A method for correcting the non-linear strain response of asphalt materials under a parallel plate based on the single-point method

Abstract

A method for correcting the non-linear strain response of asphalt materials under a parallel plate based on the single-point method. The method determines the conversion relationship of mechanical parameters under different fixture systems and explores the feasibility of solving the shear stress under the parallel plate fixture system. Based on the DIN standard, a calculation formula for the shear stress of Newtonian fluid at the maximum radial distance is established. Based on the single-point method correction theory, combined with the Herschel-Bulkley model, a relationship between asphalt viscosity and stress is established, the shear stress formula of power-law fluid is derived, and a theoretical correction method for the non-linear strain response of asphalt materials under a parallel plate is established. And the correction results are verified based on the time sweep test. This method reveals the conversion relationship of mechanical parameters between the working states of the parallel plate and the cone-and-plate fixture systems, realizes the acquisition of the true and accurate non-linear strain response of asphalt under the parallel plate fixture system, and provides an effective means for accurately measuring the viscoelasticity of asphalt materials in a wide stress range using a parallel plate.

Description

Technical Field

[0001] The present invention belongs to the field of research on the performance testing of asphalt materials, and relates to a method for correcting the non-linear strain response of asphalt materials under a parallel plate based on a single-point method. Background Art

[0002] For the development of transportation, materials come first. The breakthrough of new material technologies is of great significance to the construction of transportation infrastructure. As a typical viscoelastic material widely used in road construction and other fields, the viscoelasticity of asphalt has a direct impact on the macroscopic performance of the road surface. Understanding the viscoelasticity of asphalt is crucial for designing and building high-quality roads. Appropriate viscoelasticity can improve the rutting resistance, fatigue resistance and durability of the road. Therefore, accurately testing the viscoelasticity of asphalt materials becomes the key to the problem.

[0003] The dynamic shear rheometer is a commonly used instrument for testing the viscoelasticity of asphalt materials. By applying different stresses to asphalt based on the dynamic shear rheometer, the corresponding strain responses are obtained, and then indexes such as complex modulus, phase angle, rutting factor and loss factor are calculated to characterize the viscoelasticity of asphalt materials. The fixture is one of the most important components of the dynamic shear rheometer. As the most commonly used fixture system of the dynamic shear rheometer, the parallel plate fixture has many advantages, including: the gap size can be freely selected for each experiment, so a wide range of shear rates can be obtained; flat and solid samples can be measured without creating complex sample shapes; the measurement accuracy of the fixture is easy to test, etc. However, when one of the plates of the parallel plate deflects by a certain angle Φ, the linear displacement at the radius r is equal to Φ*r, and the strain at the radius r is Φ*r / h, that is, the true strain in the parallel plate changes in direct proportion to the radius along the radial direction, increasing from 0 at the center in direct proportion to the radius to the maximum at the edge; and when one of the plates rotates at a certain angular rate Ω, the linear rate at the radius r is equal to Ω*r, and the shear rate at the radius r is Ω*r / h, that is, the true shear rate in the parallel plate test system also changes in direct proportion to the radius along the radial direction; that is to say, the flow field constructed by the parallel plate is a non-uniform field. If the linear viscoelasticity of asphalt materials is tested using the parallel plate, the measured viscoelastic parameters do not depend on the magnitude of the strain or shear rate. However, if the parallel plate is used for the non-linear viscoelasticity test of asphalt materials, accurate results cannot be obtained. Therefore, in order to make the parallel plate also applicable to the non-linear viscoelasticity measurement of asphalt and continue to play its significant advantages, the non-linear strain response data of the parallel plate should be corrected, and the non-real strain response obtained under the parallel plate should be corrected to a strain response equivalent to the real level (that is, the strain response under the cone and plate system).

