Non-linear strain response correction method for asphalt material under parallel plate based on single-point method

Abstract

The invention discloses a nonlinear strain response correction method for an asphalt material under a parallel plate based on a single-point method, and the method comprises the steps: determining a conversion relation of mechanical parameters under different clamp systems, and exploring the solving feasibility of shear stress under a parallel plate clamp system; based on the DIN standard, a calculation formula of the shear stress of the Newtonian fluid at the maximum radial distance is established; based on a single-point method correction theory, a relation between asphalt viscosity and stress is established by combining a Herschel-Bulkley model, a power law fluid shear stress formula is deduced, and a theoretical correction method for nonlinear strain response of an asphalt material under a parallel plate is established; and the correction result is verified based on a time scanning test. According to the method, the conversion relation of mechanical parameters between the working states of the parallel plate and the conical plate clamp system is disclosed, real and accurate asphalt nonlinear strain response is obtained under the parallel plate clamp system, and an effective means is provided for accurately measuring viscoelasticity of an asphalt material in a wide stress domain by using the parallel plate.

Description

Technical Field

[0001] The invention belongs to the research field of asphalt material performance testing, and relates to a nonlinear strain response correction method of asphalt material under parallel plates based on a single-point method. Background Art

[0002] The development of transportation starts with materials, and the breakthrough of new material technology has extraordinary significance for the construction of transportation infrastructure. Asphalt is a typical viscoelastic material widely used in road construction and other fields. Its viscoelasticity has a direct impact on the macroscopic performance of the road surface. Understanding the viscoelasticity of asphalt is crucial for the design and construction of high-quality roads. Appropriate viscoelasticity can improve the road's anti-rutting performance, anti-fatigue performance and durability. Therefore, accurately testing the viscoelasticity of asphalt materials becomes the key to the problem.

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

[0004] The commonly used method for correcting the nonlinear response of asphalt materials under parallel plates was proposed by Soskey and Winter. After variable substitution, partial derivative of shear rate and Leibnitz law, the corrected strain response can be obtained. However, due to the difference in data, large errors may occur, especially near the high and low ends of the data set, and obvious systematic errors will occur. This method is only applicable to the correction of mechanical response under strain control. Therefore, it is urgent to propose a new method to correct the nonlinear strain response of asphalt materials under parallel plates under stress control. Summary of the invention

[0005] The purpose of the present invention is to solve the problem of inaccurate nonlinear strain response of asphalt under the parallel plate system of dynamic shear rheometer, and to provide a method for correcting the nonlinear strain response of asphalt materials under parallel plates based on the single-point method. The method reveals the conversion relationship between the mechanical parameters of the parallel plate and the cone-plate fixture system in the working state, thereby obtaining a true and accurate nonlinear 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 domain using parallel plates, and has positive significance for the comprehensive study of the viscoelasticity of asphalt and other materials.

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

[0007] A method for correcting the nonlinear strain response of asphalt material under parallel plates based on a single point method, the method comprising the following steps:

[0008] Step 1: Determine the conversion relationship between speed and shear rate, torque and shear stress under different fixture system conditions, and derive the general calculation formula of torque when the conversion coefficient is unknown;

[0009] Step 2: Based on the Newtonian fluid parallel plate conversion coefficient established by DIN standard, determine the torque calculation formula under a certain viscosity, and derive the Newtonian fluid shear stress calculation formula determined by the maximum radial distance;

[0010] Step 3: Based on the single-point method correction theory, the fluid rheological curve based on the Herschel-Bulkley model is introduced to establish the viscosity-stress relationship for asphalt. Combining the torque calculation formula and shear stress calculation formula determined in step 2, the shear stress formula of the power-law fluid under a certain radius and the radius ratio r of the radius to the parallel plate fixture radius are obtained. s * , and finally the theoretical derivation of the nonlinear strain response correction method under the parallel plates of the stress-controlled rheometer is established.

