping the time interval constant, find the force values within the same time interval. and the corresponding elongation of the specimen. ; 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 axial direction of the specimen 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. Calculate the corresponding stress value using the stress value F. Based on this stress value, the relationship between stress and strain is obtained, thus yielding the corresponding true stress-strain curve. The relationship between stress and strain is as follows: ; in, For stress is The true response to the situation.
[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, collecting force values, strain, and the length of the specimen being stretched during the test.
[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 experiences during high-temperature tensile testing is... 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 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: ; 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] Furthermore, the stress value is calculated based on the stress value F. : .
[0010] Compared with the prior art, the beneficial effects of the present invention are: This invention analyzes the deformation characteristics of materials and uses the law of constant volume to quickly find the relationship between the elongation of the sample as it is stretched and the radius of the smallest cross-section circle of the sample. This allows for the determination of the cross-sectional area of the sample corresponding to the force value during the deformation process, thus accurately obtaining the true stress-strain curve of the material during high-temperature tensile stress. Detailed Implementation
[0011] The specific embodiments of the present invention will be further described below: This invention provides a method for determining the true stress-strain curve of high-temperature tensile stress, 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, strain, the length of the specimen being stretched, and temperature are collected.
[0012] S2, Correspondence between 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 on the same coordinate system. Keeping the time interval constant, find the force values within the same time interval. and the corresponding elongation of the specimen. .
[0013] 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 axial direction of the specimen 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 cross-sectional area of the specimen; The force that the specimen experiences during high-temperature tensile testing is... 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 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) Then through force value The corresponding stress value can be calculated. : (10) By obtaining the force and strain values from step 1, and then using formula (10) to convert the force values into their corresponding stress values, the relationship between stress and strain can be obtained, thus yielding the corresponding true stress-strain curve. The converted formula is as follows: (11) in, For stress is The true response to the situation.
[0014] 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.
[0015] Example 1 A method for determining the true stress-strain curve of high-temperature tensile stress 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, force values, strain, and the length of the specimen being stretched were collected.
[0016] S2, Correspondence between 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 on the same coordinate system. Keeping the time interval constant, find the force values within the same time interval. and the corresponding elongation of the specimen. .
[0017] 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 axial direction of the specimen 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.
[0018] S4. Calculation of the cross-sectional area of the specimen; The force that the specimen experiences during high-temperature tensile testing is... 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 take 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, we can establish a rectangular coordinate system. 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). The equation of the curve passes through two points with coordinates of ( , ( ) ,0), (5,6.5+ Substituting these two data points into formula (2) yields the following formula: (12) (13) By combining equations (12) and (13), the undetermined constants can be solved. : (14) (15) From formulas (14) and (15), 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 equations (14), (15), and (7), and then determine the 2... Substituting 13mm, we get: (16) As can be seen from formula (16), when the specimen is subjected to 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): (17) Then through force value The corresponding stress value can be calculated. : (18) By obtaining the force and strain values from step S1 and then converting them into their corresponding stress values using formula (18), the stress-strain relationship can be obtained, thus yielding the true stress-strain curve. The converted formula is: (19) in, For stress is The true response to the situation.
Claims
1. A method for determining the true stress-strain curve of high-temperature tensile stress, 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 force value and specimen elongation; Based on the force values and the tensile length of the specimen collected in the experiment, plot the force versus time curve and the tensile length of the specimen versus time curve on the same coordinate system. Keeping the time interval constant, find the force values within the same time interval. and the corresponding elongation of the specimen. ; 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. Calculate the corresponding stress value using the stress value F. Based on this stress value, the relationship between stress and strain is obtained, thus yielding the corresponding true stress-strain curve. The relationship between stress and strain is as follows: ； in, For stress is The true response to the times.
2. The method for determining the true stress-strain curve of high-temperature tensile stress 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. During the test, the force value, strain, and the length of the specimen being stretched are collected.
3. The method for determining the true stress-strain curve of high-temperature tensile stress 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 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: ； 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: 。 4. The method for determining the true stress-strain curve of high-temperature tensile stress according to claim 1, characterized in that, The stress value is calculated by using the stress value F. : 。