[0004] The currently commonly used method for correcting the non-linear response of asphalt materials under parallel plates was proposed by Soskey and Winter. By performing variable substitution, taking the partial derivative of the shear rate, and using the Leibnitz rule, the corrected strain response can be obtained. However, due to data differences, large errors may occur, especially obvious systematic errors near the high and low ends of the data set. This method is only applicable to the correction of mechanical responses under strain control. Therefore, there is an urgent need to propose a new method to correct the non-linear strain response of asphalt materials under parallel plates under stress control. Summary of the Invention

[0005] The object of the present invention is to solve the problem of inaccurate non-linear strain response of asphalt under the parallel plate system of a dynamic shear rheometer, and to provide a method for correcting the non-linear strain response of asphalt materials under parallel plates based on the single-point method. This method reveals the conversion relationship between mechanical parameters in the working states of the parallel plate and the cone-and-plate fixture systems, thereby obtaining a true and accurate non-linear strain response of asphalt under the parallel plate fixture system, providing an effective means for accurately measuring the viscoelasticity of asphalt materials in a wide stress range using parallel plates, and having positive significance for comprehensively studying the viscoelasticity of asphalt and other materials.

[0006] The object of the present invention is achieved through the following technical solutions:

[0007] A method for correcting the non-linear strain response of asphalt materials under parallel plates based on the single-point method, the method comprising the following steps:

[0008] Step 1: Determine the conversion relationships between the rotational speed and the shear rate, and between the torque and the shear stress when working under different fixture system conditions, and derive the general calculation formula for torque when the conversion coefficient is unknown.

[0009] Step 2: Based on the conversion coefficient of Newtonian fluid parallel plates established according to the DIN standard, determine the torque calculation formula under a certain viscosity, and derive and determine the shear stress calculation formula of Newtonian fluid with the maximum radial distance.

[0010] Step 3: Based on the single-point method correction theory, introduce the fluid rheological curve based on the Herschel-Bulkley model, establish the relationship between the viscosity and stress of asphalt, and combine the torque calculation formula and the shear stress calculation formula determined in Step 2 to obtain the shear stress formula of power-law fluid at a certain radius and the radius ratio r of this radius to the radius of the parallel plate fixture. s * Finally, establish the theoretical derivation of the method for correcting the non-linear strain response under the parallel plates of a stress-controlled rheometer.

[0011] Step 4: Conduct a time sweep test on the same asphalt sample under the parallel plate and cone-and-plate fixture systems at 30 °C and 5 rad / s, and set a group of parallel samples.

[0012] Step 5: Based on the determined correction method, obtain the corrected strain response of the parallel plate and compare it with the true strain response result under the cone plate to verify the feasibility and accuracy of the above correction method.

[0013] Further, in Step 1, the conversion relationship is:

[0014] In the formula: is the shear rate; C SR is the conversion coefficient that relates the rotational speed to the shear rate; ω is the rotational speed; τ is the shear stress; C SS is the conversion coefficient that relates the torque to the shear stress; M is the torque;

[0015] The general calculation formula for torque when the conversion coefficient is unknown is:

[0016]

[0017] In the formula: r is the radius at the mechanical response; R is the radius of the fixture; is the shear stress at a certain shear rate.

[0018] Further, in Step 2, the torque calculation formula for Newtonian fluid is:

[0019]

[0020] In the formula: R is the radius of the fixture, η is the viscosity; r is the radius at the mechanical response; h is the fixture gap;

[0021] The shear stress response formula is derived as:

[0022]

[0023] In the formula: τ(r) is the shear stress at a certain radius;

[0024] The calculation formula for the shear stress of Newtonian fluid determined by derivation and the maximum radial distance is:

[0025]

[0026] Further, in Step 3, the fluid rheological curve of asphalt based on the Herschel - Bulkley model is expressed as

[0027]

[0028] According to the shear stress calculation of Newtonian fluid in Step 2, the torque required to drive the parallel plate to rotate is:

[0029]

[0030] Thus, the shear stress of the power-law fluid at a certain radius is as follows:

[0031]

[0032] The radius ratio is:

[0033]

[0034] Finally, the formula for the strain response correction method is:

[0035]

[0036] In the formula: γ α is the corrected strain response, α is the measured strain response, r s * is the radius ratio, and n is the flow index.