[0011] Step 4: Conduct a time scan test of the same asphalt sample under the parallel plate and cone-plate fixture system at 30°C and 5 rad / s, and set up a set of parallel pieces;

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

[0013] Furthermore, in step 1, the conversion relationship is:

[0014] Where: 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 factor relating torque to shear stress; M is the torque;

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

[0016]

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

[0018] Furthermore, in step 2, the Newtonian fluid torque calculation formula is:

[0019]

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

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

[0022]

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

[0024] The formula for calculating the shear stress of Newtonian fluids derived and determined at the maximum radial distance is:

[0025]

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

[0027]

[0028] According to the Newtonian fluid shear stress in step 2, the torque required to drive the parallel plates to rotate is calculated as:

[0029]

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

[0031]

[0032] The radius ratio is:

[0033]

[0034] The final strain response correction method formula is:

[0035]

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

[0037] Furthermore, in step four, the time scan refers to applying a stress response with a fixed amplitude of sine or cosine variation to the material to obtain its strain response, and the selected amplitudes are 20kPa, 40kPa, 60kPa, 80kPa, 100kPa, 140kPa, and 180kPa, among which 80kPa, 100kPa, 140kPa, and 180kPa are nonlinear stress points.

[0038] Compared with the prior art, the present invention has the following advantages: the present invention proposes a method for correcting the nonlinear strain response of asphalt materials under parallel plates, realizes the correction of the nonlinear viscoelastic strain response of asphalt under parallel plates, verifies the accuracy of the correction method, broadens the scope of use of parallel plates, and provides theoretical support for further comprehensive testing and characterization of the viscoelasticity of asphalt materials. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 It is a flow chart of the method for correcting the nonlinear strain response of asphalt material under parallel plates based on the single point method of the present invention;

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

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

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

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

[0044] The technical solution of the present invention is further described below in conjunction with the accompanying drawings, but is not limited thereto. Any modification or equivalent replacement of the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention should be included in the protection scope of the present invention.

[0045] The present invention provides a method for correcting the nonlinear strain response of asphalt materials under parallel plates based on a single-point method. The method determines the conversion relationship between mechanical parameters under different clamp systems, and explores the feasibility of solving the shear stress under the parallel plate clamp 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 correction theory of the single-point method, the relationship between asphalt viscosity and stress is established in combination with the Herschel-Bulkley model, the power-law fluid shear stress formula is derived, and a theoretical correction method for the nonlinear strain response of asphalt materials under parallel plates is established; and the correction results are verified based on a time scanning experiment.

[0046] Embodiment 1:

[0047] A correction method for the nonlinear strain response of asphalt materials under parallel plates based on the single-point method, such as Figure 1 As shown, the specific implementation steps are as follows:

[0048] Step 1: When the rheometer is working under different fixture system conditions, two conversion factors are used to achieve the mutual conversion between different parameters: one is the conversion factor C that relates the rotation speed to the shear rate. SR , and the other is the conversion factor C that relates torque to shear stress SS , as shown below.

[0049]

[0050] Where: is the shear rate; ω is the rotation speed; τ is the shear stress; M is the torque.

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

[0052]

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

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

[0055]

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

[0057] It can be further deduced that the shear stress response in a generalized form is shown in equation (4).

[0058]

[0059] Since the shear rate and shear stress of the parallel plate depend on the radial distance, in order to facilitate unified measurement, the conversion coefficient used in the parallel plate system to test the viscoelasticity of all fluids refers to the conversion coefficient calculated at the same distance. Usually, the distance is the maximum radial distance, that is, the radius r = R. The shear stress is calculated by the built-in software as follows.

[0060]

[0061] Step 3: When formula (5) is applied to non-Newtonian fluids or fluids in a nonlinear state, such as the viscoelastic test of asphalt under large oscillating shear loads, difficulties will arise. Obviously, the measured strain response is not the true strain response. In order to make the parallel plate still play its significant advantages and be suitable for the nonlinear viscoelastic measurement of asphalt materials, its mechanical response should be corrected.

[0062] The present invention introduces the single point method correction theory, which believes that there is a certain radius r s , at which the conversion based on the assumption of Newtonian fluid will be accurate, and 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 formula (4), we can get the shear stress on the corresponding radius based on the Newtonian fluid assumption:

[0065]

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

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

[0068]

[0069] Where: τ HB is the shear stress when describing the fluid based on the Herschel-Bulkley model; is the shear rate; n is the power index. When n<1, it is a pseudoplastic body, and 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 The torque required to drive the parallel plates to rotate;

[0073] Therefore, the shear stress of the power-law fluid at a certain radius is 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 index. When n<1, it is a pseudoplastic body, and n>1 is a dilatant body.