[0037] Furthermore, in step four, the time sweep refers to applying a stress response with a fixed amplitude that varies sinusoidally or cosinusoidally to the material to obtain its strain response. The selected amplitudes are 20 kPa, 40 kPa, 60 kPa, 80 kPa, 100 kPa, 140 kPa, and 180 kPa, where 80 kPa, 100 kPa, 140 kPa, and 180 kPa are non-linear stress points.

[0038] Compared with the prior art, the present invention has the following advantages: The present invention proposes a method for correcting the non-linear strain response of asphalt materials under parallel plates, realizes the correction of the non-linear viscoelastic strain response of asphalt under parallel plates, verifies the accuracy of the correction method, broadens the application range of parallel plates, and provides theoretical support for further comprehensively testing and characterizing the viscoelasticity of asphalt materials. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 is a flow chart of the method for correcting the non-linear strain response of asphalt materials under parallel plates based on the single-point method of the present invention;

[0040] Figure 2 is a schematic diagram of the strain response after correction of the parallel plate and under the cone plate with a stress amplitude of 80 kPa in the embodiment;

[0041] Figure 3 is a schematic diagram of the strain response after correction of the parallel plate and under the cone plate with a stress amplitude of 100 kPa in the embodiment;

[0042] Figure 4 is a schematic diagram of the strain response after correction of the parallel plate and under the cone plate with a stress amplitude of 140 kPa in the embodiment;

[0043] Figure 5Schematic diagram of the strain response under the parallel plate and cone plate after correction with a stress amplitude of 180 kPa in the embodiment. Detailed implementation manners

[0044] The technical solutions of the present invention will be further described below with reference to the accompanying drawings, but are not limited thereto. Any modification or equivalent replacement of the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention shall be covered by the protection scope of the present invention.

[0045] The present invention provides a method for correcting the non-linear strain response of asphalt materials under a parallel plate based on the single-point method. This method determines the conversion relationship of mechanical parameters under different fixture systems and explores the feasibility of solving the shear stress under the parallel plate fixture system; based on the DIN standard, a calculation formula for the shear stress of Newtonian fluid at the maximum radial distance is established; based on the single-point method correction theory, combined with the Herschel-Bulkley model, a relationship between asphalt viscosity and stress is established, a shear stress formula for power-law fluid is derived, and a theoretical correction method for the non-linear strain response of asphalt materials under a parallel plate is established; and the correction results are verified based on the time sweep test.

[0046] Example 1:

[0047] A method for correcting the non-linear strain response of asphalt materials under a parallel plate based on the single-point method, as Figure 1 shown, the specific implementation steps are as follows:

[0048] Step 1: When the rheometer works under different fixture systems, two conversion coefficients are used to achieve the mutual transformation between different parameters: one is the conversion coefficient C SR that associates the rotational speed with the shear rate, and the other is the conversion coefficient C SS that associates the torque with the shear stress, as shown in the following formula.

[0049]

[0050] In the formula: is the shear rate; ω is the rotational speed; τ is the shear stress; M is the torque.

[0051] However, in the parallel plate fixture system, the shear rate is not constant throughout the sample but increases linearly along the radius. This means that before the viscoelastic behavior of the fluid is defined, the integral of Equation (1) cannot be solved, that is, for the parallel plate, different conversion coefficients are used when testing different fluid types or fluid states.

[0052]

[0053] In the formula: r is the radius at the mechanical response; R is the fixture radius; Shear stress at a certain shear rate.

[0054] Step 2: The commonly used parallel plate conversion factor is established based on the DIN standard considering Newtonian fluids. This standard assumes that the viscosity η of the fluid is constant, and the torque is calculated as shown in Equation (3).

[0055]

[0056] In the formula: η is the viscosity; h is the fixture gap.

[0057] Furthermore, the shear stress response in the generalized form can be deduced as shown in Equation (4).

[0058]

[0059] Since both the shear rate and shear stress of the parallel plate depend on the radial distance, for convenient and unified measurement, the conversion factor used when the parallel plate system tests the viscoelasticity of all fluids refers to the conversion factor calculated at the same distance. Usually, this distance is taken as the maximum radial distance, that is, the radius r = R, and its shear stress is calculated through the built-in software as follows.

[0060]

[0061] Step 3: When Equation (5) is applied to non-Newtonian fluids or fluids in a non-linear state, such as the viscoelasticity test of asphalt under large-amplitude oscillatory shear loads, difficulties will occur. Obviously, the measured strain response is not the true strain response. To enable the parallel plate to still play its significant advantages and be applicable to the non-linear viscoelasticity measurement of asphalt materials, its mechanical response should be corrected.

[0062] The present invention introduces the single-point method correction theory. This correction theory believes that there is a certain radius r s , at which the conversion based on the assumption of Newtonian fluid will be accurate. The ratio of this radius to the radius of the parallel plate fixture defines the basic theory of the single-point method correction method.

[0063]

[0064] From Equation (4), the shear stress at the corresponding radius based on the assumption of Newtonian fluid can be obtained

[0065]

[0066] τ'(r s ) is the shear stress at the corresponding radius when the conversion based on the assumption of Newtonian fluid is accurate.

[0067] However, when the above equation is applied to non-Newtonian fluids or fluids in a non-linear state, difficulties arise because the viscosity and stress of the fluid are not simply linearly related at this time. The rheological curve of the fluid can be described based on the Herschel-Bulkley model, and for asphalt, it can be written as the following equation.

[0068]

[0069] In the formula: τ HB is the shear stress when describing the fluid based on the Herschel-Bulkley model; is the shear rate; n is the power exponent. When n < 1, it is a pseudoplastic body, and when n > 1, it is a dilatant body.

[0070] According to Equation (3), the torque required to drive the parallel plate to rotate is calculated as:

[0071]

[0072] M HB is the torque required to drive the parallel plate to rotate;

[0073] Thus, the shear stress of the power-law fluid at a certain radius can be obtained as follows:

[0074]

[0075] r s is the corresponding radius when the conversion is accurate based on the Newtonian fluid assumption; n is the power exponent. When n < 1, it is a pseudoplastic body, and when n > 1, it is a dilatant body.

[0076] Since the asphalt material is a non-Newtonian fluid, the flow index n at each point can be determined according to its rheological curve equation (8). By comparing Equation (5) with (10), the radius ratio r s * .

[0077]

[0078] The rheometer adopted in this patent is a stress-controlled rheometer, and the radius at the corresponding true stress is also the radius corresponding to its true strain. Therefore, the corrected true strain should be:

[0079]

[0080] In the formula: γ α is the corrected strain response, α is the measured strain response, r s * is the radius ratio, and n is the flow index.

[0081] So far, the theoretical derivation of the correction method for the non-linear strain response under the parallel plates of the stress-controlled rheometer has been completed.

[0082] Step 4: To verify the accuracy of the proposed correction method, a time sweep test of the same asphalt sample was carried out under the parallel plate and cone-plate fixture systems at 30 °C and 5 rad / s, and a set of parallel samples was set up. The strain response results are as follows:

[0083] Table 1 Comparison table of asphalt strain response (%) between parallel plate and cone-plate

[0084]

[0085] From the above results, it can be seen that the test results have good parallelism. As the stress increases, the corresponding strain response also increases continuously. When the stress input is 60 kPa and below, that is, the input stress is within the linear range, the parallel plate and the cone-plate show similar strain responses, which also indicates that both are suitable for the measurement of linear viscoelasticity. When the input stress is greater than 60 kPa, it can be found that the strain response of the cone-plate is significantly lower than that of the parallel plate. This is because the flow field constructed by the parallel plate is a non-uniform flow field, making the outermost strain detected by the strain sensor position significantly greater than the actual strain inside the sample, and the strain measured in the test is not the true strain.