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

[0077]

[0078] The rheometer used in this patent is a stress-controlled rheometer. The radius corresponding to the true stress is also the radius corresponding to the true strain, so the corrected true strain should be:

[0079]

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

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

[0082] Step 4: To verify the accuracy of the proposed correction method, a time scan test of the same asphalt sample was conducted under the parallel plate and cone-plate fixture system at 30°C and 5 rad / s, and a set of parallel parts were set up. The strain response results are shown below:

[0083] Table 1 Comparison of asphalt strain response (%) and flat cone plate

[0084]

[0085] It can be seen from the above results 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 or less, that is, the input stress is within the linear region, the parallel plate and the cone-plate show similar strain responses, which also shows 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, which makes the edge 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 real strain.

[0086] Step 5: Apply the above strain response correction theory to correct the four nonlinear points with input stress of 80kPa, 100kPa, 140kPa and 180kPa, and draw the strain response diagram after parallel plate correction and under cone-plate, as shown in 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 during the entire cycle time, especially at the peak of the strain cycle where the difference is more obvious; after correcting the strain response of the parallel plate based on the single-point method, it can be found that no matter what input stress amplitude is used, the corrected parallel plate strain response almost coincides with the strain response measured by the cone-plate, indicating that this correction method is suitable for the correction of the strain response of asphalt under large oscillation shear load measured by parallel plates based on stress control.

[0088] In summary, based on the method for correcting the nonlinear strain response of asphalt materials of the present invention, the accurate correction of the nonlinear strain response of asphalt under parallel plates is achieved. The corrected parallel plate strain response curve has a significant overlap effect with the true strain response curve under the cone-plate. The present invention broadens the scope of use of parallel plates, provides an effective means for testing the nonlinear viscoelasticity of asphalt materials using a parallel plate system, and also provides a new idea for testing the nonlinear strain response of other viscoelastic materials using a parallel plate system.

Claims

1. A method for correcting the nonlinear strain response of asphalt materials under parallel plates based on a single-point method, characterized in that: The method comprises the following steps: Step 1: Determine the conversion relationship between speed and shear rate, torque and shear stress under different fixture system conditions, and derive the general calculation formula of torque when the conversion coefficient is unknown; Step 2: Based on the Newtonian fluid parallel plate conversion coefficient established by DIN standard, determine the torque calculation formula under a certain viscosity, and derive the Newtonian fluid shear stress calculation formula determined by the maximum radial distance; Step 3: Based on the single-point method correction theory, the fluid rheological curve based on the Herschel-Bulkley model is introduced to establish the viscosity-stress relationship for asphalt. Combined with the torque calculation formula and shear stress calculation formula determined in step 2, the shear stress formula of the power-law fluid under a certain radius and the radius ratio of the radius to the parallel plate fixture radius are obtained. Finally, the theoretical derivation of the nonlinear strain response correction method under parallel plates of a stress-controlled rheometer is established.

2. The method for correcting the nonlinear strain response of asphalt material under parallel plates based on a single point method according to claim 1, characterized in that: In step 1, the conversion relationship is: Where: 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 factor relating torque to shear stress; M is the torque; The general calculation formula for torque when the conversion factor is unknown is: Where: r is the radius of the mechanical response; R is the radius of the fixture; is the shear stress at a certain shear rate.

3. The method for correcting the nonlinear strain response of asphalt material under parallel plates based on a single point method according to claim 1, characterized in that: In step 2, the Newtonian fluid torque calculation formula is: Where: R is the radius of the fixture, η is the viscosity; r is the radius of the mechanical response; h is the fixture gap; The shear stress response formula is derived as: Where: τ(r) is the shear stress at a certain radius; The formula for calculating the shear stress of Newtonian fluids derived and determined at the maximum radial distance is:

4. The method for correcting the nonlinear strain response of asphalt material under parallel plates based on a single point method according to claim 1, characterized in that: In step 3, 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 calculated as: Therefore, the shear stress of the power-law fluid at a certain radius is as follows: The radius ratio is: The final formula of the strain response correction method is: Where: γ α is the corrected strain response, α is the test strain response, r s * is the radius ratio and n is the flow index.

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