[0086] Step 5: Apply the above strain response correction theory to correct the four non-linear points with input stresses of 80 kPa, 100 kPa, 140 kPa, and 180 kPa, and draw the schematic diagram of the strain response after correction of the parallel plate and under the cone-plate, as Figures 2 to 5 shown.

[0087] From the above results, it can be seen that the strain measured by the parallel plate before correction is significantly greater than the true strain measured by the cone-plate throughout the cycle time, especially at the peak of the strain cycle, the gap between the two is more obvious. After correcting the strain response of the parallel plate based on the single-point method, it can be found that regardless of the input stress amplitude, the corrected strain response of the parallel plate almost coincides with the strain response measured by the cone-plate, indicating that this correction method is applicable to the correction of the strain response of asphalt under large-amplitude oscillatory shear loads measured by the stress-controlled parallel plate.

[0088] In summary, based on the non-linear strain response correction method of asphalt materials of the present invention, the accurate correction of the non-linear strain response of asphalt under the parallel plate is realized. The coincidence effect between the corrected strain response curve of the parallel plate and the true strain response curve under the cone-plate is significant. The present invention broadens the application range of the parallel plate, provides an effective means for testing the non-linear viscoelasticity of asphalt materials using the parallel plate system, and also provides a new idea for testing the non-linear strain response of other viscoelastic materials using the parallel plate system.

Claims

1. A method for correcting the non-linear strain response of asphalt materials under a parallel plate based on the single-point method, characterized in that: The method includes the following steps: Step 1: Determine the conversion relationships between rotational speed and shear rate, and between torque and shear stress when working under different fixture system conditions, and derive the general calculation formula for torque when the conversion coefficient is unknown; the conversion relationships are as follows: Wherein: is the shear rate; C SR is the conversion coefficient that correlates the rotational speed with the shear rate; is the rotational speed; is the shear stress; C SS is the conversion coefficient that correlates the torque with the shear stress; is the torque; The general calculation formula for torque when the conversion coefficient is unknown is: In the formula: is the radius at the mechanical response; is the fixture radius; is the shear stress at a certain shear rate; Step 2: Based on the conversion coefficient of Newtonian fluid parallel plates established according to the DIN standard, determine the torque calculation formula under a certain viscosity, and derive and determine the Newtonian fluid shear stress calculation formula with the maximum radial distance; the Newtonian fluid torque calculation formula is: In the formula: is the fixture radius, is the viscosity; is the radius at the mechanical response; is the fixture gap; The shear stress response formula is derived as: In the formula: is the shear stress at a certain radius; The Newtonian fluid shear stress calculation formula derived and determined with the maximum radial distance is: ； Step 3: Based on the single-point method correction theory, introduce the fluid rheological curve based on the Herschel-Bulkley model, establish the relationship between the viscosity and stress of asphalt, and combine the torque calculation formula and shear stress calculation formula determined in Step 2 to obtain the shear stress formula of the power-law fluid at a certain radius and the radius ratio of this radius to the radius of the parallel plate fixture , and finally establish the theoretical derivation of the correction method for the non-linear strain response under the parallel plate of the stress-controlled rheometer; the fluid rheological curve of asphalt based on the Herschel-Bulkley model is expressed as According to the Newtonian fluid shear stress in Step 2, the torque required to drive the parallel plates to rotate is: Thus, the shear stress of the power-law fluid at a certain radius is as follows: The radius ratio is: The formula for the final strain response correction method is as follows: Wherein: is the corrected strain response, is the measured strain response, is the radius ratio, n is the flow index.

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